Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Computer-Based Guidelines for 

Concrete Pavements, Volume III: 

Technical Appendices

PUBLICATION NO. FHWA-HRT-04-127 JANUARY 2006
FOREWORD 

This report documents the investigation, modeling, and validation of the enhanced High PERformance 

PAVing (HIPEPAV®) II software program. HIPERPAV II is a comprehensive, yet user-friendly 

software package. HIPERPAV II primarily incorporates as a set of guidelines for the proper selection of 

design and construction variables to minimize early-age damage to jointed plain concrete pavement 

(JPCP) and continuously reinforced concrete pavement (CRCP). In addition, the software determines the 

effect of early-age behavior factors. This report, Volume III of a three-volume set, is the Technical 

Appendices, which documents work carried out during the study. Volume I is the Project Summary

documenting the efforts undertaken for the guidelines. Volume II is the Design and Construction 

Guidelines and HIPERPAV II User’s Manual, which provides general instruction on the use and 

application of the HIPERPAV II. 

This report will be of interest to those involved in concrete pavement mix design, as well as the design 

and construction of concrete pavements. Sufficient copies of this report are being distributed to provide 

two copies to each Federal Highway Administration (FHWA) Resource Center, two copies to each 

FHWA Division Office, and a minimum of four copies to each State highway agency. Additional copies 

for the public are available from the National Technical Information Services (NTIS), 5285 Port Royal 

Road, Springfield, VA 22161. 

 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 in the 

interest of information exchange. The U.S. Government assumes 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 does not endorse products or manufacturers. Trademarks or manufacturers’ names 

appear in this report only because they are considered essential to the objective of the document. 

Quality Assurance Statement 

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

industry, and the public in a manner that promotes public understanding. Standards and policies are used 

to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA 

periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality 

improvement. 
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Final Report 

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

FHWA-HRT-04-127

Computer-Based Guidelines for Concrete Pavements, Volume III: Technical 

Appendices 

J. Mauricio Ruiz, Robert O. Rasmussen, George K. Chang, Jason C. Dick, Patricia 

K. Nelson, Anton K. Schindler, Dennis J. Turner, W. James Wilde 

The Transtec Group, Inc. 

1012 East 38 1⁄2 Street 

Austin, TX 78751 

Office of Infrastructure Research and Development 

Federal Highway Administration (FHWA) 

6300 Georgetown Pike 

McLean, VA 22101 

This report documents enhancements incorporated in the (HIgh PERformance PAVing) HIPERPAV II software. Enhancements made 

within this project include the addition of two major modules: a module to predict the performance of JPCP as affected by early-age 

factors; and a module to predict the early-age behavior (first 72 hours) and early life (up to 1 year) of CRCP. Two additional FHWA 

studies were also incorporated: one that predicts dowel bearing stresses as a function of environmental loading during the early age; 

and a module for optimization of concrete paving mixes as a function of 3-day strength, 28-day strength, and cost. Additional 

functionality to the software was also incorporated by reviewing and prioritizing the feedback provided by users of the first generation 

of the software, HIPERPAV I. 

This volume includes the following technical appendices: A) annotated outline of the references investigated during this project; B) 

description of the models selected for incorporation in HIPERPAV II; C) field investigation of JPCP and CRCP sites used for model 

validation; D) validation of the enhanced HIPERPAV II computer guidelines; and E) finite-difference temperature model validation. 

This is the third volume and last in a series of three volumes that document the different tasks carried out in accomplishing the 

objectives for this project. 

FHWA No. Vol. No. Short Title

FHWA-HRT-04-121 Volume I Project Summary 

FHWA-HRT-04-124 Volume II Design and Construction Guidelines and HIPERPAV II User’s Manual 

FHWA-HRT-04-127 Volume III Technical Appendices 

No restrictions. This document is available to the 

Public through the National Technical Information Service; 

Springfield, VA 22161 

High Performance Concrete Pavement; HIPERPAV; 

Jointed; Continuously Reinforced; Early Age Behavior; 

Long-Term Performance; Mechanistic-Empirical Models; 

Temperature; Hydration; Shrinkage; Relaxation; Creep; 

Thermal Expansion; Slab Base Restraint; Curling; 

Warping; Plastic Shrinkage; Cracking; JPCP; CRCP 
ii 

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha 

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS 

oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius 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. Appropriate rounding should be made to comply with Section 4 of ASTM E e 380. 

(Revised March 2003)
iii 

TABLE OF CONTENTS 

APPENDIX A ANNOTATED OUTLINE OF MODEL REFERENCES ...............................1

A.1 CURRENTLY AVAILABLE EARLY-AGE BEHAVIOR MODELS SIMILAR TO 

HIPERPAV ..............................................................................................................................1

A.1.1 DuCOM ..........................................................................................................................2

A.1.2 HYMOSTRUC...............................................................................................................2

A.1.3 Quadrel...........................................................................................................................2

A.1.4 4C-Temp&Stress ...........................................................................................................3

A.2 EARLY-AGE BEHAVIOR MODELS WITH POTENTIAL INCORPORATION 

INTO HIPERPAV II...............................................................................................................3

A.2.1 Concrete Hydration.......................................................................................................3

A.2.2 Concrete Maturity .........................................................................................................8

A.2.3 Drying Shrinkage of Concrete......................................................................................9

A.2.4 Moisture Transport in Concrete ................................................................................11

A.2.5 Set Time of Concrete ...................................................................................................12

A.2.6 Thermal Properties of Concrete.................................................................................12

A.2.7 Creep.............................................................................................................................14

A.3 JPCP LITERATURE REVIEW ..........................................................................................16

A.3.1 JPCP Structural Models .............................................................................................16

A.3.2 JPCP Climatic Models ................................................................................................18

A.3.3 JPCP Distresses............................................................................................................19

A.4 CRCP LITERATURE REVIEW.........................................................................................27

APPENDIX B MODELS SELECTED FOR INCORPORATION INTO HIPERPAV II...37

B.1 GENERAL EARLY-AGE BEHAVIOR MODELS ...........................................................37

B.1.1 PCC Hydration Models...............................................................................................37

B.1.2 HIPERPAV II Finite-Difference Temperature Model.............................................42

B.1.3 Shrinkage......................................................................................................................61

B.1.4 Nonlinear Restraint Model .........................................................................................70

B.1.5 Nonlinear Thermal Gradient Model..........................................................................71

B.1.6 Creep Model.................................................................................................................71

B.2 JPCP PERFORMANCE MODELS ....................................................................................81

B.2.1 Environmental Models................................................................................................82

B.2.2 Long-Term Materials Properties Models..................................................................96

B.2.3 Structural Models......................................................................................................104

B.2.4 Distress Models ..........................................................................................................123

B.2.5 Long-Term JPCP Model Assumptions and Limitations........................................ 152

B.3 CRCP EARLY-AGE MODELS.........................................................................................154

B.3.1 CRCP Stress Prediction ............................................................................................154

B.3.2 CRCP Strength Prediction .......................................................................................158

B.3.3 CRCP Temperature Prediction................................................................................159

B.3.4 CRCP Model Limitations .........................................................................................159

B.4 MODELS USED IN THE COMET MODULE ................................................................ 159

B.4.1 Comments on COMET Features and Implementations ........................................160

B.4.2 Concrete Compressive Strength Model ...................................................................161

B.4.3 Development of the Compressive Strength Prediction Model Based on 

Mix Design..................................................................................................................161
iv 

B.4.4 Relative Strength .......................................................................................................162

B.4.5 Compressive Strength Prediction Model.................................................................164

B.5 MODELS USED IN THE HIPERPAV DOWEL-CONCRETE INTERACTION 

ANALYSIS MODULE........................................................................................................165

B.5.1 Dowel Bar Bearing Stress Model..............................................................................165

B.5.2 Dowel Bar Stress Due to Shear Loading..................................................................173

B.5.3 Dowel Analysis Module in HIPERPAV II............................................................... 175

APPENDIX C FIELD INVESTIGATION.............................................................................177

C.1 JPCP SITES INVESTIGATED .........................................................................................177

C.1.1 JPCP Section on U.S. Highway 50, Illinois..............................................................177

C.1.2 JPCP Section on Ticuman Bypass, Mexico .............................................................192

C.2 CRCP SITES INVESTIGATED........................................................................................201

C.2.1 CRCP Section at I–30 and I–35 Interchange in Fort Worth, TX..........................201

C.2.2 CRCP Section on I–29 near Sioux Falls, SD ...........................................................206

C.3 MIX DESIGNS ....................................................................................................................211

C.4 STRENGTH AND STIFFNESS FOR TEXAS SITE .......................................................212

C.5 STRENGTH AND STIFFNESS FOR SOUTH DAKOTA SITE....................................214

C.6 STRENGTH AND STIFFNESS FOR MEXICO SITE.................................................... 215

C.7 STRENGTH AND STIFFNESS FOR ILLINOIS SITE .................................................. 217

C.8 DRYING SHRINKAGE FOR TEXAS AND SOUTH DAKOTA SITES ...................... 218

C.9 SETTING TIME FOR TEXAS AND SOUTH DAKOTA............................................... 220

C.10 COEFFICIENT OF THERMAL EXPANSION...............................................................222

APPENDIX D VALIDATION OF THE ENHANCED GUIDELINES...............................223

D.1 DATABASE VALIDATION ..............................................................................................223

D.1.1 Validation of JPCP Structural Response Models with LTPP Data ......................223

D.1.2 Validation of CRCP Early-Age Behavior Models ..................................................252

D.2 FIELD VALIDATION........................................................................................................260

D.2.1 Validation of Long-Term Performance Models with Inservice JPCP Sites.........261

D.2.2 Validation of Early-Age Behavior Models with Newly Constructed CRCP 

Sites .............................................................................................................................275

D.3 VALIDATION OF GENERAL EARLY-AGE BEHAVIOR MODELS........................ 293

D.3.1 Finite-Difference Temperature Prediction Model..................................................293

D.3.2 Drying Shrinkage Prediction Model ........................................................................293

D.3.3 Relaxation-Creep Model ...........................................................................................298

APPENDIX E FINITE-DIFFERENCE TEMPERATURE MODEL VALIDATION.......299

E.1 FIELD INSTRUMENTATION SITES .............................................................................299

E.2 MODEL CALIBRATION .................................................................................................. 300

E.3 MODEL VALIDATION.....................................................................................................304

E.4 SUMMARY AND RECOMMENDATIONS .................................................................... 305

E.5 TEMPERATURE PREDICTION RESULTS OBTAINED DURING 

CALIBRATION .................................................................................................................. 306

E.6 TEMPERATURE PREDICTION RESULTS OBTAINED DURING 

VALIDATION.....................................................................................................................322

REFERENCES ...........................................................................................................................339
v 

LIST OF FIGURES 

Figure 1. HIPERPAV early-age behavior framework showing improved models in HIPERPAV II........ 38

Figure 2. Heat transfer mechanisms between pavement and its surroundings........................................... 44

Figure 3. Concrete specific heat as influenced by the mixture constituents, temperature, and degree of 

hydration.............................................................................................................................................. 46

Figure 4. Comparison of different convection coefficients as influenced by the windspeed. ................... 52

Figure 5. Radiant energy exchanges between the sky and an exposed thermally black plate.(29) .............. 55

Figure 6. Emissivity of moist air at a total pressure of 1 atmosphere and a temperature of 20 °C............ 56

Figure 7. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, 

atmospheric pressure. .......................................................................................................................... 59

Figure 8. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, 

relative humidity.................................................................................................................................. 60

Figure 9. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, 

ratio of carbon dioxide to water vapor................................................................................................. 60

Figure 10. Surface layer zone subjected to drying shrinkage for a slip-formed pavement........................ 63

Figure 11. Influence of w/cm on total shrinkage predicted by the Jonasson model. ................................. 65

Figure 12. Effect of w/c on total shrinkage predicted by the Baźant-Panula model.................................. 69

Figure 13. Comparison of the Baźant-Panula and Jonasson-Hedlund shrinkage models.......................... 70

Figure 14. Time-dependent deformation at time t, for a loading at time t0.

(43)............................................ 72

Figure 15. A schematic of the additional Ψ1(t0) and Ψ2(t,t0) functions to extend the Triple Power Law 

for the early-age creep response.(43) ..................................................................................................... 75

Figure 16. Decomposition of stress history into stress steps. ..................................................................... 78

Figure 17. Discreet subdivision of time for numerical creep analysis........................................................ 79

Figure 18. Superposition of various strains intensities: Loading................................................................ 80

Figure 19. Superposition of various strains intensities: Unloading. ........................................................... 80

Figure 20. Superposition of various strains intensities: Net applied strains. .............................................. 80

Figure 21. Comparison of the results of the relaxation model and model without relaxation. ................... 81

Figure 22. Monthly moisture content variation for lean clay (CL), scenarios 1–4. ................................... 87

Figure 23. Monthly moisture content variation for well-graded silty gravel (GW–GM), scenarios 5–8... 88

Figure 24. Monthly variation for well-graded gravel (GW), scenarios 9–12. ........................................... 89

Figure 25. Monthly variation for lean clay (CL) in five U.S. cities........................................................... 91

Figure 26. Monthly variation for well-graded silty gravel (GW–GM) in five U.S. cities. ........................ 92

Figure 27. Comparison of predicted and measured values from the AASHO road test. ........................... 94

Figure 28. Texas LTPP site comparison. ................................................................................................... 95

Figure 29. Maine LTPP site comparison. .................................................................................................. 95

Figure 30. Comparison of test results with the correlation proposed in equation 122.(60) ....................... 100

Figure 31. Modulus of rupture versus compressive strength for Texas data. .......................................... 101

Figure 32. Tensile strength and elastic modulus values calculated using the CEB-FIP equation. .......... 103

Figure 33. Schematic of deflection load transfer (LTEδ) for a doweled JCP........................................... 105

Figure 34. Schematic of LTE model logic............................................................................................... 106

Figure 35. Relationship between the calculated agg/kl and measured JTE. ............................................ 110

Figure 36. Relationship between measured crack opening and the calculated agg/kl. ............................ 110

Figure 37. Free edge loading of JCP........................................................................................................ 113

Figure 38. Loaded and unloaded deflections of a JCP............................................................................. 115

Figure 39. Relationship between JTE and LTEδ...................................................................................... 119

Figure 40. Relationship between LTEσ and LTEδ. .................................................................................. 119

Figure 41. JTE results obtained from the experimental work performed by Colley and Humphrey as a 

function of loading cycles of a 4086-kg load.(70) ............................................................................... 120

Figure 42. Influence of joint opening on JTE, 229-mm concrete slab, 152-mm gravel subbase.(70) ....... 121
vi 

Figure 43. Influence of joint opening on JTE, 178-mm concrete slab, 152-mm gravel subbase.(70) ....... 122

Figure 44. Asymptote dimensionless joint stiffness as a function of joint opening................................. 122

Figure 45. Sensitivity of faulting to joint opening and cumulative traffic loading for nondoweled 

JPCP (MESAL = 1,000,000 ESAL). ................................................................................................. 127

Figure 46. Sensitivity of faulting to joint opening and cumulative traffic loading for doweled JPCP 

(MESAL = 1,000,000 ESAL)............................................................................................................ 128

Figure 47. Relationship between joint opening model predictions.......................................................... 130

Figure 48. Relationship between revised joint opening model predictions. ............................................ 131

Figure 49. Allowable loads versus stress-to-strength ratio. ..................................................................... 132

Figure 50. Fatigue cracking model with associated data.(76) .................................................................. 134

Figure 51. Flowchart of stress, damage, and cracking module................................................................ 142

Figure 52. Amount of each individual distress required to reach a PSI of 2.0. ....................................... 145

Figure 53. Shape of IRI versus PSI curve................................................................................................ 146

Figure 54. Effect of faulting on IRI. ........................................................................................................ 147

Figure 55. Comparison of faulting influence between the various IRI models. ...................................... 150

Figure 56. Effect of percent cracked slabs on FHWA–RD–00–130, 1–37A Guide, and contractor IRI 

models................................................................................................................................................ 150

Figure 57. Effect of percent spalling on FHWA–RD–00–130, 1–37A Guide, and contractor IRI 

models................................................................................................................................................ 151

Figure 58. Effect of percent patching on IRI for the 1–37A models. ...................................................... 151

Figure 59. Effect of initial IRI0 on FHWA–RD–00–130, 1–37A, and contractor IRI models. ............... 152

Figure 60. Schematic representation of analysis of concrete and steel stresses in CRCP–8. .................. 154

Figure 61. Simplified coordinate system for development of bond stress distribution functions............. 157

Figure 62. Compressive strength as a function of w/c and cement content............................................. 162

Figure 63. Schematic of dowel deformation and loading at the joint. ..................................................... 166

Figure 64. Schematic of dowel deformation without concrete compliance and with concrete 

compliance at the joint....................................................................................................................... 166

Figure 65. Effect of varying the dowel diameter (dD) on the bearing stress. ........................................... 168

Figure 66. Effect of varying the effective modulus of dowel support (KD) on the bearing stress. .......... 169

Figure 67. Effect of varying the joint opening on the bearing stress. ...................................................... 169

Figure 68. Effect of varying the concrete modulus (Ec) on the bearing stress......................................... 170

Figure 69. Effect of varying the concrete CTE (αc) on the bearing stress. .............................................. 170

Figure 70. Effect of varying the slab length (L) on the bearing stress..................................................... 171

Figure 71. Effect of varying the slab thickness (h) on the bearing stress. ............................................... 171

Figure 72. Effect of varying the modulus of subgrade reaction (k) on the bearing stress. ...................... 172

Figure 73. Effect of varying the linear temperature gradient (T) on the bearing stress. .......................... 172

Figure 74. Schematic representation of slabs loaded in shear. ................................................................ 173

Figure 75. HIPERPAV II screen capture showing typical output from the dowel bar module. .............. 175

Figure 76. Pavement temperature profiles for Illinois JPCP evaluation.................................................. 190

Figure 77. Joint movement for section AA in Illinois JPCP evaluation. ................................................. 190

Figure 78. Longitudinal profiles for section AA, 253-mm thickness. ..................................................... 191

Figure 79. Ticuman bypass project location. ........................................................................................... 193

Figure 80. Mean concrete compressive and flexural strength gain curves for the Ticuman bypass........ 195

Figure 81. Number of distressed slabs per kilometer for the Ticuman bypass. ....................................... 197

Figure 82. Faulting distribution for the Ticuman bypass......................................................................... 198

Figure 83. Measured joint opening during August 22 to 24. ................................................................... 198

Figure 84. Comparison of PSI ratings on the southbound direction (summer 2001 versus 

summer 1995). ................................................................................................................................... 200

Figure 85. Comparison of PSI ratings on the northbound direction (summer 2001 versus 

summer 1995). ................................................................................................................................... 200

Figure 86. Typical cross section for the CRCP instrumented section...................................................... 202
vii 

Figure 87. Instrumented section delineated by crack inducers. ............................................................... 203

Figure 88. Strain gages in PCC and on reinforcing steel. ........................................................................ 203

Figure 89. Shear failure as a result of pushoff test................................................................................... 205

Figure 90. Position of strain gages and thermocouples as constructed.................................................... 206

Figure 91. Typical cross section for I–29, South Dakota (from opposite direction to traffic)................. 207

Figure 92. Strain gages in PCC and on reinforcing steel. ........................................................................ 208

Figure 93. Cracking pattern on instrumented section. ............................................................................. 210

Figure 94. Location of the sensors with respect to the pavement edge and cracks as constructed. ......... 210

Figure 95. Time growth of Texas compressive strength.......................................................................... 212

Figure 96. Time growth of Texas splitting tensile strength. .................................................................... 213

Figure 97. Time growth of Texas modulus of elasticity. ......................................................................... 213

Figure 98. Time growth of South Dakota compressive strength. ............................................................ 214

Figure 99. Time growth of South Dakota splitting tensile strength......................................................... 215

Figure 100. Time growth of South Dakota modulus of elasticity............................................................ 215

Figure 101. Time growth of Mexico compressive strength. .................................................................... 216

Figure 102. Time growth of Mexico splitting tensile strength................................................................. 216

Figure 103. Time growth of Mexico modulus of elasticity. .................................................................... 217

Figure 104. Time growth of Illinois compressive strength...................................................................... 218

Figure 105. Time growth of Illinois modulus of elasticity. ..................................................................... 218

Figure 106. Drying shrinkage of South Dakota concrete......................................................................... 219

Figure 107. Drying shrinkage of Texas concrete..................................................................................... 219

Figure 108. Setting times of concrete for Texas and South Dakota concretes......................................... 221

Figure 109. Concrete and ambient air temperatures for the South Dakota concrete................................ 221

Figure 110. Concrete and ambient air temperatures for the Texas concrete............................................ 222

Figure 111. Measured versus predicted joint opening. ............................................................................ 227

Figure 112. Typical plot of PCC temperature versus joint LTE, section 37–0201.................................. 229

Figure 113. Computed LTE versus PCC temperature for section 49–3011............................................. 231

Figure 114. Average LTE above freezing and below 25 oC, section 49–3011. ....................................... 232

Figure 115. Variability of LTE for individual joints, section 49–3011. .................................................. 234

Figure 116. Effect of joint spacing on LTE, section 49–3011. ................................................................ 235

Figure 117. Computed LTE versus PCC temperature for nondoweled section 31–3018. ....................... 236

Figure 118. Computed LTE versus PCC temperature for nondoweled section 06–3042. ....................... 236

Figure 119. Computed LTE versus PCC temperature for nondoweled section 83–3802. ....................... 237

Figure 120. Computed LTE versus PCC temperature for nondoweled section 53–3813. ....................... 237

Figure 121. LTE versus PCC temperature for doweled section 04–0215................................................ 238

Figure 122. LTE versus PCC temperature for doweled section 18–3002................................................ 238

Figure 123. LTE versus PCC temperature for doweled section 13–3019................................................ 239

Figure 124. LTE versus PCC temperature for doweled section 32–0204................................................ 239

Figure 125. LTE versus PCC temperature for doweled section 89–3015................................................ 240

Figure 126. LTE versus PCC temperature for doweled section 39–0204................................................ 240

Figure 127. LTE versus joint opening for section 49–3011, joint at 5.5 m from start of section. ........... 241

Figure 128. Predicted versus computed LTE for section 31–3018, joint 5.5 m from start of section. .... 242

Figure 129. Predicted versus computed LTE for section 49–3011, joint 5.5 m from start of section. .... 243

Figure 130. Predicted versus computed LTE for section 06–3042, joint 148.1 m from start of section. 243

Figure 131. Predicted versus computed LTE for section 83–3802, joint 149.7 m from start of section. 244

Figure 132. Predicted versus computed LTE for section 53–3813, joint 0.0 m from start of section. .... 244

Figure 133. Sensitivity analysis of LTE model for nondoweled pavements. .......................................... 246

Figure 134. LTE model sensitivity for doweled sections. ....................................................................... 247

Figure 135. Predicted versus computed LTE for section 37–0201, joint 145.1 m from start of section. 248

Figure 136. Predicted versus computed LTE for section 04–0215, joint 144.5 m from start of section. 249

Figure 137. Predicted versus computed LTE for section 13–3019, joint 21.3 m from start of section. .. 249
viii 

Figure 138. Predicted versus computed LTE for section 32–0204, joint 8.5 m from start of section. .... 250

Figure 139. Predicted versus computed LTE for section 89–3015, joint 36.3 m from start of section. .. 250

Figure 140. Predicted versus computed LTE for section 39–0204, joint 0.0 m from start of section. .... 251

Figure 141. Crack spacing history for summer sections, SH–6............................................................... 256

Figure 142. Crack spacing history for winter sections, SH–6.................................................................. 257

Figure 143. Preliminary long-term crack spacing prediction................................................................... 257

Figure 144. Crack spacing prediction at 3 days from construction.......................................................... 258

Figure 145. Measured versus predicted crack widths, SH–6. .................................................................. 259

Figure 146. Conceptual representation of residual drying shrinkage effect (adapted from 

Otero et al.).(116).................................................................................................................................. 260

Figure 147. Comparison of measured and predicted strength, Illinois site.............................................. 262

Figure 148. Comparison of measured and predicted modulus of elasticity, Illinois site. ........................ 263

Figure 149. Comparison of measured versus predicted LTE................................................................... 264

Figure 150. Early-age analysis for section AA, for placement at 2 p.m. ................................................. 265

Figure 151. Early-age analysis for section IA, for placement at 2 p.m.................................................... 265

Figure 152. Early-age analysis for section NA for placement at 2 p.m. .................................................. 266

Figure 153. Predicted faulting for sections MA and NA (191-mm thick). .............................................. 267

Figure 154. Comparison of measured and predicted transverse cracking (sections NA and MA). ......... 267

Figure 155. Comparison of measured and predicted transverse cracking for sections 

(IA, JA, KA, LA)............................................................................................................................... 268

Figure 156. Transverse cracking for section AA, thickness = 241 mm................................................... 268

Figure 157. Comparison of measured and predicted longitudinal cracking (sections MA and NA) ....... 269

Figure 158. Comparison of measured and predicted IRI (section NA). .................................................. 269

Figure 159. Comparison of measured versus predicted flexural strength, Ticuman, Mexico. ................ 270

Figure 160. Comparison of measured versus predicted modulus of elasticity, Ticuman, Mexico. ......... 271

Figure 161. Comparison of measured versus predicted LTE, Ticuman, Mexico. ................................... 271

Figure 162. Analysis for 229-mm slab at different construction times and built-in gradient conditions, 

Ticuman bypass. ................................................................................................................................ 272

Figure 163. Comparison of measured versus predicted joint faulting, Ticuman, Mexico....................... 273

Figure 164. Comparison of measured versus predicted transverse cracking, Ticuman, Mexico............. 273

Figure 165. Comparison of measured versus predicted longitudinal cracking, Ticuman, Mexico.......... 274

Figure 166. Comparison of measured versus predicted present serviceability index, Ticuman, Mexico.274

Figure 167. Restraint at the slab/subbase interface.................................................................................. 275

Figure 168. Determination of set time with pulse velocity equipment. ................................................... 276

Figure 169. PCC strains during PCC set time as a function of temperature changes. ............................. 277

Figure 170. Determination of PCC CTE with the use of PCC strains on an unconfined concrete 

cylinder. ............................................................................................................................................. 278

Figure 171. Steel strains at various distances from the crack location. ................................................... 279

Figure 172. Steel strain along the slab length at different ages. .............................................................. 279

Figure 173. Concrete strains at middepth along slab length. ................................................................... 280

Figure 174. Drying shrinkage observed in the field on an unrestrained PCC cylinder............................ 281

Figure 175. Strains in concrete and steel at 68.5 hours after construction............................................... 281

Figure 176. Displacements in steel and concrete along slab length at 68.5 hours. .................................. 282

Figure 177. Steel stress along the slab at 68.5 hours. .............................................................................. 283

Figure 178. Measured versus predicted crack spacing at 3 days of age, Fort Worth, TX ....................... 284

Figure 179. PCC strains during PCC set time as a function of temperature changes. ............................. 286

Figure 180. Determination of PCC CTE with the use of PCC strains on an unconfined concrete 

cylinder. ............................................................................................................................................. 287

Figure 181. Steel strains at various distances from the crack location. ................................................... 288

Figure 182. Steel strain along the slab length at different ages. .............................................................. 288

Figure 183. Concrete strains at middepth along slab length. ................................................................... 289
ix 

Figure 184. Drying shrinkage observed in the field on an unrestrained PCC cylinder............................ 290

Figure 185. Strains in concrete and steel at 67.2 hours after construction............................................... 290

Figure 186. Comparison of measured and predicted bond development length...................................... 291

Figure 187. Steel stress along the slab at 67.2 hours. .............................................................................. 291

Figure 188. Measured versus predicted crack spacing at 3 days of age, Sioux Falls, SD. ...................... 293

Figure 189. Drying shrinkage results for North Carolina site.................................................................. 294

Figure 190. Drying shrinkage results for Texas site. ............................................................................... 295

Figure 191. Drying shrinkage results for Arizona site............................................................................. 295

Figure 192. Drying shrinkage results for Nebraska site........................................................................... 296

Figure 193. Drying shrinkage results for Minnesota site......................................................................... 296

Figure 194. Calibration of drying shrinkage factor for Houston, TX, sections constructed in summer. . 297

Figure 195. Calibration of drying shrinkage factor for Houston, TX, sections constructed in winter..... 297

Figure 196. Measured concrete and air temperatures for Minnesota, Slab 1........................................... 306

Figure 197. Measured versus predicted temperatures 25 mm from top of slab for Minnesota, Slab 1. .. 306

Figure 198. Measured versus predicted temperatures 25 mm from bottom of slab for Minnesota, 

Slab 1. ................................................................................................................................................ 307

Figure 199. Measured versus predicted temperature gradient for Minnesota, Slab 1.............................. 307

Figure 200. Measured concrete and air temperatures for Minnesota, Slab 4........................................... 308

Figure 201. Measured versus predicted temperatures 25 mm from top of slab for Minnesota, Slab 4. .. 308

Figure 202. Measured versus predicted temperatures 25 mm from bottom of slab for Minnesota, 

Slab 4. ................................................................................................................................................ 309

Figure 203. Measured versus predicted temperature gradient for Minnesota, Slab 4.............................. 309

Figure 204. Measured concrete and air temperatures for Arizona, Slab 1............................................... 310

Figure 205. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 1. ...... 310

Figure 206. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, Slab 1. 311

Figure 207. Measured versus predicted temperature gradient for Arizona, Slab 1.................................. 311

Figure 208. Measured concrete and air temperatures for Arizona, Slab 3............................................... 312

Figure 209. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 3. ...... 312

Figure 210. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, Slab 3. 313

Figure 211. Measured versus predicted temperature gradient for Arizona, Slab 3.................................. 313

Figure 212. Measured concrete and air temperatures for Arizona, Slab 6............................................... 314

Figure 213. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 6. ...... 314

Figure 214. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, Slab 6. 314

Figure 215. Measured versus predicted temperature gradient for Arizona, Slab 6.................................. 315

Figure 216. Measured concrete and air temperatures for Lufkin, TX, Slab 2. ........................................ 315

Figure 217. Measured versus predicted temperatures 25 mm from top of slab for Lufkin, TX, Slab 2. 316

Figure 218. Measured versus predicted temperatures 25 mm from bottom of slab for Lufkin, TX, 

Slab 2. ................................................................................................................................................ 316

Figure 219. Measured versus predicted temperature gradient for Lufkin, TX, Slab 2. ........................... 317

Figure 220. Measured concrete and air temperatures for Lufkin, TX, Slab 3. ........................................ 317

Figure 221. Measured versus predicted temperatures 25 mm from top of slab for Lufkin, TX, Slab 3. . 318

Figure 222. Measured versus predicted temperatures 25 mm from bottom of slab for Lufkin, TX, 

Slab 3. ................................................................................................................................................ 318

Figure 223. Measured versus predicted temperature gradient for Lufkin, TX, Slab 3. ........................... 319

Figure 224. Measured concrete and air temperatures for North Carolina, Slab 2.................................... 319

Figure 225. Measured versus predicted temperatures 25 mm from top of slab for North Carolina, 

Slab 2. ................................................................................................................................................ 319

Figure 226. Measured versus predicted temperatures 25 mm from bottom of slab for North Carolina, 

Slab 2. ................................................................................................................................................ 320

Figure 227. Measured versus predicted temperature gradient for North Carolina, Slab 2....................... 320

Figure 228. Measured concrete and air temperatures for North Carolina, Slab 3.................................... 320
x 

Figure 229. Measured versus predicted temperatures 25 mm from top of slab for North Carolina, 

Slab 3. ................................................................................................................................................ 321

Figure 230. Measured versus predicted temperatures 25 mm from bottom of slab for North Carolina, 

Slab 3. ................................................................................................................................................ 321

Figure 231. Measured versus predicted temperature gradient for North Carolina, Slab 3....................... 322

Figure 232. Measured concrete and air temperatures for Minnesota, Slab 2........................................... 322

Figure 233. Measured versus predicted temperatures 25 mm from top of slab for Minnesota, Slab 2. .. 323

Figure 234. Measured versus predicted temperatures 25 mm from bottom of slab for Minnesota, 

Slab 2. ................................................................................................................................................ 323

Figure 235. Measured versus predicted temperature gradient for Minnesota, Slab 2.............................. 324

Figure 236. Measured concrete and air temperatures for Minnesota, Slab 3........................................... 324

Figure 237. Measured versus predicted temperatures 25 mm from top of slab for Minnesota, Slab 3. .. 325

Figure 238. Measured versus predicted temperatures 25 mm from bottom of slab for Minnesota, 

Slab 3. ................................................................................................................................................ 325

Figure 239. Measured versus predicted temperature gradient for Minnesota, Slab 3.............................. 326

Figure 240. Measured concrete and air temperatures for Arizona, Slab 4............................................... 326

Figure 241. Measured versus predicted temperatures 25 mm from top of slab for Arizona, 

Slab 4. ................................................................................................................................................ 326

Figure 242. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, 

Slab 4. ................................................................................................................................................ 327

Figure 243. Measured versus predicted temperature gradient for Arizona, Slab 4.................................. 327

Figure 244. Measured concrete and air temperatures for Arizona, Slab 5............................................... 328

Figure 245. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 5. ...... 328

Figure 246. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, 

Slab 5. ................................................................................................................................................ 329

Figure 247. Measured versus predicted temperature gradient for Arizona, Slab 5.................................. 329

Figure 248. Measured concrete and air temperatures for Lufkin, TX, Slab 1. ........................................ 330

Figure 249. Measured versus predicted temperatures 25 mm from top of slab for Lufkin, TX, Slab 1. . 330

Figure 250. Measured versus predicted temperatures 25 mm from bottom of slab for Lufkin, TX, 

Slab 1. ................................................................................................................................................ 331

Figure 251. Measured versus predicted temperature gradient for Lufkin, TX, Slab 1. ........................... 331

Figure 252. Measured concrete and air temperatures for Lufkin, TX, Slab 4. ........................................ 332

Figure 253. Measured versus predicted temperatures 25 mm from top of slab for Lufkin, TX, 

Slab 4. ................................................................................................................................................ 332

Figure 254. Measured versus predicted temperatures 25 mm from bottom of slab for Lufkin, TX, 

Slab 4. ................................................................................................................................................ 333

Figure 255. Measured versus predicted temperature gradient for Lufkin, TX, Slab 4. ........................... 333

Figure 256. Measured concrete and air temperatures for North Carolina, Slab 1.................................... 334

Figure 257. Measured versus predicted temperatures 25 mm from top of slab for North Carolina, 

Slab 1. ................................................................................................................................................ 334

Figure 258. Measured versus predicted temperatures 25 mm from bottom of slab for North Carolina, 

Slab 1. ................................................................................................................................................ 335

Figure 259. Measured versus predicted temperature gradient for North Carolina, Slab 1....................... 335

Figure 260. Measured concrete and air temperatures for North Carolina, Slab 4.................................... 336

Figure 261. Measured versus predicted temperatures 25 mm from top of slab for North Carolina, 

Slab 4. ................................................................................................................................................ 336

Figure 262. Measured versus predicted temperatures 25 mm from bottom of slab for North Carolina, 

Slab 4. ................................................................................................................................................ 337

Figure 263. Measured versus predicted temperature gradient for North Carolina, Slab 4....................... 337

Figure 264. Measured concrete and air temperatures for Fort Worth, TX, Slab 1. ................................. 337
xi 

Figure 265. Measured versus predicted temperatures 25 mm from top of slab for Fort Worth, TX, 

Slab 1. ................................................................................................................................................ 338

Figure 266. Measured versus predicted temperatures 25 mm from bottom of slab for Fort Worth, TX, 

Slab 1. ................................................................................................................................................ 338

Figure 267. Measured versus predicted temperature gradient for Fort Worth, TX, Slab 1. .................... 338
xii 

LIST OF TABLES 

Table 1. Summary of how pavement design parameters influence JPCP distresses.................................. 20

Table 2. Summary of factors affecting transverse cracking in JPCP......................................................... 21

Table 3. Influence of concrete properties on JPCP pavement distresses. .................................................. 23

Table 4. Data sources and their use in the development of the hydration models.(4) ................................. 38

Table 5. Range of cement properties used to calibrate the hydration model. ............................................ 41

Table 6. Range of mixture proportions and mineral admixtures properties used for model calibration.... 41

Table 7. Typical specific heat values for concrete constituents................................................................. 45

Table 8. Typical values of thermal conductivity of moist mature concrete.(9)........................................... 47

Table 9. Thermal characteristics of various base materials.(16) .................................................................. 47

Table 10. Thermal characteristics of various pavement materials.(17)........................................................ 48

Table 11. Thermal characteristics of various soil materials.(17) ................................................................. 48

Table 12. Thermal characteristics of various insulation materials............................................................. 49

Table 13. Typical peak solar radiation values used in HIPERPAV II.(1) ................................................... 54

Table 14. Thornthwaite moisture index values.......................................................................................... 83

Table 15. Default soil characteristics......................................................................................................... 83

Table 16. Factorial for reference suction sensitivity analysis. ................................................................... 86

Table 17. Moisture contents for lean clay (CL) in scenarios 1–4. ............................................................. 86

Table 18. Moisture contents for well-graded silty gravel (GW–GM) in scenarios 5–8............................. 87

Table 19. Moisture contents for well-graded gravel (GW) in scenarios 9–12........................................... 88

Table 20. Factorial for climate and rainfall variation. ............................................................................... 89

Table 21. Soil data for climate and rainfall variation analysis................................................................... 90

Table 22. Monthly rainfall totals for locations in the U.S in millimeters.(49) ............................................. 90

Table 23. Moisture contents for lean clay (CL) in five U.S. cities. ........................................................... 91

Table 24. Moisture contents for well-graded silty gravel (GW–GM) in five U.S. cities........................... 92

Table 25. Gradation for AASHO road test soils.(50) ................................................................................... 93

Table 26. Soil parameters for AASHO road test soils. .............................................................................. 93

Table 27. Climatic data for LTPP sites. ..................................................................................................... 94

Table 28. Summary of strength test results obtained by Melis et. al.(55) .................................................... 98

Table 29. Specific gravities for different aggregate types.(62) .................................................................. 102

Table 30. Specific unit weights for different aggregate types.(62) ............................................................ 102

Table 31. LTE model variables used in developing the aggregate interlock model.(70) ........................... 109

Table 32. Distribution of pavement sections used in nondoweled faulting model.(75) ............................. 124

Table 33. Distribution of doweled pavement sections.(75)........................................................................ 125

Table 34. HIPERPAV slab-base restraint model variables...................................................................... 129

Table 35. Definition of equivalent slab-base restraint values for joint opening models.......................... 129

Table 36. Factorial of joint opening model inputs. .................................................................................. 129

Table 37. PCA edge adjustment factors................................................................................................... 137

Table 38. Comparison between IRI models............................................................................................. 149

Table 39. Input to the dowel bar bearing stress model. ........................................................................... 165

Table 40. Summary of the sensitivity analysis of the dowel model......................................................... 173

Table 41. JPCP test section descriptions.(103) ........................................................................................... 177

Table 42. Concrete mix design—88PCC0710.(104) .................................................................................. 178

Table 43. Accumulation of ESALs.......................................................................................................... 178

Table 44. Design and consumed ESALs.................................................................................................. 179

Table 45. Historical ride quality data....................................................................................................... 179

Table 46. Historical FWD data. ............................................................................................................... 179

Table 47. Section AA—historical* and current condition survey. .......................................................... 180

Table 48. Section IA—historical* and current condition survey............................................................. 181

Table 49. Section JA—historical* and current condition survey. ........................................................... 182
xiii 

Table 50. Section KA—historical* and current condition survey............................................................ 183

Table 51. Section LA—historical* and current condition survey............................................................ 184

Table 52. Section MA—historical* and current condition survey. .......................................................... 185

Table 53. Section NA—historical* and current condition survey. .......................................................... 186

Table 54. Center slab deflections in microns, normalized to 4090 kg for Illinois JPCP evaluation........ 187

Table 55. Approach slab load transfer data for Illinois JPCP evaluation. ............................................... 188

Table 56. Leave slab load transfer data for Illinois JPCP evaluation. ..................................................... 189

Table 57. Joint movement summary for Illinois JPCP evaluation........................................................... 191

Table 58. Summary of thickness measurements for Illinois JPCP evaluation......................................... 192

Table 59. Historical traffic data. .............................................................................................................. 194

Table 60. Summary statistics for 28-day PCC compressive strength in Ticuman bypass. ...................... 194

Table 61. Summary statistic for flexural strength and splitting tensile test results for the Ticuman 

bypass. ............................................................................................................................................... 195

Table 62. Summary statistics of core thickness for the Ticuman bypass................................................. 195

Table 63. Deflection indicators for the southbound direction (microns). ................................................ 199

Table 64. Deflection indicators for the northbound direction (microns). ................................................ 199

Table 65. Concrete mix design for CRCP on Jones-Stephenson access road, Texas. ............................. 202

Table 66. Concrete mix design for reconstruction project on I–29, South Dakota.................................. 207

Table 67. Laboratory testing plan of PCC concrete specimens. .............................................................. 211

Table 68. HIPERPAV II laboratory testing. ............................................................................................ 211

Table 69. Concrete mix designs for the HIPERPAV II field sites........................................................... 212

Table 70. Average concrete properties for the Illinois site (tested May 2002)........................................ 217

Table 71. Drying shrinkage model input. ................................................................................................ 220

Table 72. Quality control data for Texas and South Dakota concrete mixes........................................... 220

Table 73. Setting times of the Texas and South Dakota concrete mixes. ................................................ 221

Table 74. CTE values determined according to AASHTO TP–60–00. ................................................... 222

Table 75. Computed effective ratio of joint movement to change in temperature (ER) for SMP 

sections. ............................................................................................................................................. 225

Table 76. Data points used for LTE analysis. .......................................................................................... 228

Table 77. LTE statistics for SMP sections evaluated and some design and construction characteristics.230

Table 78. Summary statistics for effect of pavement age on LTE........................................................... 233

Table 79. Cumulative ESALs measured on design lane versus ESALs required to fit LTE model 

predictions. ........................................................................................................................................ 245

Table 80. Cumulative ESALs measured on design lane and ESALs multiplication factor required to fit 

LTE model predictions. ..................................................................................................................... 251

Table 81. Factorial design for CRCP test sections constructed in SH–6. ................................................ 253

Table 82. Mix design for SH–6 test sections. .......................................................................................... 254

Table 83. Test results (SH–6—summer).(106) ........................................................................................... 254

Table 84. Test results (SH–6—winter).(106).............................................................................................. 254

Table 85. Mix temperature for test sections in SH–6 (oC).(106) ................................................................ 255

Table 86. Time of placement for test sections in SH–6.(106)..................................................................... 255

Table 87. Comparison of average crack width predicted and measured values. ..................................... 283

Table 88. Comparison of predicted and measured average crack spacings. ............................................ 284

Table 89. Comparison of average crack width predicted and measured values. ..................................... 292

Table 90. Comparison of predicted and measured average crack spacings. ............................................ 292

Table 91. Calibration of Deff for the HIPERPAV I field sites. ................................................................. 294

Table 92. Different construction sites and their use for calibration and validation. ................................ 299

Table 93. Summary of variables collected during instrumentation of some HIPERPAV field sites.(121) 302

Table 94. Summary of hydration parameters for all the field sites.......................................................... 303

Table 95. Summary of r2 values obtained during the calibration of the temperature model. .................. 304

Table 96. Summary of r2 values obtained during the validation of the temperature model..................... 305
xiv 

LIST OF ACRONYMS AND ABBREVIATIONS 

AASHO: American Association of State Highway Officials 

AASHTO: American Association of State Highway and Transportation Officials 

AC: Asphalt concrete 

ACI: American Concrete Institute 

ACPA: American Concrete Pavement Association 

AE: Activation Energy 

AGG: Aggregate 

ASCE: American Society of Civil Engineers 

ASTM: American Society for Testing and Materials 

ATB: Asphalt-treated base 

CAM: Cement Aggregate Mixture 

CCD: Central Composite Design 

CEB-FIP: CEB stands for Euro-International Concrete Committee (Comité Euro-International du Béton), 

FIP stands for International Federation of Prestressing (Fédération Internationale de la 

Précontrainte) 

CL: Lean Clay 

COMET: Concrete Optimization, Management, Engineering, and Testing 

COPES: Concrete Pavement Evaluation System 

COST: Concrete Optimization Software Tool 

CRCP: Continuously Reinforced Concrete Pavement 

CTB: Cement-Treated Base 

CTE: Coefficient of Thermal Expansion 

CTR: Center for Transportation Research 

CV: Coefficient of Variation 

DEMEC: Demountable Mechanical Strain Gage 

DOT: Department of Transportation 

ER: Effective Ratio of Joint Movement to Change in PCC Temperature 

ESAL: 18-kip Equivalent Single Axle Loads 

FEA: Finite-Element Analysis 

FEM: Finite-Element Method 

FHWA: Federal Highway Administration 

FWD: Falling Weight Deflectometer 

GGBF: Ground-Granulated Blast-Furnace 

GPS: General Pavement Studies 

GW: Well-Graded Gravel 

GW–GM: Well-Graded Silty Gravel 

HIPERPAV: HIgh PERformance Concrete PAVing. 

HMA: Hot-Mix Asphalt 

HPC: High-Performance Concrete 

ICM: Integrated Climate Model 

IRI: International Roughness Index 

ISO: International Organization for Standardization 

JCP: Jointed Concrete Pavement 

JPCP: Jointed Plain Concrete Pavement 

JRCP: Jointed Reinforced Concrete Pavement 

JTE: Joint Transfer Efficiency 

k-value: Modulus of Subgrade Reaction 

LCB: Lean Concrete Base 
xv 

LS: Limestone 

LTE: Load Transfer Efficiency 

LTPP: Long-Term Pavement Performance 

LVDT: Linear Variable Displacement Transducers 

ML: Lean Silty Soil 

NCDC: National Climate Data Center 

NCHRP: National Cooperative Highway Research Program 

NOAA: National Oceanic and Atmospheric Administration 

PCA: Portland Cement Association 

PCC: Portland Cement Concrete 

PCCP: Portland Cement Concrete Pavements 

PSD: Particle Size Distribution 

PSI: Present Serviceability Index 

PSR: Present Serviceability Rating 

RH: Relative Humidity 

RIPPER: Performance/Rehabilitation of Rigid Pavements 

SEE: Standard Error of the Estimate 

SI: International System 

SMP: Seasonal Monitoring Program 

SRG: Siliceous River Gravel 

THMI: Thornthwaite Moisture Index 

TRB: Transportation Research Board 

TxDOT: Texas Department of Transportation 

UCS: Unified Classification System 

VST: Volumetric Surface Texture 

w/c: Water-to-Cement Ratio 

w/cm: Water-to-Cementitious Materials Ratio 

WIM: Weigh-in-Motion 

1 

APPENDIX A ANNOTATED OUTLINE OF MODEL REFERENCES 

This appendix contains a detailed annotated outline of the primary references reviewed during the 

information search performed in this study. The literature review is organized in four categories: 

1. Currently available early-age behavior models similar to the HIgh PERformance PAVing 

(HIPERPAV) System.1 

2. Early-age behavior models with potential incorporation into HIPERPAV II. 

3. Literature review on jointed plain concrete pavement (JPCP) models. 

4. Literature review on continuously reinforced concrete pavement (CRCP) models. 

The following sections document the literature reviewed on each of the above categories. 

A.1 CURRENTLY AVAILABLE EARLY-AGE BEHAVIOR MODELS SIMILAR TO 

HIPERPAV 

In addition to HIPERPAV, four other available software programs that predict the early-age behavior of 

concrete were identified. These include Durability Models of Concrete (DuCOM®), HYdration, 

MOrphology, and STRUCture (HYMOSTRUC®), Quadrel®, and 4C-Temp&Stress®. HYMOSTRUC and 

Quadrel focus on developing the adiabatic hydration curves for concrete. DuCOM and 4C-Temp&Stress 

are more robust finite-element programs that calculate the state of stress in early-age concrete structures. 

These programs are similar in some aspects to HIPERPAV, but also have differences in theory and 

application. DuCOM, HYMOSTRUC, Quadrel, and 4C-Temp&Stress are summarized below. 

 

1

 HIPERPAV alone with no succeeding numeral is used to refer to the overall concrete pavement design and 

construction guidelines, while HIPERPAV I and HIPERPAV II are used to refer to the two different software 

generations. 
2 

A.1.1 DuCOM 

Maekawa, K., Chaube, R., and Kishi, T., “Modeling of Concrete Performance,” Hydration, 

Microstructure Formation and Mass Transport, E&FN Spon, New York, NY, 1999. 

DuCOM focuses on evaluating the durability of structural concrete. This program assesses the durability 

of concrete from the green (or fresh) state up to several years of age using a finite-element-based 

program. DuCOM is a lifespan simulator that can model the microscopic behavior of concrete at early 

ages and relate this to its long-term performance. This program considers the properties of the concrete 

material’s mix proportions; the casting, curing, and environmental conditions; and the shape and size of 

the structural concrete. The concrete’s mechanistic processes are divided into short and long terms. The 

short-term processes are related to hydration, microstructure development, moisture transport, 

temperature rise, shrinkage, and creep. The long-term processes include transport of external agents into 

the concrete and its long-term creep behavior. Research on DuCOM continues at the Concrete 

Laboratory of the University of Tokyo, Japan. 

A.1.2 HYMOSTRUC 

Van Breugel, K. Simulation of Hydration and Formation of Structure in Hardening Cement-Based 

Materials, Second Edition, Delft University Press, 1997. 

HYMOSTRUC is designed to predict the adiabatic (and isothermal) hydration curves of concrete. It 

combines the fields of cement chemistry, physics, and stereology. The particle size of the cement, the 

water-to-cement ratio (w/c), the initial curing temperature, and the chemical composition of cement are all 

considered when formulating the concrete’s hydration curves. HYMOSTRUC focuses on the 

microscopic level. The overall degree of hydration is assumed to be the sum each individual cement 

particle’s degree of hydration. The output from HYMOSTRUC possibly can be used to predict the 

macroscopic behavior of hardened concrete structures. Connecting the microscopic behavior of the 

cement to its macroscopic properties, such as strength and stiffness, is one of HYMOSTRUC’s future 

objectives. 

A.1.3 Quadrel 

Digital Site Systems, Inc. Quadrel, Information Technology Solutions for Construction. 

Quadrel is a software program that makes adiabatic heat signature testing and analysis of fresh concrete 

possible in the laboratory. Fresh concrete samples are placed into a Qdrum calorimeter that 

simultaneously measures the temperature gain and heat loss. The data is processed using Quadrel, and the 

adiabatic heat of hydration curve is generated. Using the hydration curve, the concrete’s strength can be 

estimated as a function of maturity. Quadrel can be used to estimate the initial set time of the concrete, 

evaluate the performance of chemical admixtures and pozzolans, and determine how suitable concrete 

mixes are in the control of thermal cracking. 
3 

A.1.4 4C-Temp&Stress 

4C-Temp&Stress. Temperature and Stress Simulation During Hardening, Users Manual, Germann 

Instruments, Inc., Evanston, IL, 1998. 

Using the finite-element method (FEM), 4C-Temp&Stress computes the time-dependent temperatures 

and the state of stress in concrete structures. The program considers the influence of heat of hydration, 

thermal boundary conditions, and casting time and temperature on the structure’s state of stress. This 

program also calculates the influence of cooling pipes or heating wires on the concrete’s thermal state. 

Environmental factors like wind and radiation are taken into account. Loading of the structure enters by 

structural supports, self-weight, point loads, line loads, and momentum. The user can define the materials 

properties of the system, including those of concrete, soil, or insulation. Likewise, a mix design module 

for concrete specifies quantities of cement, aggregate, mineral additives, chemical additives, and water. 

In turn, each of these constituents has its own database with additional properties. Properties of the 

concrete mix, including slump, air content, thermal conductivity, and density, can be defined. The 

adiabatic heat development in the fresh concrete can be input, as can the concrete’s stiffness and 

Poisson’s ratio. Thermal expansion, creep, and compressive and tensile strength of concrete are all 

properties that 4C-Temp&Stress takes into account. The concrete structures can have several geometries. 

For output, the maturity of every point in the structure’s cross section is calculated, as are the stresses and 

strengths. 

A.2 EARLY-AGE BEHAVIOR MODELS WITH POTENTIAL INCORPORATION INTO 

HIPERPAV II 

The early-age properties of concrete are influenced significantly by the climatic conditions and 

temperatures, as well as by the concrete mix components. In this section, a literature review of early-age 

concrete properties is completed. The properties that are addressed are concrete maturity, drying 

shrinkage, moisture transport, set time, creep, and various thermal properties. 

A.2.1 Concrete Hydration 

This section briefly summarizes the primary references that contain candidate models that were identified 

to characterize the hydration of concrete at early ages. 

Byfors, J. “Plain Concrete at Early Ages,” Research 3:80, Swedish Cement and Concrete Research 

Institute, Stockholm, Sweden, 1980. 

This document contains many of the models and principles used in HIPERPAV I. This document 

emphasizes the modeling of the following mechanical properties: compressive strength, tensile strength, 

ultimate tensile strain, modulus of elasticity, Poisson’s ratio, and creep effects. Moisture transport and 

shrinkage is acknowledged, but limited information is presented. The influences of the following primary 

factors were studied: cement composition, cement fineness, w/c, curing temperature, moist curing, and 

effect of some chemical admixtures: accelerator (CaCl2) and air-entraining agents. This document 

presents many test results, but limited mechanistic models. 

The degree of hydration is used to describe the extent to which reaction between cement and water has 

developed, and the degree of hydration is linked to compressive strength and creep development. It is 

concluded that a certain critical degree of hydration is required before any strength gain can be obtained 

in the cement paste. 
4 

Byfors also documents a model that provides an estimate of heat of hydration as a function of time. The 

model defines the heat development for the four main clinker compounds at ages of 3, 7, 28, 90, and 365 

days. 

Knudsen, T., “Modeling Hydration of Portland Cement—The Effect of Particle Size Distribution,” 

Conference Proceedings, Characterization and Performance Prediction of Cement and Concrete, 

Edited by Young, J.F., United Engineering Trustees, Inc., New Hampshire, pp. 125–150, 1983. 

This paper presents a mathematical model for the development of the hydration of portland cement with 

time, called the dispersion model, which is founded on the particle size distribution (PSD) of the cement. 

The rate and duration of reaction of smaller particles is different from those of larger particles. During 

hydration, smaller particles might be fully hydrated, and the larger particles might be at a lower degree of 

hydration. Therefore, at any given time, the degree of hydration has a distribution that is dependent on 

the PSD. All cement particles are assumed to react independently of each other. It is shown that the 

particle size has a dominant effect on the shape of the hydration curve. 

The model development is based on kinetic theory for solid-state reactions, with the assumption that 

spherical grains react according to the shrinkage core model. In this model, the growing reaction zone is 

surrounding the unreacted core. The assumed kinetic function is used with the Rosin-Rammler PSD to 

obtain a very simple formulation of the degree of hydration in terms of a constant that characterizes the 

PSD and a rate constant that accounts for the effect of temperature on the form of the hydration curve. 

The model is compared to data obtained by other researchers, and good agreement with the data is found. 

Pinto, R.C.A., “The Effect of Curing Temperatures on the Development of Mechanical Properties of 

Fresh and Hardened High-Strength Silica Fume Mixtures—A Maturity Approach,” Dissertation, 

Cornell University, Ithaca, NY, 294 pp., 1997. 

In this dissertation, Pinto presents expansions on the dispersion model presented by Knudsen, and fits the 

shape of the strength gain to a hyperbolic model, which has been shown to provide the best fit. Because 

the different reactions of cement hydration can be controlled through kinetics and/or diffusion processes, 

Pinto states that “one would not expect a constant value for Ea for all stages of cement hydration.” 

Diffusion-controlled processes are expected to be less temperature sensitive than kinetically-controlled 

ones. Therefore, a lower activation energy (AE) value is expected as the hydration process progresses. 

Pinto reports that “as an average, the AE of C3S hydration, or the apparent AE of portland cement 

hydration, is twice as high during the early chemically (kinetically) controlled stages than at the late, 

diffusion-controlled stage.” Pinto provides a method to select an appropriate AE value for each of the 

five stages of hydration. This method is called the variable E-method. Data is further presented to 

address the selection of the most appropriate value for the AE, and it is shown that if AE values are 

selected based on strength data, different AE values can be obtained depending on the shape (hyperbolic, 

exponential, parabolic-hyperbolic) of the strength-age relationship. 

Van Breugel, K., Simulation of Hydration and Formation of Structure in Hardening Cement-Based 

Materials, Second Edition, Delft University Press, Netherlands, 305 pp., 1999. 

This book presents a complete review of literature and available techniques to model concrete hydration 

and structural development in cement-based materials, and the model developed is referred to as 

HYMOSTRUC. The models are able to allow for the effects of cement composition, PSD, w/c, and the 

initial mix temperature. For simplicity, the Rosin-Rammler function is recommended to model the 

cement PSD. A formulation similar to the current model in HIPERAV is recommended to determine the 

maximum heat of hydration. The degree of hydration is defined in terms of structural formation, and 
5 

modeled as the ratio of the amount of cement that has reacted, at a certain time relative to the original 

amount of cement. 

The ultimate degree of hydration is determined based on the amount of water available for reaction with 

the cement particles, and the space available for the hydration products. However, this model is rather 

complex, and the relative humidity within the pore structure must be modeled. The model also does not 

account for different cement compositions and fineness of the cement, which will most likely influence 

this value. 

Models are presented to determine the AE of the mix design in terms of the C3S content of the cement 

used, the degree of hydration of the mix, and the temperature of the concrete. 

Maekawa, K., Chaube, R., and Kishi, T., Modeling of Concrete Performance—Hydration, 

Microstructure Formation, and Mass Transport, E&FN Spon, New York, NY, 308 pp., 1999. 

Models are presented to predict the pore structure development of hydrating concrete, which then is used 

to determine the mechanical and physical properties of the concrete with respect to long-term durability. 

To determine the pore structure development, the following components are modeled: heat generation, 

water consumption, pore water pressure, equilibrium of pore water pressure, and moisture migration. The 

model described in this book is referred to as DuCOM. 

A multicomponent heat of hydration model is presented, where the heat of hydration is determined 

through summing the heat rates of the different clinker minerals. The heat of hydration rate for each of 

the mineral compounds is divided into stages in terms of cumulative heat generation. The heat generation 

rate of the most critical stage (stage 2) was fitted according to values obtained from adiabatic tests. 

Stage 3 was identified as the diffusion control stage, and a slower heat generation rate was assigned to 

each compound. Other blending minerals, such as slag or fly ash, are incorporated as additional mineral 

components. The effect of the development of ettringite on the formation of C3A and gypsum with C4AF 

is accounted for in the proposed multicomponent model. 

A temperature model is proposed similar to the one initially developed by Byfors, but numerous 

modification factors are added. These modification factors account for the reduction of probability of 

contact between unhydrated compounds and free pore water, the effect of mineral composition of 

portland cement, the reduction of the pozzolan’s reaction due to the shortage of calcium hydroxide, the 

relative cement fineness expressed as a ratio of the Blaine fineness, and the retardation of the overall rate 

of cement and slag reaction caused by the presence of fly ash. 

A moisture transport model for cementitious materials is presented, which considers the multiphase 

dynamics of liquid and gas phases. The moisture transport characteristics are dependent on the previously 

determined microstructure. The model can also consider the effect of wetting and drying cycles for 

concrete exposed to natural environments with fluctuating moisture levels. 

Onken, P. and Rostásy, F.S., “A Practical Planning Tool for the Simulation of Thermal Stresses and 

for the Prediction on Early Thermal Cracks in Massive Concrete Structures,” Proceedings of the 

RILEM ( French acronym for Réunion Internationale des Laboratoires et Experts des Matériaux, 

Systèmes de Constructions et Ouvrages) Symposium on Thermal Cracking in Concrete at Early Ages, 

Edited by Springenschmid, R., E&FN Spon, London, pp. 289–296, 1995. 

Models similar to those developed by Byfors are presented, however, the degree of hydration model is 

modified to only contain two parameters, compared to the three initially proposed by Byfors. It is 

reported that the shape of the hydration curve is a function of the clinker composition, PSD, the w/c, and 
6 

the initial mix temperature. No models are presented to define the effect of these variables on the heat of 

hydration. 

Bentz, D.P., Garboczi, E.J., Haecker, C.J., and Jensen, O.M., “Effects of Cement Particle Size 

Distribution on Performance Properties of Portland Cement-Based Materials,” Cement and 

Concrete Research, 1999. 

The effects of cement PSD on a variety of performance properties are demonstrated. Laser diffraction 

techniques were used to determine the PSD of the two cements analyzed. It is shown that finer grinding 

results in enhanced hydration, heat release, and strength at all investigated ages. At later ages, the 

cumulative degree of hydration and heat release of the different cements are nearly equivalent. Even 

though the finer particles require less time to achieve set due to its increased hydration rate, it actually 

requires more hydration, as more particle-to-particle bridges need to be built. 

Komonen, J. and Penttala, V., “Influence of Admixture Type and Concrete Temperature on Strength 

and Heat of Hydration of Concrete,” 10th International Symposium on the Chemistry of Cement, 

Edited by Justnes, H., Trondheim, Norway, 8 pp., 1997. 

In this paper, the authors present some valuable results that quantify the effect of different admixtures and 

initial concrete temperatures on the heat of hydration of concrete. Based on the variables considered, it is 

concluded that the mixing temperature is the most significant variable. The higher the mixing 

temperature, the earlier the heat gain took place. Numerous heat of hydration curves are presented for all 

the variables evaluated. The efficiency of the different plasticizers varied considerably at early ages. 

Ma, W., Sample, D., Martin, R., and Brown, P.W., “Calorimetric Study of Cement Blends Containing 

Fly Ash, Silica Fume, and Slag at Elevated Temperatures,” Cement, Concrete, and Aggregates, Vol. 

16, No. 2, pp. 93–99, December 1994. 

In this paper, the hydration of blended cements containing fly ash, silica fume, and ground-granulated 

blast-furnace (GGBF) slag over the temperature range of 0 degrees Celsius (°C) to 55 °C was studied by 

isothermal calorimetery, and the heat evolution during the first 24 hours of hydration was examined. The 

AE for the different blended cements were determined and the following values were obtained: 39.0, 

26.7, 30.4 and 49.3 kilojoule per mole (kJ/mol) for portland cement, fly ash, silica fume, and slag blended 

cements, respectively. 

Andersen, P.J., Andersen, M.,E., and Whiting, D., A Guide to Evaluating Thermal Effects in Concrete 

Pavements, SHRP–C–321, Strategic Highway Research Program, National Research Council, 

Washington, DC, 104 pp., 1993. 

This paper briefly summarizes all the models required to determine the temperature development in 

concrete at early ages due to the exothermic reaction and the influence of climatic conditions. The 

models used are very similar to those developed by Byfors (as mentioned above) and heat transport by 

thermal conduction, convection, and radiation also is introduced. Based on the analysis performed, final 

recommendations are made to the extent of thermal cracking based on the slab thickness, concrete 

placement temperature, air temperatures, and the cement type used in the concrete mixture. In this project 

it is assumed that the problems could occur when any of the following three conditions are encountered: 

• Risk of thermal cracking becomes too large when the temperature differential exceeds 20 °C. 

• Risk of temperatures within the concrete slab becoming too high. Permanent strength loss 

can be experienced when the concrete temperatures are higher than 60 °C. 
7 

• Risk of early freezing. According to American Concrete Institute (ACI) 308, freezing must 

be prevented until the concrete has reached a compressive strength of 3.45 kPa. 

The degree of hydration in this study is also defined in terms of two adiabatic parameters, one that defines 

the curvature of hydration, and the other that defines the time of hydration initiation. Typical values for 

different cement types are provided. In this study, activation energies for a variety of cement were 

determined to be as follows: Type I = 48.8 kJ/mol, Type II = 41.3 kJ/mol, Type III = 42.5 kJ/mol, Type I 

+ fly ash = 38.2 kJ/mol, and Type II + fly ash = 36.8 kJ/mol. 

Eren, O., Brooks, J.J., and Celik, T., “Setting Times of Fly Ash and Slag-Cement Concretes as 

Affected by Curing Temperature,” Cement, Concrete, and Aggregates, Vol. 17, No. 1, pp. 11–17, 

June 1995. 

The time of setting of different concrete pastes by penetration resistance (American Society for Testing 

and Materials (ASTM) C 403) is presented. Penetration resistance was determined under isothermal 

curing temperatures ranging from 6 oC to 80 oC for concrete containing up to 50 percent of fly ash or 

GGBF slag. At high temperatures, slag concrete has shorter setting times than Type I cement concrete. 

The setting times of fly ash concrete are longer than those of Type I cement concrete and slag concrete. 

Empirical relationships are presented for setting time as a function of penetration resistance, temperature, 

and cement replacement level. 

Douglas, E., Elola, A., and Malhotra, V.M., “Characterization of Ground-Granulated Blast-Furnace 

Slags and Fly Ashes and Their Hydration in Portland Cement Blends,” Cement, Concrete, and 

Aggregates, Vol. 12, No. 2, pp. 38–46, 1990. 

In this paper, chemical analysis, PSD, heat evolution rate, total heat evolution, and strength development 

were studied for three GGBF slags, and two fly ashes of low and high CaO content. At all stages, the 

heat evolution rates and total heat evolution by the fly ashes were lower than the corresponding values for 

the GGBF slag. 

Rahhal, V.F. and Batic, O.R., “Mineral Admixtures Contribution to the Development of Heat of 

Hydration and Strength,” Cement, Concrete, and Aggregates, Vol. 16, No. 2, pp. 150–158, December 

1994. 

This paper presents a wide range of test results to quantify the benefits of adding mineral admixtures, 

such as natural pozzolan, fly ash, and GGBF slag, to control heat development. Blended cements were 

prepared using ordinary portland cement clinker, gypsum, and mineral admixtures. The percentages of 

mineral admixtures investigated were 0, 10, 20, 33, 40, 50, 70, and 90, by mass. Tests were performed at 

3, 7, 28, 90, and 180 days. Empirical coefficients of the contribution of mineral admixtures to heat of 

hydration have been obtained, as well as a mathematical expression to estimate the heat of hydration of 

blended cements based on the mineral admixture selected, the percentage used, and the heat of hydration 

of the control cement. The following conclusions pertinent to the HIPERPAV II project include: 

• The rate of heat evolution of blended cements containing the mineral admixtures accelerates 

up to 7 days, decelerates towards 28 days, and remains constant toward 180 days. 

• Liberated heat at a given age decreases as replacement percentages of the mineral admixtures 

increase. 

Each mineral has an optimum range of replacement percentage that increases mechanical strength, and 

lowers the heat of hydration. 
8 

Tazawa, E. and Miyazawa, S., “Influence of Cement Composition on Autogenous Shrinkage of 

Concrete,” Proceedings on the 10th International Congress on the Chemistry of Cement, Gothenburg, 

Sweden, Vol. 2, June 1997. 

Autogenous shrinkage is defined as the macroscopic volume reduction caused by hydration of cement. 

Based on the test performed by the authors, it was concluded that autogenous shrinkage was strongly 

influenced by the type of cement, which is due to the difference in cement composition, and especially the 

content of C3A and C4AF. Compared to normal portland cement, autogenous shrinkage is large for high 

early strength cement, and is lower for moderate heat cement. Autogenous shrinkage is very low for low 

heat cement with high C2S contents. For the mixtures investigated, autogenous shrinkage increases with a 

decrease in w/c. This ratio is, therefore, the main variable in the prediction model. An empirical equation 

is presented to estimate the autogenous shrinkage strain of the concrete based on the time elapsed, the 

type of cement, and the w/c used. The prediction model is valid for concrete with w/c ranging from 0.2 to 

0.56, a coarse aggregate factor of 0.55 to 0.65, and an environmental temperature of 20 °C. 

Coole, M.J., “Heat Release Characteristics of Concrete Containing Ground-Granulated BlastFurnace Slag in Simulated Large Pours,” Magazine of Concrete Research, Vol. 140, No. 144, 

September 1988. 

This paper investigates the effect of three different European sources of GGBF slag blended with ordinary 

portland cement. It is shown that both the peak temperature and the time to reach this temperature are 

influenced strongly by the slag source. Five levels of slag replacement were investigated, and with a 

reactive slag at a moderate replacement of cement (20–40 percent), the temperature rise at the center of 

the pour was higher than when an equivalent cement was used. 

A.2.2 Concrete Maturity 

Maturity is a technique used to estimate the strength gain of concrete based on the measured temperature 

history during curing. A maturity function is a mathematical expression that accounts for the combined 

effects of time and temperature on the concrete’s strength development. This function usually is assumed 

to be a linear function of temperature, or to obey the exponential Arrhenius equation. 

Carino, N.J., “CRC Handbook on Nondestructive Testing of Concrete, Chapter V—The Maturity 

Method,” Edited by Malhorta, V.M., CRC Press, Florida, 1991. 

This reference presents a historical review of all the widely used maturity methods. The equivalent age 

concept is explained, and the importance of temperature on early-age concrete properties is stressed. The 

maturity concept was initiated by Saul, where maturity is the sum of change in temperature multiplied by 

the time interval (Nurse-Saul function). Limitations of this method are that a datum temperature is 

needed to calculate the temperature change. The equivalent age concept was initiated in 1960 to 1977 by 

Arrhenius. This age conversion factor is a function of absolute temperature. Maturity is equal to the rate 

constant multiplied by age (where the rate constant depends on temperature). To relate strength to 

maturity, hyperbolic, and other empirical functions have been developed. The empirical formulas have 

coefficients that follow the shape of the curve. Equivalent age is the most flexible technique available to 

represent maturity. 
9 

Method of Testing the Strength of Portland Cement Concrete Using the Maturity Method, Iowa 

Department of Transportation (DOT), Materials. Iowa Method 383. Office of Materials. 

The Iowa DOT uses maturity to measure the in-place strength of the concrete. Part 1 describes the 

destructive testing method to get the relationship between maturity and concrete strength. Part 2 

describes instrumentation of the concrete to obtain in-place temperatures. The Nurse-Saul method is 

used. 

Carino, N., Lew, H.S., and Volz, C.K., “Early-Age Temperature Effects on Concrete Strength 

Prediction by the Maturity Method,” ACI Journal, pp. 93–101, March–April 1983. 

Early-age temperature is found to influence strength-maturity relationship at later ages. Maturity is 

calculated using the simplified Nurse-Saul equation. Mathematical models that represent maturity can 

have either log or hyperbolic functions. 

Marzouk, H. and Hussein, A., “Effect of Curing Age on High-Strength Concrete at Low 

Temperatures,” Journal of Materials in Civil Engineering, Vol. 7, No. 3. pp. 161–167, August 1995. 

The effect of curing age on the strength of silica fume concrete containing fly ash at cold temperatures is 

given. This paper describes how properties of the concrete change as a function of temperature, 

composition, modulus of rupture, and splitting tensile strength. The effect of pozzolans and admixtures 

are considered. Maturity methods are discussed. This paper states that the maturity method may not be 

appropriate for concrete placed under freezing temperatures. 

Jensen, O. M. and Hansen, P.F., “Influence of Temperature on Autogenous Deformation and Relative 

Humidity Change in Hardening Cement Paste,” Cement and Concrete Research, Vol. 29, pp. 567– 

575, 1999. 

The autogenous deformation, relative humidity, and temperature changes in hardening cement paste are 

investigated. Maturity concepts do not apply to these phenomena. Concrete self-desiccates because of 

the low w/c, shrinking in bulk, which can cause cracking. Self-desiccation shrinkage is a form of 

chemical shrinkage that can eventually lead to failure of the entire structure. 

Kim, J.K., Moon, Y.H., and Eo, S.H., “Compressive Strength Development of Concrete with Different 

Curing Time and Temperature,” Cement and Concrete Research, Vol. 28, No. 12, pp. 1761–1773, 

1998. 

Previous maturity work focuses on predicting concrete strength under isothermal conditions. In practice, 

this is not the case. Varying temperatures must be taken into account, and this paper tries to develop a 

maturity model that does that. 

A.2.3 Drying Shrinkage of Concrete 

Drying shrinkage happens when the rate of moisture loss from the pavement surface is greater than the 

rate at which it can be replenished by free moisture in the slab. The desiccated concrete shrinks, and this 

can lead to warping and cracking of the structure. Most typically, drying shrinkage affects exposed 

surfaces. 
10 

Al-Sugair, F. H. and Almudaiheem, J.A., “Further Modification of the Ross Equation to Predict the 

Ultimate Drying Shrinkage of Concrete,” ACI Materials Journal, Vol. 87, No. 3, May–June 1990. 

The Ross equation is used to predict drying shrinkage. A large amount of experimental data (drying 

shrinkage versus time) is used, and the effect of volume-to-surface-area ratio on drying shrinkage is the 

focus. Its error is ±25 percent. Drying shrinkage was predicted from 1 to 28 days in some cases. 

Han, M.W. and Lytton, R.L., “Theoretical Prediction of Drying Shrinkage in Concrete,” Journal of 

Materials in Civil Engineering, Vol. 7, No. 4, November 1995. 

The water potential is used to estimate the degree of drying shrinkage. Water potential is a type of stress 

that forces moisture to move and causes hydrated cement particles to shrink and expand. Drying 

shrinkage is related to water potential by a logarithmic curve. 

Kim, J.K. and Lee, C.S., “Prediction of Differential Drying Shrinkage in Concrete,” Cement and 

Concrete Research, Vol. 28, No. 7, pp. 985–99, 1998. 

The effect of creep is incorporated into the drying shrinkage prediction. The drying shrinkage profile is 

obtained; this depends on the distance from the exposed concrete surface and on time. 

Persson, B., “Experimental Studies on Shrinkage of High-Performance Concrete,” Cement and 

Concrete Research, Vol. 28, No. 7, pp. 1023–1036, 1998. 

Relationships are developed to predict the amount of autogenous shrinkage and drying shrinkage in 

concrete as a function of w/c, amount of silica fume in the concrete, the ratio of evaporated water to 

mixing water, and internal relative humidity. The focus of this paper is relating silica fume content 

(slurry or granular) to total, drying, and autogenous shrinkage. 

Shah, S.P., Ouyang,C., Marikunte, S., Yang, W., and Becq-Siraudon, E., “A Method to Predict 

Shrinkage Cracking of Concrete,” ACI Materials Journal, pp. 339–346, July–August 1998. 

Nonlinear fracture mechanics are used in this reference to predict drying shrinkage of a ring specimen. 

Cracking of concrete is caused by its creep, free shrinkage, elastic modulus, tensile strength, and fracture 

toughness properties. Cracking results when there is a difference in the amount of free shrinkage and 

creep. The effect of creep on shrinkage cracking was determined using the CEB-FIP (French acronym for 

European Committee for Concrete-International Federation for Prestressing) model. The time 

dependence of concrete fracture toughness is measured. To use this model, fracture toughness and critical 

crack tip opening displacement are needed. 

Shimomura, T. and Maekawa, K., “Analysis of the Drying Shrinkage Behavior of Concrete Using a 

Micromechanical Model Based on the Micropore Structure of Concrete,” Magazine of Concrete 

Research, Vol. 49, No. 181, pp. 303–322, December 1997. 

A micromechanical drying shrinkage model is developed by the researchers who developed DuCOM. 

This model takes into account the concrete’s pore structure and microscopic phenomena, described 

according to simplified mechanical and thermodynamic assumptions. Drying shrinkage is determined 

using a four-step procedure: 1) analytical pore size distribution; 2) time-dewatering relationship; 3) 

dewatering-shrinkage relationship; and 4) time-shrinkage relationship. A limitation of this model is that it 

has been validated on only two specimens. In addition, the theoretical equations require extensive 

amounts of data and subsequent experimental testing. 
11 

A.2.4 Moisture Transport in Concrete 

The properties of concrete are highly dependent upon the moisture conditions within. By appropriately 

monitoring the moisture content of concrete, it is possible to minimize the development of some 

distresses. Three different pavement distresses associated with moisture loss are plastic shrinkage 

cracking, delamination spalling, and drying shrinkage cracking. Plastic shrinkage cracking is caused by 

the loss of water from the surface of a concrete pavement at early ages. If the pavement is cured properly, 

this cracking can be prevented. Moisture lost from the surface of the concrete pavement can also cause 

delamination spalling and drying shrinkage. Delamination of the concrete surface results when pavement 

strength decreases due to insufficient moisture in the concrete at the time of curing. This weakened 

portion of concrete detaches from the monolithic slab to form a delamination (or flat bottom) spall. 

Drying shrinkage is caused by moisture lost from the pavement surface during curing. This can lead to 

increased levels of stress in the pavement, and to subsequent crack formation. 

RILEM Bulletin, “Properties of Set Concrete at Early Ages—State of the Art Report,” Materials and 

Structures, Vol. 14, No. 84, pp. 398–450, 1981. 

Most mechanical and physical properties of concrete are affected by moisture. Concrete is a porous 

material, and volume changes occur due to the presence of water, such as shrinkage and swelling. All 

porous materials bind water from the atmosphere with a certain relative humidity or from water on 

contact. Water in concrete is either chemically combined or physically adsorbed. The sorption isotherm 

relates the material’s equilibrium content of water to that of the ambient environment’s humidity. To 

reach an equilibrium state with a higher relative humidity, an adsorption isotherm is used. To decrease 

the concrete’s moisture, a desorption isotherm is used. These isotherms are a function of the concrete’s 

degree of hydration, among other factors. There is no data on sorption isotherms at early ages. The 

transport of moisture in the concrete is governed by Darcy’s law and Fick’s first law. Moisture transport 

depends on the concrete’s moisture content. For a fixed relative humidity, transport depends on the 

concrete’s composition, age, and temperature. Age significantly affects the concrete’s diffusion prior to 

28 days. For mature concrete, w/c and air content are the influential factors. 

Xi, Y., Baźant, Z.P. Molina, L., and Jennings, H. M., “Moisture Diffusion in Cementitious Materials,” 

Moisture Capacity and Diffusivity, Journal of Advanced Cement-Based Materials, Vol. 1, pp. 258–

266, 1995. 

This paper discusses the diffusion of water in concrete. Concrete dries due to three different diffusion 

mechanisms. They are ordinary drying, Knudsen diffusion, and surface diffusion. An equation for 

moisture diffusivity is given that is highly dependent on the concrete’s w/c. Increasing a concrete’s w/c 

causes diffusivity to increase at low humidity levels. 

Maekawa, K., Chaube, R., and Kishi, T., Modeling of Concrete Performance: Hydration, 

Microstructure Formation and Mass Transport, E&FN Spon, New York, NY, 1999. 

Moisture transport in concrete is modeled by the DuCOM researchers. This model should be able to 

account for the effect of crack formations on water distribution in the concrete structure. 

Mjornell, K.N., Moisture Conditions in High-Performance Concrete: Mathematical Modeling and 

Measurements, Department of Building Materials, Chalmers University of Technology, Sweden, 

1997. 

A moisture model has been developed for high-strength concrete that accounts for both self-desiccation 

and moisture transport. The effect of curing on the concrete has been studied at very early ages, as well. 
12 

A.2.5 Set Time of Concrete 

Concrete set is typically divided into two stages. The first is initial set, when the concrete paste stiffens 

considerably. The second stage is final set, where the concrete has hardened so that it can sustain load. 

The setting of concrete referred to here is the final set. This parameter is very important when 

determining the early-age stress state of the concrete. 

Byfors, J., Plain Concrete at Early Ages, Swedish Cement and Concrete Research Institute, 1980. 

This paper investigates how different aggregate and admixtures affect the setting time of concrete and its 

time-dependent stiffness. Aggregates in the concrete that are investigated include quartzite, granite, 

dolomite, and andesite. Blended cements are investigated, such as ordinary portland cement with silica 

fume, slag, and fly ash. The linear and nonlinear growth of the concrete modulus as a function of time is 

recorded at early ages and at later ages. 

Uchikawa, H., Hanehara, S., Shirasaka, T., and Sawaki, D., Effect of Admixture on Hydration of 

Cement, Adsorptive Behavior of Admixture and Fluidity and Setting of Fresh Cement Paste,” Cement 

and Concrete Research, Vol. 22, pp. 1115–1129, 1992. 

A rheological discussion on concrete setting times is presented. The yield stress is related to the mortar 

specimen’s set time. 

De Siqueira Tango, C.E., “An Extrapolation Method for Compressive Strength Prediction of 

Hydraulic Cement Products,” Cement and Concrete Research, Vol. 28, No. 7, pp. 969–983, 1998. 

The determination of concrete set time for pavements is discussed in this report. If drying shrinkage and 

creep of the concrete are not taken into account, the zero stress point corresponds to the zero set 

temperature. However, if these factors are considered, the zero stress point occurs at a higher 

temperature. Compressive stresses can be alleviated by shrinkage and creep effects. A novel method to 

determine set temperature is presented. The procedure is to fill a mold with fresh cement mix and 

determine the set temperature when the mix separates from the sides of the mold. 

Struble, L.J. and Lei, W.-G., “Rheological Changes Associated with Setting of Cement Paste,” 

Advances in Cement-Based Materials, Vol. 2, p. 244, 1995. 

Set times can be a measure of the cement hydration’s AE. The Arrhenius method is used to determine 

how the rate of chemical reaction depends on temperature. The thermal sensitivity of the reaction is the 

AE. AE is time dependent, but it is usually assumed to be a single value during all stages of hydration. 

The hotter the mix, the faster the setting time. 

A.2.6 Thermal Properties of Concrete 

Because temperature is one of the primary factors that influence the behavior of jointed concrete 

pavements (JCP) at early ages, the thermal properties of the concrete must be understood. HIPERPAV II 

incorporates seven thermal properties of concrete. They are coefficient of thermal expansion (CTE), 

thermal conductivity, specific heat, thermal diffusivity, convection, emissivity, and solar absorptivity. 

This section defines these parameters and summarizes how these properties change at early ages. Earlyage factors that influence concrete’s thermal properties are its degree of hydration, the amount and type of 

aggregate, and the water-to-cementitious materials ratio (w/cm). HIPERPAV II requires an 

understanding of concrete thermal properties at early ages and in the long term. 
13 

A.2.6.1 Coefficient of Thermal Expansion 

CTE is defined as the relative length change of a material caused by changing its temperature one degree. 

In concrete, CTE is a function of the paste and the aggregate. The aggregate’s CTE depends upon its 

mineralogical composition, and only slightly on its moisture content. The CTE of paste depends 

primarily on the moisture content, w/cm, and age of the paste. 

Khan, A.A., Cook, W.D., and Mitchell, D., “Thermal Properties and Transient Thermal Analysis of 

Structural Members During Hydration,” ACI Materials Journal, Vol. 95, No. 3, pp. 293–303, 

May–June 1998. 

CTE of concrete is assumed to be equal to the volumetrically weighted average of its ingredient’s CTE. 

Concrete CTE is known to increase with increasing concrete density. CTE is highly dependent on age 

only during the first few hours after construction. The early-age CTE is significantly higher than the 

hardened concrete’s CTE. After 10 hours of hydration, it decreases, then remains constant. 

LaPlante, P. and Boulay, C., “Evolution du Coefficient de Dilation Thermique du Beton en Fonction 

de sa Maturite Aux Tout Premiers Ages,” Materials and Structures, Vol. 27, pp. 596–605, 1994. 

CTE of concrete was measured at early ages and plotted as a function of equivalent age at 20 °C. 

A.2.6.2 Thermal Conductivity 

Thermal conductivity is the ratio of heat flux to temperature gradient. Thermal conductivity is defined as 

the amount of heat flowing per unit time between two parallel faces of unit area when the faces are unit 

distance apart. The plates are maintained at a temperature difference of 1 degree. All the heat entering 

one face leaves the opposite face. 

Khan, A.A., Cook, W.D., and Mitchell, D., “Thermal Properties and Transient Thermal Analysis of 

Structural Members During Hydration,” ACI Materials Journal, Vol. 95, No. 3, pp. 293–303, May–

June 1998. 

Thermal conductivity varies with concrete density. Heavier aggregates typically have concrete with a 

higher thermal conductivity. Because thermal conductivity of water and air are different from that of the 

hydration products, thermal conductivity is expected to change during early hydration. Water has lower 

conductivity than aggregate. Concrete made with a low w/c and a higher density should have a high 

thermal conductivity. This is why lightweight concrete with high porosity and, therefore, low 

conductivity, has good insulating properties. 

It is difficult to measure thermal conductivity in early-age concrete. Some researchers report a drop in 

thermal conductivity from 6 hours to 7 days, while others say there is no change in thermal conductivity 

after 24 hours. For normal strength concrete (30 megapascals (MPa)), its thermal conductivity during 

maturation is 33 percent higher than when hardened. For high-strength concrete (100 MPa), there is only 

a 2 percent difference in the thermal conductivity of maturing and hardened concrete. Thermal 

conductivity is typically independent of temperature within the normal climactic range. However, above 

100 °C, thermal conductivity decreases linearly. 
14 

Properties of Set Concrete at Early Ages—State of the Art Report, Materials and Structures, Vol. 14, 

No. 84, November–December 1981. 

This article reports that aggregate type is the most important factor affecting the thermal conductivity of 

concrete. 

Brown, T.D. and Javaid, M.Y., “The Thermal Conductivity of Fresh Concrete,” Materials and 

Structures, Vol. 3, No. 13, pp. 411–416, 1970. 

These researchers report a decrease in thermal conductivity of concrete with age for fresh conventional 

concrete. 

A.2.6.3 Specific Heat 

Specific heat is defined as heat capacity. Specific heat is determined by measuring the temperature rise in 

a calorimeter using a predetermined supply of energy. There is limited information about specific heat of 

concrete in the literature, and some of it is contradictory. 

Khan, A.A., Cook, W.D., and Mitchell, D., “Thermal Properties and Transient Thermal Analysis of 

Structural Members during Hydration,” ACI Materials Journal, Vol. 95, No. 3, pp. 293–303, 

May–June 1998. 

Specific heat is a function of time. A 15 percent drop in specific heat a few hours after casting to 5 days 

later for rapid hardening concrete with a w/c of 0.5 is reported. Moisture content has a significant effect 

on specific heat. Oven dry specimens have lower specific heat than do saturated samples. Also, specific 

heat increases with temperature and decreases with increasing concrete density. 

Mindess, S. and Young, J. F., Concrete, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981. 

Specific heat of concrete is not affected by aggregate type. It varies by only 8 percent due to a change in 

aggregate. Typically, specific heat ranges from 800 to 1200 joules per kilogram (J/kg) °C. It is 

dependent on porosity (w/c), water content, and temperature. In the reference synthesis, a decrease 

between 1 and 20 percent in the concrete’s specific heat is reported as it hardens. Specific heat is a 

function of the cement’s degree of hydration. 

A.2.7 Creep 

Knowledge of the nonlinear creep behavior is important when accurately estimating axial stresses. The 

behavior of young concrete under load is best modeled by including viscoelastic deformations and plastic 

flow. In HIPERPAV I, the effect of relaxation is accounted for empirically, and a more sophisticated 

model that combines the effects of creep and viscous response (relaxation) of concrete at early ages is 

required. This section provides a brief summary of the primary references that contain candidate models. 

Umehara, H., Uehara, T., Iisaka, T., and Sugiyama, A., “Effect of Creep in Concrete at Early Ages 

on the Thermal Stresses,” Proceedings of the International RILEM Symposium, Munich, Germany, 

pp. 79–86, E&FN Spon, October 1994. 

This document contains the approach followed to model the creep behavior in HIPERPAV I and II. 

Models were developed based on tensile and compressive creep tests. The stress level, period of loading, 

and temperature at the test were the parameters investigated. The effective modulus method is used to 
15 

characterize the creep, and the viscoelastic nature of concrete loaded at early ages, therefore, cannot be 

modeled. 

Baźant, Z.P., “Numerical Determination of Long-Range Stress History From Strain History in 

Concrete,” Materials and Structures, RILEM Paris, Vol. 5, No. 27, pp. 135–141, May–June 1972. 

This paper presents an efficient systematic numerical algorithm for computing the stress history from any 

prescribed strain history in a linear age-dependent viscoelastic material such as hardening concrete. The 

method is applicable for any form of the creep function. It is assumed that stress history is a series of 

sudden (discontinuous) stress increments, then the algebraic equations resulting from the superposition of 

creep responses due to all the individual stress increments are solved. The disadvantage of this method is 

that large storage space could be required to store the complete history of stresses for all the elements in 

the structure. Uncertainty exists about the applicability of the principle of superposition in the case of 

creep recovery. Baźant and Panula (as referenced below) address this issue more directly and provide an 

example of the measured creep versus predicted creep where the theory works very well. 

Baźant, Z.P., and Panula, L., “Practical Predictions of Time-Dependent Deformations of Concrete,” 

Materials and Structures, Third RILEM, Vol. 11, 1978. 

In this document, the Double Power Law is developed to predict concrete creep at constant humidity and 

temperature from the composition of the concrete mix, strength, age at loading, and load duration. The 

Double Power Law is perhaps the most well known compliance function, and it has been used by many 

researchers since its development. With the Double Power Law, creep of concrete at constant moisture 

and thermal state is described by power curves for load duration (t–t0), and by inverse power curves to 

account for the effect of the loading age t0. The Double Power Law was modified later to the Triple 

Power Law (discussed next) to improve the accuracy of the long-term creep prediction. 

Baźant, Z.P., and Chern, J.C., “Strain Softening with Creep and Exponential Algorithm,” Journal of 

Engineering Mechanics Division, American Society of Civil Engineers (ASCE), Vol. 111, No. 3, 1985. 

In this paper, Baźant provides an improved creep model for concrete at constant temperature and water 

content. It gives the creep rate as a product of power functions of the load duration, the age of loading, 

and the current age of the concrete. This model was called the Triple Power Law, and the Double Power 

Law was modified with a binomial function to provide a more accurate description of long-term creep. 

This model is extensively calibrated with test data obtained from literature. 

Emborg, M., Thermal Stress in Concrete Structures at Early Ages, Doctoral Thesis, Luleå University 

of Technology, Division of Structural Engineering, 285 pp, 1989. 

Emborg tested the validity of both the Double and Triple Power Laws at early ages and concluded that 

neither was calibrated for loading at early ages, and their use was not intended to predict creep for young 

concrete. Therefore, Emborg adjusted the Triple Power Law to account for loading at ages earlier than 

about 2 days, and the extended Triple Power Law was developed. Most of the parameters for the Triple 

Power Laws remained unchanged, and two additional functions were added: one that accounts for the age 

dependence of the instantaneous deformation, and another to increase the creep when the load has been 

applied at early ages. 
16 

Westman, G., Concrete Creep and Thermal Stresses. Doctoral Thesis, Luleå University of 

Technology, Division of Structural Engineering, 301 pp, 1999. 

Westman modified the shape of the two additional functions first developed by Emborg in 1989 based on 

early-age creep tests performed. In this thesis, Westman provides the necessary values for each of the 

parameters in the extended Triple Power Law. 

A.3 JPCP LITERATURE REVIEW 

The literature review of JPCP models is presented in this section. The models are divided into seven 

sections. The first section reviews pavement structural models, such as the stresses that develop in the 

pavement due to temperature, moisture, and traffic loading, for example. The second section reviews 

available climatic models that can be used in conjunction with the structural models to account for 

climatic conditions at the time of pavement curing and also over the years as the pavement is subjected to 

long-term use. Third, the JPCP distress models are presented. These models are primarily empirical in 

nature. This means that the models are valid only for the pavement sections for which they were 

developed. In HIPERPAV II, it is preferable that mechanistic models be used that have been calibrated 

and validated with actual experimental data. Literature review on faulting, transverse cracking, and 

spalling are presented. 

A.3.1 JPCP Structural Models 

The JPCP structural models are used to predict the stresses acting on the pavement due to the different 

forms of loading, such as temperature, moisture, and traffic. Eight references are described below in the 

annotated bibliography. 

Huang, Y.H., Pavement Analysis and Design, Prentice Hall, Englewood Cliffs, NJ, 1993. 

Huang discusses KENSLABS, a finite-element program that can be used to predict pavement behavior, in 

detail. The types of foundations that can be accounted for are liquid, solid, and layer. Pavement layers 

can either be bonded or unbonded and have different or the same material properties. Likewise, the load 

transfer at multiple slabs can be taken into account, as can the curling/warping loading response. 

Arbitrary pavement dimensions, loading conditions, and shoulder conditions can all be considered. This 

program requires a substantial amount of computer storage. 

Smith, K.D., Peshkin, D.G., Darter, M.I., and Mueller, A.L., “Performance of Jointed Concrete 

Pavements, Volume III—Summary of Research Findings,” FHWA–RD–89–138, Federal Highway 

Administration (FHWA), McLean, VA, November 1990. 

The ILLI-SLAB program is described in this reference. ILLI-SLAB is a finite-element program that 

analyzes pavements. It calculates stresses, deflections, and moments directly due to loading or 

temperature effects. This program is able to analyze pavements of arbitrary dimensions with any number 

of slab arrangements. Two layers either can be bonded or not bonded, and these layers can have the same 

or different material properties. The subgrade can either be a liquid or solid subgrade, and the program 

can account for uniform or nonuniform support due to erosion. Similarly, arbitrary loading (axle) 

conditions and pavement shoulder conditions can be taken into account with ILLI-SLAB. This program, 

however, requires large amounts of computer storage. 
17 

Lee, Y-H. and Darter, M.I., “Mechanistic Design Models of Loading and Curling in Concrete 

Pavements,” Airport Pavement Innovations: Theory to Practice, Proceedings of the Conference. 

Edited by Hall, J.W. Jr., ASCE, September 1993. 

FEMs are used to analyze the edge stresses on the pavement. The FEM can account for finite slab length, 

finite slab width, and slab curling. These correction factors can be used to correct Westergaard’s 

solutions based on the infinite slab assumption. 

Lee, Y-H. and Lee Y-M., Corner Stress Analysis of Jointed Concrete Pavements, Transportation 

Research Record No. 1525, Transportation Research Board (TRB), National Research Council, 

Washington, DC, 1996. 

FEMs again are used to determine the corner stresses on a pavement, similar to the reference above. 

Design factors considered are widened outer lanes, tied concrete shoulders, and different loading 

configurations. These correction factors can be used in the fatigue equation for predicting corner cracks. 

Ramsamooj, D.V., “Stresses in Jointed Rigid Pavements,” Journal of Transportation Engineering, 

pp. 101–108, March–April 1999. 

Fracture mechanics is used to determine design stresses midway between the edge of the rigid pavement 

and at the corner. The solutions generally agree with Westergaard, finite-element, and American 

Association of State Highway and Transportation Officials (AASHTO) road test solutions. However, 

stresses predicted by this equation are 30 percent greater than the Westergaard stresses. Pavement 

deflections and stresses also are calculated. When wheel load is placed at the middle of the slab, critical 

stresses are at the bottom. Convex curling in a pavement occurs due to thermal temperature gradients. 

Traffic loading is critical for this condition. 

Liang, R.Y. and Niu, Y-Z., “Temperature and Curling Stress in Concrete Pavements: Analytical 

Solutions,” Journal of Transportation Engineering, Vol. 124, No. 1., pp. 91–101, January–February 

1998. 

The objective of this paper is to develop a theoretical model to predict the temperature and curling 

stresses in a concrete pavement. Based on nonlinear temperature gradients through the slab, the authors 

are able to develop the equivalent temperature bending moment. If a pavement experiences a severe 

temperature change (10 °C in 1 hour), the nonlinear temperature gradient must be taken into account. 

However, for more gradual temperature changes, linear temperature gradients are sufficient. 

Kuo, C.-M., “Effective Temperature Differential in Concrete Pavements,” Journal of Transportation 

Engineering, Vol. 124, No. 2., pp. 112–116, March–April 1998. 

Three-dimensional FEM code is used to evaluate curling stresses in pavements due to temperature 

gradient, slab self weight, and support under the concrete slab. The number of allowable traffic loads can 

be calculated before terminal serviceability is reached. 

Grater, S.F. and McCullough, B.F., “Analysis of Jointed Concrete Pavement,” Research Report 

1244–10, Center for Transportation Research, The University of Texas at Austin, Austin, TX, 1994. 

The mechanisms that cause cracking in JCPs are discussed in this report. Climatic factors, such as 

changing temperatures and moisture conditions 1 year after construction, are used in the analysis. The 

climatic analysis is extended from several days to 1 year. This program has been revised extensively at 

the University of Texas at Austin, evolving from JRCP–1 to JRCP–6. 
18 

A.3.2 JPCP Climatic Models 

The JPCP climatic models are used to predict pavement temperatures and moisture conditions. Climatic 

conditions are especially influential during early-age curing, but are also critical to the pavement’s longterm performance. In the following section, several climatic models are described. 

McCullough, B.F. and Rasmussen, R.O., Fast-Track Paving: Concrete Temperature Control and 

Traffic Opening Criteria for Bonded Concrete Overlays, Publication No. FHWA–RD–98–167, 

October 1999. 

This reference describes the theory behind the software package HIPERPAV I. This program predicts 

early-age pavement behavior caused by temperature and moisture changes during the first 72 hours after 

concrete placement. At its core is a finite-element temperature prediction model. The model takes into 

account heat generated internally due to hydration, solar absorption, convection, irradiation, and agedependent specific heat and thermal conductivity. The early-age variations in temperature can have a 

significant influence on the behavior of young concrete. Thermal and moisture stresses must be 

controlled to minimize early-age damage to the concrete pavements. 

Muller, A.L., Peshkin, D.G., Smith, M.I., Darter, M.I., Performance of Jointed Concrete Pavements, 

Volume VI, Appendix C—Synthesis of Concrete Pavement Design Methods and Analysis Models, 

FHWA–RD–89–141, FHWA, McLean, VA, July 1990. 

A review of climatic models is given in this reference. The models mentioned include Climatic-MaterialStructural and Liu-Lytton drainage models. 

Lytton, R.L., Pufahl, D.E., Michalak, C.H., Liang, H.S., and Dempsey, B.J., “An Integrated Model of 

the Climate Effects on Pavements,” FHWA–RD–90–033, 285 pp., FHWA, McLean, VA, November 

1989. 

The Integrated Climate Model (ICM) is a one-dimensional coupled heat and moisture flow program that 

is intended for use with pavements. Based on the location of the selected site, the structure’s material 

properties, and the historical climatic data, the ICM internally generates weather patterns of rainfall, solar 

radiation, air temperature, cloud cover, windspeed, and snowfall throughout the year. The ICM 

determines the temperature, frost and heave zone depths, frost heave, layer elastic moduli, and pore water 

pressure profile at different depths throughout the pavement structure at different stages during the year. 

The model is the combination of three models developed during previous research efforts. They are the 

Climatic-Materials-Structures Model, the Infiltration and Drainage Model, and the Frost Heave and Thaw 

Settlement Model. 

Barber, E.S., “Calculation of Maximum Pavement Temperatures from Weather Reports,” Bulletin 

168, Highway Research Board, Washington, DC, pp. 1–8, 1957. 

This reference describes a model that could be used in pavements to determine the initial temperature 

profile. The model is based on air temperature, wind velocity, and solar radiation inputs, which can all be 

obtained from weather records. This model provides a solution to the differential equation of conduction 

of heat in a homogeneous isotropic material. The model has the following limitations: 

• Only one pavement layer can be analyzed. 

• The effect of rain, snow, and clouds on the pavement surface is not taken into account. 

• The model assumes a semi-infinite mass. 
19 

A.3.3 JPCP Distresses 

Guidelines have been developed in the past that relate design features to pavement distresses. These 

references are summarized here. Most of the guidelines are based on empirical data, so it is best not to 

extrapolate these models to sets of inputs outside the realm of those used in their development. 

Smith, K.D., Wade, M J., Peshkin, D.G., Khazanovich, L.H. Yu, T., and Darter, M.I., Performance of 

Concrete Pavements, Volume II: Evaluation of In-Service Concrete Pavements, FHWA–RD–95–110, 

FHWA, McLean, VA, June 1998. 

This report synthesizes the behavior of more than 300 concrete sections. It provides critical levels of 

distress for the JPCP with regard to joint faulting, transverse cracking, longitudinal cracking, joint 

spalling, and roughness in terms of Present Serviceability Rating (PSR) and International Roughness 

Index (IRI). It also synthesizes the behavior of the pavements in terms of the design features. Design 

features that are investigated are pavement thickness, base type, subgrade type, joint spacing, joint 

orientation, transverse joint load transfer, joint sealant, drainage, shoulder type, widened lanes, 

reinforcement, and maximum coarse aggregate size. For example, an increase in pavement thickness 

translates to a decrease in transverse cracking and joint spalling, while there is no significant change in 

faulting. The mechanisms behind these trends also are discussed. For the example given, thicker slabs 

theoretically reduce stresses in the concrete, so the pavement will not be subjected to as severe a load. 

This translates to a reduction in spalling and transverse cracking. A summary of the influence of design 

features on pavement distresses is given in table 1. 

 
20 

Table 1. Summary of how pavement design parameters influence JPCP distresses. 

Variable 

Faulting 

Spalling 

Transverse 

Crackin

g

Longitudinal 

Crackin

g

Corner 

Breaks 

Roughness 

Comments 

Slab thickness ↑ x ↓ ↓ – – – – 

Joint spacing ↓ JPCP x – ↓ – – – – 

 —random – – ↑ – – – 3.6-, 3.9-, 5.8-, 5.5-meter (m) 

joints JPCP 

Joint orientation ↓ ↓ – – ↑ – Nondoweled designs 

Transverse joint load transfer ↑ – – – – – Nondoweled joints 

↓ – – – – – Doweled joints 

Dowel diameter—small (2.54 cm) ↑ – – – – – – 

 —large (3.2 cm) ↓ – – – – – – 

Dowel covering ↓ ↓ – – – – Epoxy or plastic 

Joint sealant—sealed ↓ ↓ – – – – Preformed compression seals 

best 

Joint sealant—none – – ↑ – ↑ – – 

Base type—JPCP on AGG* – – ↓ – – – – 

Base type—ATB* / CTB* – – ↑ – – – Stabilizing >6% for benefits 

No base course ↑ – – – – – No dowels in pavements 

Base type—permeable x – – – – – Less moisture distress 

Requires good drainage 

Drainage—good ↓ ↓ ↓ – – – More pronounced effect on 

nondoweled sections 

Shoulder type—tied PCC* – – – – ↓ – Tied PCC better than AC* 

shoulders 

Widened lanes ↓ – – ↑ – – Reduce pavement stresses 

Reinforcement—type – – ↓ – – ↑ JRCP* (steel >0.17%) 

 —quantity – – ↑ – – – JRCP (steel <0.10%) 

Coarse aggregate—large size ↓ – ↓ – – – – 

*AC – asphalt concrete, AGG – aggregate, ATB – asphalt-treated base, JRCP – jointed reinforced concrete pavement, 

PCC – portland cement concrete 

 

The arrows indicate the conditions that cause the distresses to increase or decrease, and the dash implies 

that there is no influence. Cells with an “x” indicate that no trend could be concluded or there was not 

enough data. This reference also examined European and Chilean concrete pavements to learn how 

pavements in the United States can be improved. In Europe, the four modernity categories expected to 

increase pavement performance are nonerodible base courses, positive pavement drainage, strengthened 

structure (dowel bars and CRCP), and the optimization of material use (wider lanes and trapezoidal cross 

section). Only 25 percent of U.S. pavements incorporate two or more of these features. 
21 

Yu, H.T., Smith, K.D., Darter, M.I., Jiang, J., and Khazanovich, L., Performance of Concrete 

Pavements, Volume III: Improving Concrete Pavement Performance, FHWA–RD–95–111, FHWA, 

McLean, VA, June 1998. 

This reference develops models that predict joint faulting, slab cracking, joint spalling, pavement 

serviceability, and pavement roughness. Three hundred pavements were used to formulate these 

empirical models, and most of the pavements are located in the Upper Midwest, have carried 10 million 

18-kip equivalent single axle loads (ESALs) and are 10 to 15 years old. The majority of the JPCP 

pavements are in the wet-freeze climatic zone and have nonstabilized bases. Trends are given for the 

distresses as a function of traffic, dowel bearing stress, drainage, annual precipitation, freezing index, 

dowel bar size, joint spacing, and stabilized bases. The distresses investigated in this report are faulting 

for doweled and nondoweled pavements, transverse cracking, transverse joint spalling, and roughness. 

Guidelines are developed that recommend the preferred pavement design for minimal pavement distress. 

Titus-Glover, L., Owusu-Antwi, E B., Hoener, T., and Darter, M.I., Design and Construction of PCC 

Pavements Volume II: Design Features and Practices that Influence Performance of Pavements, 

FHWA–RD–98–127, FHWA, McLean, VA, October 1998. 

This report uses canonical discriminant analysis to assess how design factors affect the performance of 

JPCP. The pavement distress analysis is performed for the four climatic regions of wet-freeze, wet-no 

freeze, dry-freeze and dry-no freeze. The distresses that are analyzed are faulting with and without 

dowels, transverse cracking, and pavement roughness. A summary table showing the influence of longterm factors and design parameters on pavement transverse cracking is shown in table 2. The pavements 

are subdivided into slabs that are less than 254 millimeters (mm) thick and those that are more than 254 

mm thick. The arrows indicate the conditions that cause transverse cracking to increase or decrease, and 

“N/A” implies that these factors had no influence. A dash means that no trend could be concluded or that 

there was not enough data. 

Table 2. Summary of factors affecting transverse cracking in JPCP. 

Transverse Cracking <25.4 cm >25.4 cm 

*DF *DNF *

WF *WNF DF DNF WF WNF

Freezing index (>277 °C days) ↑ ↑ ↑ ↑ N/A N/A N/A N/A 

Annual average precipitation (>1 m) ↑ ↑ ↑ ↑ – – – – 

Subgrade type (coarse) ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

Subgrade k value (>41 kPa/mm) – ↑ ↑ ↑ – – ↑ ↑

Subgrade k value (<41 kPa/mm) – – – – – – – – 

Joint spacing (>4.6 m) ↑ ↑ ↑ ↑ N/A N/A N/A N/A 

Joint spacing (<4.6 m) – – – – – – – – 

Base type (granular) – – – – – – – – 

Base type (stabilized) ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

28 day MOR (>4.5 MPa) – – – – ↑ ↑ ↑ ↑

28 day MOR (<4.5 MPa) ↑ ↑ ↑ ↑ N/A N/A N/A N/A 

Paver type (slip form) ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

Paver type (side form) – – – – – – – – 

Transverse joint form method (saw) ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

Transverse joint form method 

(plastic) 

– – – – – – – – 

*DF – dry freeze, DNF – dry-no freeze, WF – wet freeze, WNF – wet-no freeze 
22 

 

 Sensitivity Analyses for Selected Pavement Distresses, SHRP–P–393, Strategic Highway Research 

Program, National Research Council, Washington, DC, 1994. 

This reference provides models for predicting JPCP distresses, namely joint faulting in doweled and 

nondoweled pavements, transverse cracking, joint spalling, and roughness of doweled and nondoweled 

JPCP. The models are based on mechanistic and empirical concepts, and a fatigue analysis is used to 

predict distress formation. A sensitivity analysis is completed for each model, and trends are given 

showing how the input affects the distress magnitude. Several limitations of these models are apparent. 

Only a limited number of pavement sections were used to develop these models, so they should not be 

used to extrapolate to other pavements. Likewise, the data from all four climatic regions is lumped 

together. The researchers rank input parameters to show the parameters’ importance in influencing the 

performance of PCC pavements. The first parameter is age, followed by traffic loading, slab thickness, 

modulus of subgrade reaction (k-value), precipitation, percent steel tied with joint spacing, edge support 

tied with freeze-thaw cycles, and subgrade type. 

Smith, K.D., Peshkin, D.G., Darter, M.I. and Mueller, A.L., Performance of Jointed Concrete 

Pavements, Volume III—Summary of Research Findings, FHWA–RD–89–138, FHWA, McLean, VA, 

November 1990. 

This reference assesses how design features influence the behavior of 95 pavements. Trends show how 

each design parameter influences pavement distresses. Limitations of these models are the limited 

database used to develop them and their inability to account for construction-related distresses. The 

models were developed empirically, and because pavement performance is highly variable, these models 

should be used only on the pavements for which they were developed. 

Titus-Glover, L., Owusu-Antwi, E.B., and Darter, M.I., Design and Construction of PCC Pavements, 

Volume III: Improved PCC Performance Models, FHWA–RD–98–113, FHWA, McLean, VA, January 

1999. 

This research report gives a history of JPCP distress model development, and lists the prediction 

equations. The mechanisms behind faulting, spalling, transverse cracking, corner breaks, and roughness 

are discussed. A mechanistic-empirical basis is used to develop these equations. The empirical data is 

extracted from the Long-Term Pavement Performance (LTPP) Program database. The regression 

equations were developed using multiple linear regression, nonlinear regression techniques, and the 

Statistical Package for Social Sciences. To develop the transverse and corner cracking models, a linear 

fracture mechanics approach is used in conjunction with the fatigue damage approach. To develop the 

spalling model, the spall stress is calculated using a mechanistic model. It is a function of traffic, 

environment, incompressibles in the joint, and the concrete properties. The IRI model depends on the 

initial pavement IRI, traffic loading, and pavement aging. 

Darter, M.I., Becker, J.M., Snyder, M.B., and Smith, R.E., Portland Cement Concrete Pavement 

Evaluation System: COPES, National Cooperative Highway Research Program (NCHRP)–277, 

National Cooperative Highway Research Program, September 1985. 

A total of 418 sections were used to develop regression models for predicting JPCP performance. Design 

factors, material/soil factors, climatic factors, and maintenance-related factors were examined in 

developing the model. Several recommendations were to use stabilized bases, PCC shoulders, increased 

subgrade k modulus, increased concrete modulus of rupture, larger dowels, and increased slab thickness. 
23 

Perera, R.W., Byrum, C. and Kohn, S.D., Investigation of Development of Pavement Roughness, 

FHWA–RD–97–147, FHWA, McLean, VA, May 1998. 

Roughness models were developed using data taken from the LTPP databases. A model was formulated 

for each climatic region, and for doweled and nondoweled pavements. Correlation methods were used to 

find the most influential parameters affecting pavement distresses. 

Hansen, W., Jensen, E.A., Mohr, P., Jensen, K., Pane, I., and Mohamed, A., The Effects of Higher 

Strength and Associated Concrete Properties on Pavement Performance, Volume I—Final Technical 

Report, The University of Michigan, Department of Civil and Environmental Engineering, July 2000. 

This report subdivides pavement variables into six sections: environmental, design, concrete, subbase, 

traffic loading, and distress factors. It examines how each one influences pavement behavior. The 

distresses investigated are joint faulting, joint spalling, transverse cracking, and corner breaks. Focus is 

placed on examining how specific concrete properties influence the distresses. Table 3 shows how 

flexural strength impacts joint spalling, transverse cracking, and corner breaks, but not joint faulting. 

Table 3. Influence of concrete properties on JPCP pavement distresses. 

PCC Properties Joint 

Faulting 

Joint 

Spalling 

Transverse 

Cracking 

Corner 

Breaks 

PCC flexural strength – X X X 

PCC compressive strength X – – – 

PCC elastic modulus X X X – 

CTE X – X – 

PCC shrinkage X – – – 

PCC fracture energy – – X X 

PCC permeability – X – – 

PCC air void system – X – – 

Reactive aggregate – X – – 

This meets one of the study objectives: to determine the concrete properties that contribute to exceptional 

long-term pavement performance. The key properties with regard to pavement distress are concrete 

flexural strength, elastic modulus, CTE, and fracture energy. Fracture properties of the concrete are 

important with regard to transverse cracking and corner breaks. 

A.3.3.1 JPCP Faulting 

Faulting often is reported to be caused by the erosion of subbase material from under the approach side of 

the slab, and its deposition under the leave side. When the slab deflects on the leave side, material is 

pushed toward the approach slab due to hydraulic action. When the approach slab is loaded by the 

passing wheel, the material is pushed back to the leave side. The fines accumulate under the leave slab. 

Over time, there is a difference in the vertical profile of the approach and leave sides of the pavement; this 

is termed faulting. Erosion of the subbase is due to shear stresses induced by water at the joint. In the 

following section, several references are summarized that relate to pavement faulting. 
24 

Ksaibati, K. and Staigle, R., “Faulting Performance Modeling for Undoweled Plain Concrete 

Pavements,” Transportation Research Record 1482, TRB, pp. 1–6, Washington, DC, 1995. 

Faulting of nondoweled JPCP in Wyoming is modeled using an empirical regression model. Wyoming is 

part of the dry-freeze region of the United States. Factors incorporated into the faulting regression 

equation are environmental factors, average joint width, edge support, subgrade soil classification, traffic 

loads, and the presence of positive drainage. 

Bendana, L.J. and Yang, W.-S., “Rehabilitation Procedures for Faulted Rigid Pavement,” 

Transportation Research Record 1388, TRB, pp. 200–210, Washington, DC, 1993. 

Initially, faulting is found to increase linearly with age. When the fault distance is greater than 1.6 mm, 

faulting increases nonlinearly. Faulting is caused primarily by traffic loading. Faulting is very difficult to 

correct after it has occurred. Severe faulting has been found on New York State highways, and 

remediation efforts are needed. Two rehabilitation methods used were to pump grout under the slab and 

to grind the pavement surface. If the grout is not installed evenly, or if there is too much grout or too little 

grout, it is possible that the JCP will blowout or crack due to uneven subbase. Installing load transfer 

devices is the most effective way to reduce faulting in JPCP. 

Bustos, M., de Solminhac, H.E., Darter, M.I., Caroca, A., and Covarrubias, J.P., “Calibration of 

Performance Models for Jointed Concrete Pavements Using Long-Term Pavement Performance 

Database,” Transportation Research Record 1629, TRB, pp. 108–116, Washington, DC, 1998. 

Faulting data found in the LTPP database is analyzed for JPCP pavements. Calibration factors are 

presented based on the climatic region. It is found that faulting in the dry-no freeze sections is the lowest 

of all the regions. 

Ioannides, A.M., Lee, Y. and Darter, M.I., “Control of Faulting through Joint Load Transfer 

Design,” Transportation Research Record 1286, TRB, pp. 49–56, Washington, DC, 1990. 

A mechanistic-empirical faulting model is developed for JPCP with dowels. The major influencing factor 

is the bearing stress at the dowel-concrete interface, which is determined mechanistically. It is a function 

of the modulus of dowel support, joint width, wheel load, load transfer efficiency (LTE) (assumed to be 

45 percent), dowel stiffness, dowel moment of inertia, critical dowel distribution factors, and relative 

stiffness of the dowel-concrete system. This model uses both Westergaard and Timoshenko theory. A 

concern is how close the dowels must be to the joint to provide effective load transfer. In addition, an 

equation for the faulting of nondoweled pavements is given where the load transfer is provided by 

aggregate interlock. 

Hansen, E.C., Johannesen, R., and Armaghani, J.M., “Field Effects of Water Pumping Beneath 

Concrete Pavement Slabs,” Journal of Transportation Engineering, Vol. 117, No. 6, November–

December 1991. 

This reference investigates water pressures and velocities due to pumping under slabs. Traffic produces 

high pressure under the approach slab and suction under the leave slab. Frictional erosion generates 

loose, fine material. Water flow at the joint is generally in the opposite direction of the traffic. Pumping 

is more severe under pavements with upward thermal curling. 
25 

Van Wijk, A J. and Lovell, C.W., “Prediction of Subbase Erosion Caused By Pavement Pumping,” 

Transportation Research Record 1099, TRB, pp. 45–57, Washington, DC, 1985. 

This paper lists erosion tests of subbase material, such as the rotational shear device, the brush test, the 

jetting test, and the vibrating table. The rotational shear device can be used to investigate the erosion of 

clay and stabilized materials. Noncohesive materials cannot be tested with it. The jetting test is used for 

noncohesive materials. The brush test is primarily used for stabilized materials. The most commonly 

used subbases in the United States are portland cement stabilized, crushed stone, dense graded, asphalt 

concrete, sand, and asphalt stabilized subbases. The climatic conditions at the pavement location 

determine the performance of the pavement layers, especially its temperature and moisture content. 

Regression equations are given that relate erosion to variables such as pavement age and portland cement 

content. Materials that resist erosive shear stresses of 50 Pa or greater should not erode for the life of the 

pavement. Materials that erode for a shear stress between 25 and 50 Pa should have low erosion and 

those that erode at a shear stress less than 25 Pa should have high erosion. 

LTPP Data Analysis: Frequently Asked Questions About Joint Faulting with Answers from LTPP, 

LTPP Tech Brief, FHWA–RD–97–101, FHWA, McLean, VA, 1997. 

The LTPP database was mined to determine the site conditions and pavement design features that affect 

transverse joint faulting. Dowels are the most effective means of controlling joint faulting. Larger 

dowels reduce the amount of faulting because of the reduced dowel-concrete bearing stress. Increasing 

pavement drainage reduces faulting; this is more effective for nondoweled pavements than for doweled 

pavements. Short joint spacing and widened slabs also reduce faulting. 

A.3.3.2 JPCP Transverse Cracking—Midslab 

Cracking in JPCP pavements reduces their long-term performance. An annotated bibliography follows of 

references that discuss pavement design features and their relation to transverse cracking. 

Bustos, M., de Solminhac, H.E., Darter, M.I., Caroca, A., and Covarrubias, J.P., “Calibration of 

Performance Models for Jointed Concrete Pavements Using Long-Term Pavement Performance 

Database,” Transportation Research Record 1629, TRB, pp. 108–116, Washington, DC, 1998. 

The LTPP database is used to develop correlation factors between JPCP pavement distress and climatic 

conditions at the pavement location. To do so, several pavement sections in the database are disregarded, 

such as those without a subgrade k-value. This decreases the reliability of the transverse cracking model. 

However, this study finds that transverse cracking depends on climatic conditions. The least severe 

cracking is found in the dry-no freeze zone, while the most severe is in the wet-no freeze region. These 

correlations are not obvious, but this may be because cracking is not heavily dependent on environment, 

as faulting is, for example. 

Moody, E.D., “Transverse Cracking Distress in Long-Term Pavement Performance Jointed Concrete 

Pavement Sections,” Transportation Research Record 1629, TRB, pp. 6–12, Washington, DC, 1998. 

The mechanisms that cause midslab transverse cracking are divided into three sections. The primary ones 

are due to pure bending stresses, curling stresses, and subgrade friction. The secondary transverse 

cracking mechanisms (at the joint) are due to joint saw cutting timing, loss of load transfer, and locked 

transverse joints due to dowel bar corrosion or misalignment. These transverse cracks near the joint 

should not be considered when calibrating the midslab cracking model. The third mechanism causing 

transverse cracking is related to drying shrinkage. Drying shrinkage cracks do not penetrate the entire 
26 

pavement thickness. Correlations also are found between traffic loading and transverse cracking. No 

section with fewer than 600,000 ESALs had transverse cracks. Transverse cracks increased due to 

increased traffic, increased monthly temperature changes, and the use of cement-treated bases (increased 

curling and warping stresses). Transverse cracking decreases with thicker pavements and stronger 

concrete (tensile strength). 

Frabizzio, M.A. and Buch, N.J., “Investigation of Design Parameters Affecting Transverse Cracking 

in Jointed Concrete Pavements (JCPs): A Field Study,” paper presented at the TRB 78th Annual 

Meeting, Washington, DC, 1999. 

This paper investigates several design features that influence the formation of transverse cracks in 

pavements. This is a synthesis of experimental data; no theoretical model is developed. Aggregate 

interlock across joints is studied using volumetric surface texture (VST) testing. VST measures the 

roughness of the crack surface. VST shows that the crack propagating through aggregate results in a 

smoother crack surface (and therefore lower aggregate interlock) than does the crack that propagates 

around the aggregate (high aggregate interlock). This implies that a poor aggregate-cement bond has 

improved load transfer at the joint due to aggregate interlock. Four parameters commonly are used to 

quantify the efficiency of the load transfer across the joint for the doweled and nondoweled pavements. 

They are the deflection load transfer, the transferred load efficiency, the total load transferred from loaded 

side to unloaded side, and the aggregate interlock shear stiffness per unit length of crack. Also, it is 

shown that aggregate type influences the number of transverse cracks in the JPCP. Pavements reinforced 

with recycled aggregate have more transverse cracks than do those with good quality aggregate. Shoulder 

type also influences transverse cracking in the pavements, depending on type of aggregate used. Other 

causes of transverse cracking are plastic and drying shrinkage cracks, fatigue cracking, and induced 

frictional stresses due to expansion and contraction of the slabs. An increase in temperature causes the 

slabs to expand and the joint to close if the LTE is between 30 to 50 percent. If it is 90 percent, then 

increased temperature does not affect the LTE. 

A.3.3.3 JPCP Spalling 

Spalling of concrete pavements typically has been studied qualitatively. Researchers present possible 

causes of spalling based on pavement condition surveys. The majority of the models that have been 

developed to predict spalling are empirical in nature. They often relate rainfall, evaporation rate, and 

other factors to spalling. An annotated bibliography of spalling references is given below. 

Senadheera, S.P. and Zollinger, D.G., “Framework for Incorporation of Spalling in Design of 

Concrete Pavements,” Transportation Research Record 1449, TRB, pp. 114–122, Washington, DC, 

1994. 

This reference reviews the majority of prior research on spalling, especially on CRCP. The most 

important factors that affect the rate of spalling are rainfall, coarse aggregate type, and subbase type. 

Spalling is a two-step process. First, a horizontal delamination crack forms in the pavement. Then 

fatigue damage accumulates due to traffic and temperature-induced strains, and the concrete spalls. Two 

forms of spalling have been seen in pavements—a deep spall caused by the popout of an aggregate 

particle, and a shallow spall due to the horizontal delamination of the concrete. The long-term 

performance curve for spalling has an ‘S’ shape and can be modeled using the Weibull probability 

distribution function. 
27 

McCullough, B.F. and Dossey, T., “Considerations for High-Performance Concrete Paving: 

Recommendations from 20 Years of Field Experience in Texas,” Transportation Research Record 

1684, TRB, pp. 17–24, 1999. 

This reference deals primarily with CRCP, but also discusses spalling. Factors that significantly 

influence spalling are surface moisture evaporation at the time of placement and ambient temperatures 

above 0 °C. To prevent spalling, the amount of water that evaporates from the surface of the pavement 

must be minimized. High evaporation rates drive delamination cracking deeper into the pavement after 

construction. The traffic later causes the vertical fracture plane to intersect with the horizontal 

delamination plane, and the concrete breaks out to form a spall. Wet cotton mats are efficient at reducing 

surface evaporation, as are plastic sheeting, double membrane curing, and single membrane curing. 

Constant monitoring of surface evaporation is suggested during concrete construction. 

Rollings, R.S., “Joint Spalling in Newly Constructed Concrete Pavement,” Journal of Performance of 

Constructed Facilities, pp. 137–144, August 1998. 

A review of spalling work is presented in this paper. Qualitative studies have been performed that list 

potential causes of spalling. On airport pavements, it appears that poor workmanship is the major cause 

of spalling. Other possible causes of spalling are listed, such as poor concrete properties, freeze-thaw 

cycles, poor consolidation and finishing of the concrete, poor repair of the pavement edges, and 

inadequate curing. 

Bustos, M., de Solminhac, H.E., Darter, M.I., Caroca, A., and Covarrubias, J.P., “Calibration of 

Performance Models for Jointed Concrete Pavements Using Long-Term Pavement Performance 

Database,” Transportation Research Record 1629, TRB, pp. 108–116, Washington, DC, 1998. 

In this paper, JPCP distress models were calibrated using LTPP data. Adjustment factors are made to 

predict JPCP distresses for each region of the United States. Researchers found that a wet climate 

prevents spalling better than does a dry climate. This agrees with the hypothesis that increased 

evaporation causes horizontal delamination, a forerunner of spalling. 

A.4 CRCP LITERATURE REVIEW 

During task B of this project, a literature review of references on CRCP early-age behavior was 

accomplished. From this effort, a number of references have been compiled and models identified 

describing the early-age behavior of CRCP. 

This section briefly summarizes the primary references identified, including candidate models and useful 

information on CRCP early-age behavior. 

McCullough, B.F, Abou-Ayyash, A., Hudson, W.R. and Randall, J.P., “Design of Continuously 

Reinforced Concrete Pavements for Highways,” Research Project NCHRP 1–15, Center for Highway 

Research, The University of Texas at Austin, Austin, TX, August 1975. 

This document provides some history of CRCP use. To establish optimum CRCP design specifications, it 

is necessary to understand the major influences controlling the mechanistic behavior of CRCP at early 

ages. This work is one of the first studies that attempts to correlate the primary factors influencing CRCP 

behavior to predict theses factors’ effects on pavement performance. Based on the findings of that work, 

a mechanistic design procedure was developed that takes into account the early-age behavior of the 

pavement. This mechanistic design method proved that the crack spacing and crack width could be 
28 

properly controlled to fall within certain limits to minimize undesirable conditions. Major factors 

influencing crack spacing and crack width are explained. A crack spacing between 1.5 and 2.4 m is 

considered effective in minimizing distress occurrence. Also, it is concluded that crack width should be 

limited to no more than 0.6 mm to minimize steel corrosion. The limiting criteria for crack spacing and 

crack width is based on the performance of CRC pavements in several highways nationwide and 

laboratory tests. Primary factors that were found to influence CRCP performance include: 

• Concrete strength: It was found that concrete tensile strength plays an important roll in the 

development of spalling. For pavements with a concrete tensile strength less than 2756 kPa, 

a significant increase in spalling is observed. 

• Crack spacing distribution and crack width: It was found that the larger the crack spacing, 

the larger the crack widths, resulting in loss of load transfer. On the other hand, for small 

crack spacings, load deflections tend to increase, contributing to the development of stresses 

that can lead to punchouts. 

• Coarse aggregate type: The coarse aggregate type, and in particular its angularity, seem to 

have an important effect on spalling development. Since siliceous river gravel (SRG) tends 

to be more roundly shaped, it tends to have a lack of bond with the paste. Crushed aggregate 

tends to have a better bond strength at the aggregate-paste interface, and therefore, fewer 

spalling problems. 

Palmer, R.P., Olsen, M.P.J., and Lytton, R.L., “TTICRCP—A Mechanistic Model for the Prediction 

of Stresses, Strains, and Displacements in Continuously Reinforced Concrete Pavements,” Research 

Report 371–2F, Texas Transportation Institute, The Texas A&M University System, College Station, 

TX, 1988. 

This study improves on behavior prediction models CRCP–1, CRCP–2, and CRCP–3 by better modeling 

bond stress distribution and stress-slip prediction. The TTICRCP software program developed under this 

study has the objective of better characterizing the behavior of CRCP pavements using a more 

sophisticated, mechanistic-based approach. The model includes the means to better simulate the 

interaction between the steel reinforcement and the concrete. During its development, numerous 

derivations were made based on engineering mechanics and energy concepts. The result was a system of 

linear, second-order ordinary differential equations describing the complex behavior of the CRCP system. 

The solution to this system of equations is conducted using a combination of matrix and iterative solution 

schemes. This program was developed as an analysis routine with the crack spacing as an input rather 

than an output, as opposed to the CRCP–8 program. In addition, it has not been fully validated and is 

subject to further modification. However, initial review of the model has demonstrated that it can better 

predict the crack widths due to the improved characterization of the slip zone between the steel and the 

concrete. Therefore, this program shows promise as a possible improvement to the CRCP–8 modeling 

system. This report also provides a literature review on bond-stress and stress-slip relationships. 

Won, M., Hankins, K., and McCullough, B. F., “Mechanistic Analysis of Continuously Reinforced 

Concrete Pavements Considering Material Characteristics, Variability, and Fatigue,” Research 

Report 1169–2, Center for Transportation Research, The University of Texas at Austin, Austin, TX, 

March 1991. 

This is one of the main references for the CRCP–8 program. Although it describes the CRCP–5 program, 

no major improvements to the software have been made after this study. This reference briefly describes 

the purpose of transverse steel and why the States do not commonly use it. It also describes the factors 

affecting transverse cracking in CRCP. The primary purpose of this study is to provide enhanced bond 

stress/slip relationships for the University of Texas at Austin Center for Transportation Research (CTR) 
29 

software program CRCP series. It describes a stochastic method (Monte Carlo) to account for the effect 

of the variability of materials on CRCP performance variability. The report concludes that variability of 

steel amount, size, and depth, subbase friction, environmental conditions, slab thickness, CTE, and drying 

shrinkage are small compared to the variability of tensile strength. Therefore, the report concentrates on 

the variability of concrete tensile strength as the most significant factors affecting crack spacing. It is 

assumed that concrete tensile strength has a normal distribution. It is considered that the coefficient of 

variation (CV) of tensile strength is close to 20 percent, based on the above references. A mechanistic 

model to predict punchout distress is also presented, taking into account wheel loads and previously 

predicted crack spacing distribution. The subroutine in CRCP–8 that predicts punchouts is based on a 

mechanistic-empirical model. During the study, a number of ILLISLAB FEM runs for CRCP of different 

thicknesses and crack spacings were run. The effect of aggregate interlock and longitudinal steel on load 

transfer at cracks was ignored during stress calculations. The results of this analysis were used to fit a 

regression model predicting transverse tensile stress from thickness and crack spacing. Fatigue is then 

incorporated in this analysis to predict punchout development. 

Zollinger, D.G., Buch, N., Xin, D., and Soares, J., “Performance of CRC Pavements Volume 6—CRC 

Pavement Design, Construction, and Performance,” FHWA–RD–97–151, FHWA, McLean, VA, 

1997. 

This reference presents the FHWA CRCP punchout model. In this work, new predictive models for the 

behavior and performance of CRCP were developed. Although an explicit punchout prediction model 

was not included in this reference, several derivations were proposed to improve the prediction of the loss 

of load transfer across a crack, which is intuitively one of the key factors in punchout prediction. The 

basic framework of the proposed model includes a more mechanistic-based approach to characterizing the 

change in stress due to load transfer. The load transfer is comprised of a combination of aggregate 

interlock, base support, and reinforcement interaction. The study found that accurately characterizing the 

load transfer due to aggregate interlock could significantly improve the overall distress prediction. The 

LTE was found to be a function of aggregate interlock, support stiffness, and radius of relative stiffness. 

This reference also provides guidelines for designing and constructing CRCP. It also extensively 

describes the factors affecting cracking and describes punchout distress mechanisms. A thickness design 

procedure for CRCP is presented based on crack spacing, LTE, and fatigue cracking concepts. In this 

procedure, shear stresses at transverse cracks and curling and warping due to traffic and environmental 

loads are investigated to predict punchouts. A methodology to take into account design reliability is 

presented. The authors also present construction methods to improve CRCP crack patterns. Based on 

experimental test sections, the document concludes that surface crack initiation is more effective than 

interior crack initiation. From previous recommendations of crack spacing from 1.5 to 2.4 m, it 

demonstrates results of studies recommending spacings of 0.9 m as a minimum, warning about crack 

spacings less than 0.9 m. To minimize spalling at cracks, the maximum crack spacing is limited to 1.8 to 

2.7 m. 

Kim, S.-M., Won, M.C., and McCullough, B.F., “Development of a Finite-Element Program for 

Continuously Reinforced Concrete Pavements,” Research Report 1758–1F, Center for 

Transportation Research, The University of Texas at Austin, Austin, TX, November 1997. 

This report describes the CRCPFEM model, developed under a Texas DOT (TxDOT) effort with the 

objective of developing a more mechanistic-based model to predict the various responses in CRCP. The 

CRCPFEM model is a two-dimensional, plane-strain finite-element program developed using a 

sophisticated set of submodels to predict the behavior of the CRCP due to shrinkage, creep, temperature 

change, and slab-base restraint. Although the validation of the current version of the software is not 

extensive, it does show promise as a candidate model for this effort. If selected, further validation of this 

model can be performed. The ability for this model to account for relaxation creep makes it a worthy 
30 

candidate for incorporation into the proposed system. This effect, modeled in HIPERPAV, is quite 

significant for JPCP. The ability to model this important phenomenon is critical to the accuracy of the 

early-age prediction. Parametric studies were performed in this study to evaluate the effect of factors 

influencing CRCP responses. Further investigation of an accurate bond slip relationship is recommended. 

Suh, Y.C., Hankins K., and McCullough, B.F., “Early-Age Behavior of Continuously Reinforced 

Concrete Pavement and Calibration of the Failure Prediction Model in the CRCP–7 Program,” 

Research Report 1244–3, Center for Transportation Research, The University of Texas at Austin, 

Austin, TX, March 1992. 

The main purpose of this study was to calibrate the failure (punchout distress) prediction model in the 

CRCP program. The calibration is based on data from the Texas CRCP database. The report also 

presents the results of test sections constructed in Houston, TX, to monitor the early-age behavior in 

CRCP. The effect of different factors such as concrete properties, aggregate type, steel content, concrete 

curing temperature, and time of day of construction was investigated, among other factors. Condition 

surveys were performed to monitor cracking patterns and slab movements. This report may provide 

some ideas for future instrumentation of CRCP sections. The model was validated for only two aggregate 

types: limestone and siliceous river gravel. 

McCullough, B.F., Ma, J.C.M., and Noble, C.S., “Limiting Criteria for the Design of CRCP,” 

Research Report 177–17, Center for Transportation Research, The University of Texas at Austin, 

Austin, TX, August 1979. 

This reference provides limiting criteria for the design of CRCP. Factors considered include crack 

spacing, crack width, and maximum steel stresses. The limiting criteria are a function of the target 

pavement distresses (punchouts, spalling, steel corrosion, and steel permanent deformation). This study 

also recommends fatigue relationships to be used in the design procedure for CRCP. It also provides 

information on the CTE of various steel types. 

McCullough, B.F. and Rasmussen, R.O., “Fast Track Paving: Concrete Temperature Control and 

Traffic Opening Criteria for Bonded Concrete Overlays: Task G, Volume 1: Final Report,” Federal 

Highway Administration Report, FHWA–RD–98–167, Washington, DC, 1999. 

This research demonstrates the importance of early-age behavior on the long-term performance of JPCP 

and bonded concrete overlays. The authors mention that a number of factors influence early-age 

behavior, and these can be placed into four different categories: pavement design, materials and mix 

design, environment, and construction operations. This approach is believed to be applicable to any type 

of concrete pavement. 

“Continuously Reinforced Concrete Pavement,” National Cooperative Highway Research Program, 

Synthesis of Highway Practice No. 16, Highway Research Board, 1973. 

This document describes current CRCP construction practices. It provides a table with the primary 

factors affecting crack spacing and some guidelines for design and construction of CRCP. The authors 

emphasize the need for good subgrade support and warn about the practice of designing for less thickness 

than that required for JCP. They also warn about using wire fabric as reinforcement. The guidelines limit 

the maximum crack width to 0.5 mm and limit the steel percentage to not less than 0.7 percent where high 

temperature drops and deicing chemicals are used. The document warns about steel strengths greater than 

60 ksi that may lead to wide cracks and loss of aggregate interlock, and questions the use of transverse 

steel. 
31 

Tayabji, S.D., Selezneva, O., Jiang, Y.J., “Preliminary Evaluation of LTPP Continuously Reinforced 

Concrete Pavement Test Sections,” FHWA–RD–99–086, FHWA, July 1999. 

In this reference, an attempt is made to find initial correlations of factors collected on General Pavement 

Studies (GPS) sections GPS–5 from the LTPP database to long-term CRCP performance. No definitive 

correlations were found with the available data. The study concludes that additional data, including earlyage information, is required for good correlations of factors influencing pavement performance. 

Lee, Ying-Haur, Darter, M. I., “Development of Performance Prediction Models for Illinois 

Continuously Reinforced Concrete Pavements.” Transportation Research Record 1505, TRB, 

pp. 75–84, Washington, DC, 1995. 

In this study, a failure prediction model based on regression techniques was developed. The Illinois 

Pavement Feedback System database was used for this purpose. The model is limited to a small range of 

steel content (0.60 to 0.62 percent) and slab thickness (203–229 m). According to this study, crack 

spacing had no effect on pavement performance. 

McCullough, B.F., Hudson, W.R., and Noble, C.S., “Summary and Recommendations for the 

Implementation of Rigid Pavement Design, Construction, and Rehabilitation Techniques,” Research 

Report 177–22F, Center for Transportation Research, The University of Texas at Austin, Austin, TX, 

March 1981. 

This reference presents a supplementary CRCP design procedure for thickness, subbase, and steel 

reinforcement for TxDOT. Most of this material is based on the AASHTO Pavement Design Guide. 

Won, M., McCullough, B.F., and Hudson, W.R., “Evaluation of Proposed Texas State Department of 

Highways and Public Transportation (SDHPT) Design Standards for CRCP,” Research Report 472–

1, Center for Transportation Research, The University of Texas at Austin, Austin, TX, April 1988. 

The TxDOT design standards for CRCP are evaluated, taking in consideration the variability in pavement 

response due to different aggregate types using the software program CRCP. 

Won, M., Hankins, K., and McCullough, B.F., “A Twenty-Four Year Performance Review of 

Concrete Pavement Sections Made with Siliceous and Lightweight Coarse Aggregates,” Research 

Report 472–3, Center for Transportation Research, The University of Texas at Austin, Austin, TX, 

April 1989. 

This study investigates the effect of design variables on long-term pavement performance of experimental 

test sections constructed in Houston, TX. Variables studied include percent steel, crack spacing, and 

aggregate type. The findings from that study indicated that lightweight aggregate performed better than 

sections constructed with standard SRG aggregate. Condition surveys and structural capacity studies 

were performed to observe the performance of the pavement sections at different ages. Crack spacing for 

the test sections was preformed, however this crack spacing was reduced with time. Preforming was 

found to be beneficial, because it reduces spalling and punchouts. Intermediate cracking was reduced. 

Weissman, A.J., McCullough, B.F., and Hudson, W.R., “Development of Pavement Performance 

Models for Continuously Reinforced Concrete Pavements in Texas,” Research Report 472–7F, 

Center for Transportation Research, The University of Texas at Austin, Austin, TX, August 1989. 

Performance prediction models for CRCP are developed with the use of the Texas CRCP database. A 

distress index is used to describe the CRCP deterioration as a function of punchouts and patches. The 
32 

validity of the model is believed to be to limited, and therefore is not recommended for general practical 

use. 

Aslam, M.F., Carrasquillo, L.R., and McCullough, B.F., “Design Recommendations for Steel 

Reinforcement of CRCP,” Research Report 422–2, Center for Transportation Research, The 

University of Texas at Austin, Austin, TX, November 1987. 

A procedure for comparing the effects of aggregate type on the requirements for steel reinforcement is 

developed. Lab testing of mixes with limestone and SRG aggregates are tested to determine concrete 

properties for those aggregate types. The CRCP–4 program is used to develop steel design methods 

based on the differences in concrete properties for both aggregate types. 

Wei, C., McCullough, B.F., Hudson, W.R., and Hankins, K., “Development of Load Transfer 

Coefficients for Use with the AASHTO Guide for Design of Rigid Pavements Based on Field 

Measurements,” Research Report 1169–3, Center for Transportation Research, The University of 

Texas at Austin, Austin, TX, February 1992. 

This report provides procedures to measure load transfer at joints and cracks for CRCP. 

Otero, M.A., McCullough, B.F., and Hankins, K., “Monitoring of Siliceous River Gravel and 

Limestone Continuously Reinforced Concrete Pavement Test Sections in Houston 2 Years After 

Placement, and Development of a Crack Width Model for the CRCP–7 Program,” Research Report 

1244–4, Center for Transportation Research, The University of Texas at Austin, Austin, TX, March 

1992. 

A model for predicting crack width for CRCP is developed based on experimental sections in Houston, 

TX. The principal variables having an effect on crack width are identified. 

McCullough, B.F., Zollinger, D.G., and Allison, B.T., “Preliminary Research Findings on the Effect 

of Coarse Aggregate on the Performance of Portland Cement Concrete Paving,” Research Report 

1244–5, Center for Transportation Research, The University of Texas at Austin, Austin, TX, 

October 1993. 

This report provides concrete properties of mixes made with various coarse aggregates. It summarizes 

findings of research reports 1244–1 to 1244–4 and describes an experiment to evaluate different curing 

techniques, saw cutting techniques, and skewed transverse steel on crack width, crack spacing, and 

concrete strength. In addition, it provides background on the development of different versions of the 

CRCP program. A description of drying shrinkage and moisture models also are provided. 

McCullough, B.F. and Rivero-Vallejo, F., “Drying Shrinkage and Temperature Drop Stresses in 

Jointed Reinforced Concrete Pavement,” Research Report 177–1, Center for Transportation 

Research, The University of Texas at Austin, Austin, TX, August 1975. 

This is a research report for JRCP–1, a tool to predict the behavior of JRCP, which can be used to predict 

the behavior of CRCP steel in the transverse direction. 
33 

Strauss, J.P., McCullough, B.F., and Hudson, W.R., “Continuously Reinforced Concrete Pavement: 

Structural Performance and Design/Construction Variables,” Research Report 177–7, Center for 

Transportation Research, The University of Texas at Austin, Austin, TX, May 1977. 

Probabilistic models are used to predict pavement performance based on several factors. Models for load 

transfer through steel reinforcement and aggregate interlock are developed. The report describes a 1977 

condition survey of CRCP pavements in Texas. 

McCullough, B.F. and Ma, J., “CRCP–2, An Improved Computer Program for the Analysis of 

Continuously Reinforced Concrete Pavements,” Research Report 177–9, Center for Transportation 

Research, The University of Texas at Austin, Austin, TX, August 1977. 

This report presents modifications made to the CRCP–1 program to account for wheel load stresses to 

predict crack spacing, to modify the steel-stress model to cover conditions in which the development 

length for bond exceeds one-half the crack spacing, and to account for the increase in strength after 28 

days for analysis of minimum temperature drop. 

McCullough, B.F. and Strauss, J.P., “A Performance Survey of Continuously Reinforced Concrete 

Pavements in Texas,” Research Report 21–1F, Center for Transportation Research, The University 

of Texas at Austin, Austin, TX, November 1974. 

A method for performing condition surveys of CRCP is discussed. A distress index for evaluation of 

CRCP is developed. 

Zollinger, D. and Barenberg, E., “Continuously Reinforced Pavements: Punchouts and Other 

Distresses and Implications for Design,” Project IHR–518, Illinois Cooperative Highway Research 

Program, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, March 1990. 

This report describes the factors affecting CRC pavement cracking behavior. It also provides an analysis 

of factors affecting punchout distress. The authors describe previous steel instrumentation efforts and 

provide mechanistic modeling for prediction of punchout distress, including load transfer mechanisms, 

shear, spalling on the transverse crack, and transverse bending analysis. Most of this research is also 

presented in FHWA publication FHWA–RD–97–151. 

Wimsatt, A.W., McCullough, B.F., and Burns, N.H., “Methods of Analyzing and Factors Influencing 

Frictional Effects of Subbases,” Research Report 459–2F, Center for Transportation Research, The 

University of Texas at Austin, Austin, TX, November 1987. 

This report provides information on pushoff test procedures and typical friction values. 

Chia, W.S., McCullough, B.F., and Burns, N.H., “Field Evaluation of Subbase Friction 

Characteristics,” Research Report 401–5, Center for Transportation Research, The University of 

Texas at Austin, Austin, TX, September 1986. 

This report provides information on pushoff test procedures and typical friction values for various 

subbase types and bond breakers. 
34 

Haque, M., Zaman, M., and Soltani, A., “Cracking Characteristics of Model CRC Pavements,” TRB 

77th Annual Meeting, Washington, DC, January 11–15, 1998. 

The authors investigate the effect of steel reinforcement (rebar spacing) on crack spacing behavior of 

CRCP using numerical methods and small-scale laboratory experiments. They also evaluate the effect of 

skewed reinforcement. 

Nishizawa, T., Shimeno, S., Komatsubara, A., and Koyanagawa, M., “Study on Thermal Stresses in 

Continuously Reinforced Concrete Pavement,” paper presented at the TRB 77th Annual Meeting, 

Washington, DC, 1998. 

The authors investigate development of thermal stresses in CRCP. Test sections are instrumented in the 

field, and measured stresses are compared to calculated stresses. 

Mains, M.R., “Measurement of the Distribution of Tensile and Bond Stresses Along Reinforcing 

Bars,” ACI Journal, Vol. 48, pp. 225–252, November 1951. 

This article investigates bond stresses and bond slip of reinforced concrete. It includes experimentation 

with strain gauges to measure bond stress and bond slip. Bond stress and bond slip relationships are 

discussed. 

Nilson, A.H., “Internal Measurement of Bond Slip,” ACI Journal, Vol. 69, pp. 439–441, July 1972. 

Similar to the above article, this reference also investigates bond stresses and bond slip of reinforced 

concrete. 

Haque, M., Zaman, M., and Soltani, A., “Cracking Characteristics of Model CRC Pavements,” TRB 

77th Annual Meeting, Washington, DC, January 11–15, 1998. 

This article investigates the effect of rebar spacing on crack spacing and crack patterns with the use of 

small-scale laboratory experiments and numerical simulation. 

Zollinger, D. and Senadheera, S., “Spalling of Continuously Reinforced Concrete Pavements,” 

Journal of Transportation Engineering, Vol. 120, No. 3, May–June 1994. 

This article presents a mechanistic flat-bottom spalling model for CRCP/JCP. 

Kerr, A.D., “Assessment of Concrete Pavement Blowups,” Journal of Transportation Engineering, 

Vol. 123, No. 2, pp. 123–131, March–April 1997. 

A mechanistic model for analysis of concrete pavement blowups is described. The model can be used for 

both CRCP and JCP. 

Nishizawa, T., Shimeno, S., Komatsubara, A., and Koyanagawa, M., “Study on Thermal Stresses in 

Continuously Reinforced Concrete Pavement,” Transportation Research Record 1629, pp. 99–107, 

November 1998. 

A procedure for estimating the thermal stresses in CRCP is proposed. Measured thermal strains are 

compared with FEM-predicted strains and divided into axial, curling, and nonlinear components. 
35 

Kim, S.-M., Won, M., and McCullough, F., “Three-Dimensional Analysis of Continuously Reinforced 

Concrete Pavements,” TRB 79th Annual Meeting, Washington, DC, January 9–13, 2000. 

A three-dimensional analysis of CRCP is performed and compared with results of two-dimensional 

analysis performed with CRCPFEM. Nonlinear bond slip relationships are studied in this analysis. 

Primary conclusions include the effect of transverse steel amount and location on crack width; significant 

stresses at the edge on the farthest transverse steel bar from the crack; significant effect of nonlinear 

bond-slip relationships on concrete stress; analysis with the two-dimensional model gives a good 

approximation, compared to the three-dimensional model. 

Schindler, A., Henry, P., and McCullough, F., “Validation of CRCP–8 to Predict Long-Term 

Transverse Crack Spacing Distributions in Continuously Reinforced Concrete Pavements,” TRB 79th 

Annual Meeting, Washington, DC, January 9–13, 2000. 

This paper describes validation efforts of the CRCP–8 program to predict crack spacing for experimental 

sections in Houston, TX. 

McCullough, F., Zollinger, D., and Dossey, T., “Evaluation of the Performance of Texas Pavements 

Made with Different Coarse Aggregates” Research Report 3925–1, Center for Transportation 

Research, The University of Texas at Austin, Austin, TX, September 1998. 

This report presents information on crack spacing and crack width of CRCP for sections monitored in 

Houston, TX, and Hempstead, TX. It presents the results of an effort to validate CRCP–8 crack spacing 

and presents information on delamination spalling and the thermal coefficient of concrete. The report 

describes practices of CRCP design and construction for the State of Texas over a 23-year period. 

37 

APPENDIX B MODELS SELECTED FOR INCORPORATION 

INTO HIPERPAV II 

Chapter 3 of the first volume in this report series documents the models that were identified and the ones 

selected for incorporation into HIPERPAV II. This appendix provides a detailed description of the 

models that were selected. The models incorporated are divided into: 

• General early-age behavior models. 

• JPCP performance models. 

• CRCP early-age behavior models. 

• Models used in the Concrete Optimization, Management, Engineering, and Testing 

(COMET) module. 

• Model used in the dowel analysis module. 

B.1 GENERAL EARLY-AGE BEHAVIOR MODELS 

A number of potential model enhancements were identified over the course of previous implementation 

efforts of HIPERPAV I. In this section, early-age behavior models incorporated into HIPERPAV II are 

presented. These models are divided in the following categories: 

• PCC hydration models. 

• PCC temperature prediction models. 

• Drying shrinkage models. 

• Relaxation-creep models. 

• Nonlinear thermal gradient model. 

• Nonlinear axial restraint model. 

All other models in HIPERPAV I that were kept in HIPERPAV II are not presented here because they 

have been defined previously elsewhere.(1,2,3) Figure 1 shows a schematic of the enhancements made to 

the early-age behavior models in HIPERPAV II. 

B.1.1 PCC Hydration Models 

During the development of this project, the project team closely followed recent developments by the 

University of Texas at Austin on characterization of cement and admixtures. Based on these findings, 

improved models capable of predicting the hydration development of concrete mixes based on chemical 

composition of the cement and mix proportions were incorporated in HIPERPAV II. These models are 

based on a database of U.S. cements as shown in table 4.(4) 
38 

STRESS STRENGTH

Axial Stress Axial Stress

Axial Restraint * Axial Restraint *

Shrinkage Stress * Shrinkage Stress *

Curling Stress

Vertical Restraint * Vertical Restraint *

Critical Stress Models Critical Stress Models

Coefficient of Coefficient of

Thermal Expansion Thermal Expansion

Relaxation-Creep 

Model 

Tensile Strength Tensile Strength

Mechanical Properties Mechanical Properties

Temperature Prediction * Temperature Prediction *

PCC Hydration * PCC Hydration *

Environmental Effects * Environmental Effects *

STRESS STRENGTH

Axial Stress Axial Stress

Axial Restraint * Axial Restraint *

Shrinkage Stress * Shrinkage Stress *

Curling Stress

Vertical Restraint * Vertical Restraint *

Critical Stress Models Critical Stress Models

Coefficient of Coefficient of

Thermal Expansion Thermal Expansion

Relaxation-Creep 

Model 

Tensile Strength Tensile Strength

Mechanical Properties Mechanical Properties

Temperature Prediction * Temperature Prediction *

PCC Hydration * PCC Hydration *

Environmental Effects * Environmental Effects *

Temperature Prediction * Temperature Prediction *

PCC Hydration * PCC Hydration *

Environmental Effects * Environmental Effects *

* Improved models 

Figure 1. HIPERPAV early-age behavior framework showing improved models in HIPERPAV II. 

Table 4. Data sources and their use in the development of the hydration models.(4)

Portland Cement Association 

(PCA)—Lerch and Ford(5)

Schindler(4)

Materials Characterization Phase 

Calibration 

Data Sources 

U.S. cements sources. 

Eight Type I, five Type II, three 

Type III, three Type IV, one 

Type V. 

All cement properties known. 

Well known and recognized data 

source. 

Conduction calorimeter heat of 

solution tests. 

Texas materials. 

Three different cement sources. 

Different fineness. 

Class C and F fly ash. 

GGBF slag. 

All cement properties known. 

Semiadiabatic testing. 

Kjellsen et al.(6) Schindler(4)

Field Work Phase 

Validation 

Data Sources 

Swedish cements source. 

All cement properties known. 

Type I cement. 

Nonevaporable water 

calculations. 

Texas materials. 

Typical paving mixtures. 

Different cements. 

All cement properties known. 

Field data collected. 

Mixed usage of Class C and F fly 

ash, and GGBF slag. 

Semiadiabatic testing. 
39 

The model used in HIPERPAV II to predict the hydration of a cementitious mixture is presented below. 

The degree of hydration is defined as in equation 1: 

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝

⎛

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

= ⋅ −

β

τ

α α

e

e u t

(t ) exp

 (1) 

where, 

 α(te) = degree of hydration at equivalent age, te, 

te = equivalent age at reference temperature (21.1°C), (hours (h)), 

αu = ultimate degree of hydration, 

 τ = hydration time parameter (h), and 

 β = hydration shape parameter. 

The rate of heat liberation is defined as in equation 2: 

( ) ⎥

⎦

⎤ ⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ − + ⋅ ⋅ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⋅ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = ⋅ ⋅

r c

e

e e

h e u c R T T

E

t

t t

Q t H C

273

1

273

1 ( ) α exp

τ β β

 (2) 

where, 

 Qh(te) = rate of heat liberation at equivalent age, te, (Watts per cubed meter (W/m3

)), 

E = AE (J/mol), 

R = universal gas constant (8.3144 J/mol/°C), 

Tc = nodal PCC temperature (°C), 

Tr = reference PCC temperature (°C), 

Cc = cementitious materials content (kilogram per cubed meter (kg/m3

)), and 

Hu = total heat of hydration of cementitious materials at 100 percent hydration 

(J/kg), defined as in equation 3: 

Hu Hcem pcem pSLAG pFA CaO pFA = ⋅ + ⋅ + ⋅ ⋅ 461 1800 − (3) 

where, 

 pSLAG = slag mass ratio to total cementitious content, 

 pFA = fly ash mass ratio to total cementitious content, 

 pFA-CaO = fly ash CaO mass ratio to total fly ash content, 

 pcem = cement mass ratio to total cementitious content, and 

 Hcem = heat of hydration of the cement, defined by Bogue as in equation 4:(7) 

Hcem pC S pC S pC A pC AF pSO pFreeCa pMgO =500⋅ + 260⋅ + 866⋅ + 420⋅ + 624⋅ +1186⋅ + 850⋅ 3 2 3 4 3 (4) 
40 

where, 

 pi = mass ratio of i-th component to total cement content. 

To predict the ultimate degree of hydration, and time and shape parameters in equation 1, multivariate 

nonlinear regression models were developed as shown in equations 5, 6, and 7: 

66.78 exp(2.187 9.50 ) 0.154 0.401 0.804 0.758pC3A pC3S Blaine pSO3 pSLAG pFA pFA−CaO

− − − − τ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + ⋅ ⋅ (5) 

181.4 exp( 0.647 ) 0.146 0.227 0.535 0.558

3 3 3 pC A pC S Blaine pSO pSLAG = ⋅ ⋅ ⋅ ⋅ ⋅ − ⋅ − β (6) 

0.50 0.30 1.0

0.194 /

1.031 /

+ ⋅ + ⋅ ≤

+

⋅ u = pFA pSLAG

w cm

w cm

α

 (7) 

where, 

 PC3A = weight ratio of tricalcium aluminate to total cement content, 

PC3S = weight ratio of tricalcium silicate to total cement content, 

PSO3 = sulfate weight ratio to total cement content, 

 Blaine = Blaine value, specific surface area of cement (m2

/kg), and 

 w/cm = the water-cementitious material ratio. 

The above models are based on heat of solution, conduction calorimeter, and semiadiabatic calorimeter 

test data. From a multivariate analysis, an r2 of 0.988 was achieved. The isothermal curing temperature 

considered for the test data was 21.1 °C. 

The recommended AE model (E) is defined in equation 8: 

0.30 0.25 0.35

3 4 E 22,100 f p p Blaine E C A C AF = ⋅ ⋅ ⋅ ⋅ (8) 

where, 

 PC3A = weight ratio of tricalcium aluminate Bogue compound, 

PC4AF = weight ratio of tetracalcium aluminoferrite Bogue compound, 

 Blaine = Blaine value, specific surface area of cement (m2

 /kg), and 

 fE = AE modification factor for mineral admixtures, defined as in equation 9: 

SLAG

FA CaO

E FA p

p f p ⎟ + ⋅ ⎠

⎞ ⎜

⎝

⎛ = − ⋅ ⋅ − − 0.40

0.40

1 1.05 1

 (9) 

where, 

 pFA = mass ratio replacement of the fly ash, 

 pFACaO = mass ratio of the CaO content in the fly ash, and 

 pSLAG = mass ratio replacement of the GGBF slag. 
41 

A sensitivity analysis of the effect of temperature on the hydration of the cement was performed over a 

temperature range of 4.4 to 40.6 °C. From this analysis, the AE (E) model was found to be independent 

of curing temperature. 

The limitations and assumptions to the model above presented are: 

• Due to the nature of the model, its validity holds only for the range within it was calibrated. 

The model should not be used to predict hydration outside this range, as listed in tables 5 and 

6. Table 5 presents the range of chemical and physical cement properties. Table 6 presents 

the range of mixture proportions and mineral admixtures properties. 

• The effects of chemical admixtures are currently not considered in the hydration model. 

• The model assumes that the same interaction between the mineral admixtures and the base 

cement source applies to all combinations of cement and mineral admixtures. 

Table 5. Range of cement properties used to calibrate the hydration model. 

 C3S 

(%) 

C2S 

(%) 

C3A 

(%) 

C4AF 

(%) 

SO3

(%) 

Free CaO 

(%) 

MgO 

(%) 

Alkalis Blaine 

(m2

/kg) 

Average 52.5 20.8 8.4 9.3 2.6 1.4 1.8 0.6 373.7 

Min 20.0 9.3 3.5 5.5 1.2 0.1 0.6 0.2 289.1 

Max 64.5 55.0 13.2 16.6 4.4 2.9 4.0 1.1 579.5 

*

 Equivalent alkalis as per ASTM C150 = Na2O + 0.658 K2O 

Table 6. Range of mixture proportions and mineral admixtures properties used for model 

calibration. 

 w/cm Fly Ash 

CaO 

(%) 

Fly Ash 

SiO2

(%) 

Fly Ash 

Alkalis 

(%) 

Fly Ash 

Dosage (%)

GGBF Slag 

Dosage (%) 

Average 0.42 – – – – – 

Min 0.36 10.8 35.8 0.3 0.0 0.0 

Max 0.54 24.3 54.1 1.4 45.0 50.0 

Based on the empirical results reported, the degree of hydration at initial and final set are determined as 

shown in equations 10 and 11: 

ASTM C 403 initial set: αi = 0.15 (w/cm)

 (10) 

ASTM C 403 final set: αf = 0.26 (w/cm)

 (11) 

where, 

 αi = degree of hydration at initial set, 

αf = degree of hydration at final set, and 

w/cm = water-cementitious materials ratio. 
42 

With equations 10 and 11, the equivalent age at setting can directly be determined from the hydration 

parameters. The closed form solutions are shown in equations 12 and 13. They are very useful, since the 

setting time at the reference temperature can now be obtained. 

ASTM C 403 initial set: 

β

α

τ

1

0.14 / ln

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎥

⎦

⎤ ⎢

⎣

⎡ ⋅ = ⋅ −

u

ei

w cm

t

 (12) 

ASTM C 403 final set: 

β

α

τ

1

0.26 / ln

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎥

⎦

⎤ ⎢

⎣

⎡ ⋅ = ⋅ −

u

ef

w cm

t

 (13) 

where, 

 tei = equivalent age at initial set (hours), 

 tef = equivalent age at final set (hours), and 

 w/cm = water-cementitious materials ratio. 

It is customary to express the effect of chemical admixtures on cement mixes in terms of their effect on 

initial set at different temperatures. With equation 12, the initial set time for the cement without a 

chemical admixture can be estimated. Next, the effect recommend by the supplier of the chemical 

admixture can be added to the calculated initial set time. In the case of retarders, the initial set time will 

be increased, and with accelerators, the initial set time will be reduced. With this approach, it is assumed 

that only the hydration time parameter is affected by the chemical admixtures. Then, the new hydration 

time parameter can be determined that includes the use of chemical admixtures, as shown in equation 14: 

ASTM C 403 initial set: 

( ) β

α

τ

1

0.14 / ln ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎥

⎦

⎤ ⎢

⎣

⎡ ⋅ = + Δ ⋅ −

u

chem ei chem

w cm

t

 (14) 

where, 

τchem = adjusted hydration time parameter to include the effect of retarder or 

accelerators (h), 

tei = equivalent age at initial set of the cement without chemical admixtures 

determined from equation 12 (h), and 

Δchem = effect of mineral admixture on the time at initial set at the reference 

temperature (21.1 °C), where positive retards and negative accelerates. 

B.1.2 HIPERPAV II Finite-Difference Temperature Model 

In HIPERPAV I, a one-dimensional finite-element technique was used, but this procedure has proven to 

be a computational burden, and may not be appropriate for the large number of time-steps involved in 
43 

long-term analyses. The finite-difference method is another numerical technique that is available to solve 

the transient heat transfer problem. In HIPERPAV II, the previous finite-element procedure for heat 

transfer analysis was replaced with a finite-difference method after extensive calibration and validation. 

The finite-difference model is used for both early-age and long-term predictions of concrete temperature. 

A description of this model follows: 

The basic equation of the heat transfer model with respect to distance, x, and time, t, can be written as 

shown in equation 15:(8) 

 

dt

dT Q c

dx

dT k

dx

d

H p ⎟ + = ⋅ ⋅ ⎠

⎞ ⎜

⎝

⎛ ⋅ ρ

 (15) 

where, 

 T = temperature (°C), 

ρ = density (kg/m3), 

cp = specific heat capacity (J/kg/°C), 

QH = generated heat per unit time and volume (W/m3

), and 

k = thermal conductivity (W/m/°C). 

With this approach, the concrete temperature can be evaluated at discrete times after placement. 

Boundary conditions have to be chosen to satisfy compatibility with field conditions. 

 

In concrete placed under field conditions, heat will be transferred to and from the surroundings, and the 

temperature development in the concrete structure is determined by the balance between heat generation 

in the concrete and heat exchange with the environment. The surroundings could either be an additional 

source of heat or at a lower temperature than the hydrating concrete. Heat transfer with the surroundings 

may take place in four basic ways: conduction, convection, irradiation, and solar absorption. Figure 2 

illustrates how each of these methods exchange heat in a pavement system. The evaporation of moisture 

from the pavement surface causes a change in phase, which reduces the surface temperature due to the 

withdrawal of latent heat of vaporization. The models that will be used to model each of the heat 

exchange mechanisms will now be discussed in more detail. Due to the scope of this project, the 

parameters were not determined through physical testing, but instead parameters were obtained from 

published research. Therefore, normal ranges found acceptable in previous calibration efforts of these 

models are used. 
44 

Hydrating Concrete

CONDUCTION

IRRADIATION

SOLAR ADSORPTION

Solar Radiation

sun

Base Layer

Hydrating Concrete

CONDUCTION

CONVECTION

Wind

IRRADIATION

SOLAR ADSORPTION

Solar Radiation

Sun and cloud cover

Base Layer

Subbase Layer

Hydrating Concrete

CONDUCTION

IRRADIATION

SOLAR ADSORPTION

Solar Radiation

sun

Base Layer

Hydrating Concrete

CONDUCTION

CONVECTION

Wind

IRRADIATION

SOLAR ADSORPTION

Solar Radiation

Sun and cloud cover

Base Layer

Subbase Layer

Figure 2. Heat transfer mechanisms between pavement and its surroundings. 

Appropriate values for all the thermal material properties involved must be selected for the system. New 

methods to model early-age thermal properties and boundary conditions also were investigated. 

B.1.2.1 Specific Heat 

The specific heat of a material can be defined as the ratio of the amount of heat required to raise a unit 

weight of a material 1 °C to the amount of heat required to raise the same weight of water by 1 °C. The 

International System (SI) units for specific heat are J/kg/oC, whereas the U.S. customary units are 

expressed in British Thermal Unites per pound per degrees Fahrenheit (BTU/lb/°F). Both the temperature 

of the concrete and the water content impact the specific heat of the mixture.(9,10)

Based on tests performed on hardening concrete, it is reported that the heat capacity is linear with the 

logarithm of time, which for common cement types is very similar to a linear decline with degree of 

hydration.(10,11) Test data shows a 13 percent decrease in specific heat of concrete during hardening.(11) 

The following model shown in equation 16 is used in HIPERPAV II, as it accounts for the effect of 

temperature and mix proportions, and also decreases the specific heat as the concrete hardens:(12) 

 

( (1 ) ) 1 p c cef c c a a w w c = ⋅ W ⋅α ⋅ c +W ⋅ −α ⋅ c +W ⋅ c +W ⋅ c

ρ (16) 

where, 

 cp = current specific heat of the concrete mixture (J/kg/oC), 

ρ = unit weight of concrete mixture (kg/m3), 

 Wc, Wa, Ww = amount by weight of cement, aggregate, and water (kg/m3

), 

 cc, ca, cw = specific heats of cement, aggregate, and water (J/kg/oC), 

 ccef = fictitious specific heat of the hydrated cement (J/kg/oC), determined as 

8.4 Tc + 339, where Tc is the current concrete temperature (oC), and 

α = degree of hydration. 
45 

 

Based on the literature reviewed, the following specific heat values are recommended for cement, 

aggregate, and water (table 7): 

Table 7. Typical specific heat values for concrete constituents. 

Material Specific Heat 

(J/kg/oC) Reference 

Cement 1140 (13) 

Water 4187 (9) 

Limestone/dolomite 910 (14) 

Sandstone 770 (14) 

Granite/gneiss 780 (14) 

Siliceous river gravel 770 (14) 

Basalt 900 (14) 

To evaluate the proposed specific heat model, a mix design typically used in pavement construction was 

used.(1) The mix design per cubic meter consisted of 380 kg cement, 154 kg water, and 1631 kg of coarse 

and fine aggregate, which provided a unit weight of 2224 kg/m3

. Figure 3 was developed based on the 

model shown in equation 16, and it may be concluded that it provides an adequate estimate of the specific 

heat as it fulfills the following requirements: 

• The calculated values are between the recommended range of 800 and 1200 J/kg/°C. 

• The specific heat decreases linearly with an increase in degree of hydration. 

• There is 8 to 14 percent difference in specific heat of the mature and hardened concrete. 

• The specific heat increases with an increase in concrete temperature. 

• It accounts for the effect of mixture constituents. 
46 

900

950

1000

1050

1100

1150

1200

0.00 0.25 0.50 0.75 1.00

Degree of Hydration

Specific Heat (J/kg/°C)

Tc = 5 °C

Tc = 20 °C

Tc = 35 °C

Series4

Series5

Series6

Siliceous River Gravel

Limestone

Figure 3. Concrete specific heat as influenced by the mixture constituents, temperature, and degree 

of hydration. 

B.1.2.2 Conduction 

Thermal conduction is defined as heat transport in a material by transfer of heat between portions of the 

material that are in direct contact with each other. In a pavement system, conduction occurs between the 

pavement layers, and between the surface of the concrete slab and the surface protection (insulation) used 

at early ages, such as water fogging, plastic sheets, blankets, and urethane foams. The governing equation 

for thermal conduction reveals that heat transfer is a function of the thermal conductivity, density, and 

specific heat of the materials in contact. 

Thermal conductivity of concrete (k) measures the ability of the concrete to transfer heat, and is defined 

as the ratio of the rate of heat flow to the temperature gradient.(9) The thermal conductivity is of great 

importance, since it determines the rate of penetration of heat into the concrete and hence the magnitude 

of temperature gradients and thermal stresses.(13) The SI units for thermal conductivity are W/m/oC, 

whereas the U.S. customary units are expressed in BTU/h/ft/°F. 

B.1.2.2.1 Heat Conduction of Concrete

It is reported that the water content, density, and temperature of the concrete may significantly influence 

the thermal conductivity.(9) The conductivity of ordinary concrete depends on its composition and 

especially the aggregate type used. Typical values proposed for the thermal conductivity of mature 

concrete are listed in table 8. 
47 

Table 8. Typical values of thermal conductivity of moist mature concrete.(9)

Moist Density of 

Concrete 

Thermal 

Aggregate Type Conductivity 

(kg/m3

) (W/m/oC) 

Quartzite 2350–2440 4.1–3.1 

Dolomite 2500 3.3 

Limestone 2450–2440 3.2–2.2 

Sandstone 2400–2130 2.9 

Granite 2420 2.6 

Basalt 2520–2350 2.0–1.9 

Thermal conductivity values, similar to the ones presented in table 8, are also recommended by ACI 

Committee 207.(15) In contrary to the values reported above, work performed at McGill University in 

Canada reports for normal strength concrete, thermal conductivity values of 1.723–1.740 W/m/oC for 

maturing concrete and values of 1.14–1.17 W/m/oC for hardened concrete.(10) These values are 

significantly lower than those listed in table 8. It was concluded that the average thermal conductivity of 

maturing concrete is 33 percent higher than that of the hardened concrete. This value is in agreement 

with that obtained by others, which showed a 21 percent decrease in thermal conductivity from the 

maturing state to the hardened state.(11)

From this information, assuming that the decline in this parameter is linear with the logarithm of time, 

which for common cement types is very similar to a linear decline with degree of hydration, a relationship 

that considers these initial and final values could be expressed as shown in equation 17: 

ki = k∞(1.33 – 0.33 ⋅ α) 

 (17) 

where, 

ki = current thermal conductivity of the concrete (W/m/oC), 

k∞ = thermal conductivity of mature concrete (W/m/oC), and 

α = degree of hydration. 

B.1.2.2.2 Conduction to Supporting Layers

The temperature and properties of the base underlying the concrete have a significant influence on the 

temperature development of the hardening concrete. Tables 9 and 10 present typical thermal 

characteristics of some commonly used base materials. 

Table 9. Thermal characteristics of various base materials.(16)

Density Thermal 

Base Material Conductivity 

(kg/m3

) (W/m/oC) 

Specific 

Heat 

(J/kg/oC) 

Gravel, dry 1703 0.52 838 

Gravel, moist 1898 2.42 1047 

Asphalt 2302 1.38 1047 
48 

Table 10. Thermal characteristics of various pavement materials.(17)

Base Material Density 

(kg/m3

) 

Unfrozen Thermal 

Conductivity 

(W/m/oC) 

Unfrozen Specific Heat 

(J/kg/oC) 

Asphalt concrete 2371 1.21 921 

Stabilized base 2339 3.32 1005 

Cohesive subgrade 2066 1.59 1214 

During the development of the ICM,(18) different values for the thermal conductivity and specific heat was 

determined based on the moisture condition of the soil and three different material conditions—unfrozen, 

freezing, and frozen. The soil moisture content has a great influence upon the thermal conductivity and 

heat capacity of the soil. In later reports on the development of the ICM, the values listed in table 11 

were recommended based on the AASHTO soil type classification. 

Table 11. Thermal characteristics of various soil materials.(17)

Soil Type Dry Density 

(kg/m3

) 

Dry Thermal 

Conductivity 

(W/m⋅oC) 

Specific Heat Capacity 

(J/kg⋅°C) 

Stabilized 1188 1.50 1047 

A–1 1188 0.90 712 

A–2 950 0.81 712 

A–3 1045 1.02 838 

A–4 856 1.02 712 

A–5 808 0.45 712 

A–6 856 0.60 712 

A–7 760 0.30 712 

B.1.2.2.3 Conduction to Surface Protection

Conduction further transpires between the surface coverings of the concrete slab commonly placed over 

during construction. These include insulation blankets, curing compound, plastic sheets, urethane foams, 

closed cell polystyrene foam, and many patented products. Insulation blankets often are used to provide a 

uniform temperature gradient, to prevent concrete freezing under cold weather conditions, and where 

opening requirements dictate very quick strength gain.(19) The use of blankets in cold weather conditions 

will increase the strength gain considerably, as some of the concrete heat generated during hydration is 

trapped, which allows concrete hydration at increased temperatures. It is also reported that when a period 

of less than 16 hours is required for early opening to traffic, the use of blankets become beneficial.(19) 

These blankets should be placed after the sawing operation and near the time the slab temperature begins 

its decent from the peak temperature. 

Other membranes and surface coverings are also commonly placed over the concrete during construction. 

These include curing compound, plastic sheets, urethane foams, closed cell polystyrene foams, and many 

other products. The steady state heat transfer to the surrounding, excluding any radiation, can be 

expressed as shown in equation 18:(20)

 
49 

q = h0 ⋅ (Ts – Ta) 

 (18) 

where, 

 q = heat flux (W/m2

), 

h0 = overall heat transfer coefficient (W/m2

/°C), 

Ts = surface temperature (°C), and 

Ta = air temperature (°C). 

Where more than one layer of insulation is used, the overall heat transfer coefficient can be calculated, 

which is a single coefficient that defines the thermal resistance of all the materials. The overall heat 

transfer coefficient can be calculated as shown in equation 19:(20)

 

1

2

2

1

1

0

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

= + + +

n

n

k

d

k

d

k

d h K

 (19) 

where, 

 h0 = overall heat transfer coefficient (W/m2

/°C), 

d1, d2, ... dn = thickness of n successive layers (m), and 

k1, k2, ... kn = thermal conductivity of n successive layers (W/m/oC). 

Table 12 contains some properties of various insulation materials that could be encountered during 

concrete construction operations. 

Table 12. Thermal characteristics of various insulation materials. 

Base Material 

Thermal 

Conductivity 

(W/m/oC) 

Typical 

Thickness 

(mm) 

Reference 

No cover 0 0 – 

Polyurethane foam 0.035 25 (21) 

Plastic sheet 0.043 0.1 (22) 

Water 2.168 Variable (22) 

Blankets: 

 Mineral fiber: ρ = 6.4–32 kg/m3 0.039 75 (22) 

 Textile organic fiber: 

 ρ = 12–24 kg/m3

 ρ = 24–48 kg/m3

0.043 

0.033 

25 

25 

(22) 

 Glass fibers: ρ = 16–32 kg/m3 0.055 25 (21) 

 Alumina fibers: ρ = 48–64 kg/m3 0.058 25 (21) 

 Cotton wool mats: ρ = 80 kg/m3 0.042 25 (20) 

 Mineral wool: 

 ρ = 151 kg/m3

 ρ = 316 kg/m3

0.039 

0.042 

50 

50 

(20) 

ρ = unit weight 
50 

B.1.2.3 Convection 

Thermal convection is the heat transferred from a surface to a gas (or fluid), where convection is the 

movement of a mass of gas (or liquid) due to the temperature difference, and physical contact of the gas 

(or liquid) is the actual method of heat transfer. Convection is, therefore the mechanism of heat transfer 

between the concrete surface and the environment, and as illustrated above in figure 2, includes the effect 

of wind and evaporation. For flat surfaces such as concrete pavements, the wind velocity across the 

concrete surface determines whether convection is forced or free. In the case of free convection, the 

transport of heat is the result of temperature gradients. In HIPERPAV II convective heat transfer is 

modeled through the use of equation 20:(22)

 

qc = hc ⋅ (Ts – Ta) 

 (20) 

where, 

 qc = heat transferred due to convection (W/m2

), 

hc = surface convection coefficient (W/m2

/°C), 

Ts = surface temperature (°C), and 

Ta = air temperature (°C). 

The rate of heat flow from a horizontal surface is controlled by the magnitude of the temperature 

difference, the speed of the air flow, and also the surface texture of the member. As heat is transferred 

from the warmer horizontal plate to the adjacent air, the air is heated, its density decreases, and it tends to 

rise. As the heated air rises, it is replaced by cooler air, which in turn is heated and rises; this is a 

continuous recurring process until the heat balance is eliminated. This complex phenomenon has been 

thoroughly investigated by numerous researches in the heat transfer field. From combinations of 

experimental work from Heilman and Langmuir, a model that is also used in ASTM C 680 is available for 

use on a smooth horizontal surface that is valid for both forced and free convection.(21,22,23) However, this 

model does not include any modification due to surface roughness, and it is recommended that the surface 

convection coefficient above be increased by 6 percent to account for this effect.(20) Therefore, the 

following model (shown in equation 21) was incorporated in HIPERPAV II: 

hc = ⋅C ⋅( ) ⋅( ) Ts + Ta + ⋅ Ts − Ta ⋅ + ⋅ w − 3.727 0.9 32 1 2.857 0.181 0.266

 (21) 

where, 

 hc = surface convection coefficient (W/m2

/°C), 

C = constant depending on the shape and heat flow condition, equal to 1.79 for 

horizontal plates warmer than air, or 0.89 for horizontal plates cooler than air, 

Ts = surface temperature (°C), 

Ta = air temperature (°C), and 

w = windspeed (m/s). 

In some programs that model the convection boundary conditions, it is common to use equations 22 and 

23 to determine the magnitude of the convection coefficient:(24,25,26)
51 

If w ≤ 5 m/s, then hc = 20 + 14⋅w

 (22) 

If w > 5 m/s, then hc = 25.6 ⋅ 0.78w

 (23) 

where, 

 hc = surface convection coefficient (kJ/m2

/h/°C), and 

 w = windspeed (m/s). 

These equations were obtained from experimental data for the flow of air at room temperature parallel to 

a smooth vertical copper plate.(20) The original equation presented by McAdams is very similar to 

equations 22 and 23, and after converted to similar units, is as shown in equations 24 and 25:(20)

If w ≤ 4.87 m/s, then hc = 20.24 + 14.08w

 (24) 

If w > 4.87 m/s, then hc = 25.82 ⋅ 0.78w

 (25) 

These equations do not incorporate the fact that the surface convection coefficient is influenced by the 

magnitude of the temperature difference, as the tests were all performed at room temperature (21 °C). 

McAdams acknowledged this relationship, and recommended that the windspeed in the above equations 

be modified by a multiplier to account for this effect.(20) Using this form of the convection equation 

(equations 22 and 23) is, therefore, more appropriate to determine the effect of convection on vertical 

elements such as beam webs or retaining walls. However, the multiplier to the windspeed must be 

incorporated when the air temperature is above room temperature, and the effect of a rough concrete 

surface as opposed to a smooth plate must be taken into account. Figure 4 compares the surface 

convection coefficient associated with a vertical (equations 22 and 23) and horizontal plate (equation 21) 

as presented in this section. Note that with a vertical plate there is a significant increase in the amount of 

heat transferred as the windspeed is increased above a value of 5 m/s. 
52 

0

20

40

60

80

0 5 10 15 20

Windspeed (meter/second)

Convection Coefficient (W/m2/°C)

Equation (21), Tc=30°C, Ta=20°C

Equation (21), Tc=30°C, Ta=25°C

Equations (22 and 23)

HIPERPAV

(Horizontal Surface)

(Vertical Surface)

Figure 4. Comparison of different convection coefficients as influenced by the windspeed. 

Because the heat transfer due to convection on the surface could occur simultaneously with the presence 

of surface insulations over the pavement top surface, the overall heat transfer coefficient that includes 

both these effects must be determined. The overall heat transfer coefficient can be calculated as shown in 

equation 26 (will all the parameters as defined elsewhere): 

1

2

2

1

1

0

1 −

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

= + + + +

n

n

c k

d

k

d

k

d

h

h K

 (26) 

In some cases, liquid-curing membranes, water fogging of the pavement surface, or other porous 

coverings are used. When evaporation of the water on the surface occurs, the energy associated with the 

phase change is the latent heat of vaporization. Evaporation occurs when liquid molecules near the 

surface experience collisions that increase their energy above that needed to overcome the surface binding 

energy. The energy required to restrain the evaporation must come from the internal energy of the liquid, 

which then must reduce in temperature. The amount of energy transferred through evaporative cooling 

can be determined in equation 27: 

 

qevap = –Er ⋅ hlat

 (27) 

where, 

 qevap = heat flux due to latent heat of vaporization (W/m2

), 

Er = evaporation rate (g/m2

/s), and 

hlat = latent heat of vaporization (W⋅s/g). 
53 

In metric units, the latent heat of vaporization is the quantity of heat, in joules, required to evaporate 1 

gram of water, and it varies with temperature.(22) The latent heat of vaporization can be defined as shown 

in equation 28:(22)

hlat = 2500 + 1.859⋅ Ta

 (28) 

where, 

 hlat = latent heat of vaporization (W⋅s/g), and 

 Ta = air temperature (°C). 

Where curing membranes and water fogging are used, the duration of latent heat development can be 

identified by determining the evaporation rate per unit area and by knowing the thickness of the applied 

membrane. Most States specify the curing compound application rate, and ASTM C309(27) recommends a 

rate of application of 5 m2/l if the rate of application is not specified. 

B.1.2.4 Solar Absorption 

Solar absorption is the flux absorbed by the pavement surface through exposure to the incoming sunrays. 

In HIPERPAV II, the following simplified equation for solar absorption (equation 29) is used: 

qs = βε ⋅ If ⋅ qsolar

 (29) 

where, 

 qs = solar absorption heat flux (W/m2

), 

βε = solar absorptivity, 

 If = intensity factor to account for angle of sun during a 24-hour day, and 

 qsolar = instantaneous solar radiation, (W/m2

) as defined in table 13. 

In HIPERPAV II, the solar radiation used is based on the 95 percentile value of solar radiation from 

historical records at any given weather station considered in the HIPERPAV II weather database. The 

solar radiation in the simulation varies with time of day, ranging from zero at sunrise and sunset to a peak 

value midday. 

In table 13, the solar radiation is a function of the cloud cover, and even with an overcast sky, some of the 

longer wavelengths can still penetrate the sky and be a source of heat. During nighttime, the solar 

radiation is negligible. The intensity of solar radiation (If) is assumed to follow a sinusoidal distribution, 

with the simplifying assumption that the highest solar radiation occurs at 5 p.m. 

The solar absorptivity of PCC is a function of the surface color, with typical values ranging from 0.5 to 

0.6. An ideal white body would have a value of 0.0, and an ideal black body would have a value of 1.0. 
54 

 Table 13. Typical peak solar radiation values used in HIPERPAV II.(1)

Sky Conditions Solar Radiation (W/m2

) 

Sunny 1000 

Partly cloudy 700 

Cloudy (overcast) 300 

B.1.2.5 Irradiation 

Irradiation is the reason that a frost occurs on a clear night even though the air temperature remains well 

above the freezing point. Irradiation heat transfer also affects the concrete surface, which is the heat 

transfer that is accomplished by electromagnetic waves between a surface and its surroundings. The 

Stefan-Boltzmann law is commonly used for this type of heat transfer, which is defined in equation 30:(20)

qr = ε⋅σ⋅ (Tc

4 – T∞

4) 

 (30) 

where, 

 qr = heat flux of heat emission from the surface (W/m2

), 

σ = Stefan-Boltzmann radiation constant (5.67×10-8 W/m2/°C4), 

ε = surface emissivity of concrete, 

Tc = concrete surface temperature, (°C), and 

 T∞ = surrounding air temperature, (°C). 

The surface emissivity is a function of the concrete’s surface color. An “idealized” black surface would 

have a value of 1.0. A value of 0.88 was selected for use in HIPERPAV II.(28) However, in the above 

equation, T∞ is the temperature of the surrounding environment, and this value cannot arbitrarily be 

assumed to be equal to the ambient temperature. This equation would be valid for use in enclosed spaces, 

but where long wave radiation toward the open sky is involved, using this equation requires an 

appropriate estimate of the effective surrounding air temperature in terms of the atmosphere’s ability to 

reflect and absorb the radiation. In figure 5, an idealized thermally black body with a surface temperature 

(Ts) equal to the air temperature is receiving and absorbing solar energy at a rate, qr. Because the plate is 

at the same temperature as the air, there will be no heat transfer through convection, but the plate will 

exhibit a radiation loss in the far infrared wavelength. The loss rate (R) is defined as the difference 

between the black body radiation (σ⋅Ts

4

) emitted by the surface and the incoming long wave atmospheric 

radiation (AR), which is striking the surface.(29) 
55 

Thermally Black Plate at Temperature Ts

ATMOSPHERIC 

RADIATION

Thermal Insulation

R = σ ⋅Ts

4-AR

AR

σ ⋅Ts

4

TOTAL SOLAR

RADIATION

qr

Thermally Black Plate at Temperature Ts

ATMOSPHERIC 

RADIATION

Thermal Insulation

R = σ ⋅Ts

4-AR

AR

σ ⋅Ts

4

TOTAL SOLAR

RADIATION

qr

Figure 5. Radiant energy exchanges between the sky and an exposed thermally black plate.(29)

Atmospheric radiation originates from gasses in the air. When radiation at the ground level is of concern, 

only water vapor and carbon dioxide are the main contributors, and water vapor is the most important.(29) 

Only the presence of these small gases prevents the atmosphere from being completely transparent in the 

far infrared. Therefore, to accurately model the radiation from the atmosphere to the surface, it is 

essential to determine the radiation expected from the gas mixture of water vapor and carbon dioxide. 

The fact that the composition, temperature, and pressure of these mixtures vary with height above ground 

level also must be considered. 

The emissivity of a particular radiating gas is a function of the number of molecules of the radiating gas 

in the column of air under investigation. At a given temperature, the number of molecules of the radiating 

gas is linearly proportional to the density-length product, mg ≡ pgLg, where pg is the density of the gas and 

Lg is the length of the gas column.(29) The total emissivity (εw) of a column of water vapor and 

nonradiating gas is primarily a function of the following: the density-length product (mw) of the water 

vapor, the partial pressure (Pw) of the water vapor, the total pressure (PT) of the mixture, and the 

temperature of the mixture (T).(29) However, the total emissivity is not strongly influenced by either the 

partial pressure of the water or the temperature of the mix. When carbon dioxide is added to the gas 

mixture, the radiative behavior of the gas column is only slightly changed. Based on the established work 

from Hottel and Egbert,(30) Bliss expressed the total emissivity of moist atmospheric air as a function of 

mw, and the ratio of carbon dioxide to water vapor concentrations at a total pressure of 1 atmosphere and a 

temperature of 20 °C, which can mathematically be presented in equation 31 as: 

( ) ( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⋅ − ⋅ − − ⋅ + ⋅ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ × = + +

− −

w

c

w w

w w

atm m m

m m ρ

ρ ε 0.185 exp 3.060 exp 1.8 1.7 50 0.2191 1.547 10 1.009

1

1.5

5

 (31) 

where, 

 εatm = total atmospheric emissivity (unitless), 

mw = density-length product of the water vapor (mw ≡ pgLg = g/cm2

), and 

 ρc /ρw = ratio of carbon dioxide density to water vapor density (unitless). 
56 

In equation 31, the first term accounts for the emissivity of water vapor (moist air), and the second term 

accounts for the added emissivity caused by the presence of carbon dioxide. Figure 6 shows the 

individual contribution of the water vapor and carbon dioxide to the calculated emissivity of moist air. 

Note that the presence of carbon dioxide adds a maximum of only 0.185 to the overall emissivity. This 

figure further shows the effect of water vapor in the air, on the atmospheric emissivity. As the 

concentration of water vapor becomes less (dry air) the atmospheric radiation (total emissivity) decreases. 

Figure 6. Emissivity of moist air at a total pressure of 1 atmosphere and a temperature of 20 °C. 

The nature of the earth’s atmosphere is that the pressure and temperature decreases with altitude, which, 

due to gas equilibrium principles, causes a change in the moisture condition of the body of gas. 

Therefore, to determine the total atmospheric emissivity, the earth’s atmosphere should be considered as 

several layers, all at different temperatures, pressures, and moisture conditions. The composition of the 

atmosphere varies significantly, but it varies with height in typical ways. It can be shown that the 

variation of pressure with height above ground level can be determined by equation 32:(29)

Pz = Pi ⋅ exp(-1.2 × 10-4⋅ z) 

 (32) 

where, 

 Pz = atmospheric pressure at height z (atm), 

Pi = atmospheric pressure at ground level (atm), and 

z = height above ground level (m). 

As the total pressure is decreased, the emissivity of the gas is decreased. Equation 31 provided the total 

atmospheric emissivity at a pressure of 1 atmosphere, and by determining an adjusted density-length 

0.0

0.2

0.4

0.6

0.8

1.0

0.0001 0.001 0.01 0.1 1 10

Water Vapor Density-Length Product (mw) (g/cm2)

Total Emissivity

ρc/ρw = 0.10

Water vapor

Correction due to the pressence of carbon dioxide

Mixture of water vapor and carbon dioxide
57 

product of the water vapor, the effect of different pressures on emissivity can be incorporated. The 

adjusted density-length product of the water vapor (m’w) can be determined as in equation 33:(29) 

m’w = mw ⋅ Pz / P0

 (33) 

where, 

 Pz = actual pressure of the moist air (atm), and 

P0 = pressure of known emissivity versus water vapor relationship (1 atm). 

The variation of temperature with height is less uniform, but it is reported that at heights above a few 

meters off the ground surface, it often obeys the following relationship in equation 34:(29)

Tz = Ti – 0.006 × z

 (34) 

where, 

 Tz = atmospheric temperature at height z (°C), 

Ti = atmospheric temperature at ground level (°C), and 

z = height above ground level (m). 

As the total energy of a moist air column changes with a change in temperature, a temperature correction 

must be applied to the calculated total atmospheric emissivity. The total energy radiated by a gas of 

specified water-vapor content is function of its temperature only, and is directly proportional to the fourth 

power of its absolute temperature.(29) The temperature adjustment factor (Tf), which can be multiplied to 

the emissivity determined at a temperature different than the actual condition, can be determined as in 

equation 35:(29) 

Tf = [(Ti + 273) / (T0 + 273)]4

 (35) 

where, 

 Ti = actual temperature of the moist air (°C), and 

T0 = assumed temperature during calculation of the emissivity (°C). 

The water vapor density is variable with height, and the total precipitable water contained below a certain 

height (z) can be determined with the following relationship in equation 36:(29)

( ) [ ] 6

6

0

1 exp 5.7 10

5.7 10 ' −

− − − ⋅ ×

× = ∫ z

p dm wi

z

w

(36) 

where, 

 ∫

z

dm w

0

' = total precipitable water contained below a height z (g/cm2

), 

pwi = water vapor density at ground level (g/cm2

), and 

z = height above ground level (m). 
58 

 

In HIPERPAV II, the climatic conditions are defined in terms of the relative humidity and the air 

temperature (dry-bulb temperature). Through the use of established gas relationships, the water vapor 

density can be determined. The water vapor saturation pressure for a given dry-bulb temperature can be 

determined as in equations 37 and 38:(22)

For dewpoint range of -100 to 0 °C: 

( ) () [ ] pws C TR C C TR C TR C TR C TR C TR ln 0.68 / 7 ln 4

6

3

5

2

1 2 3 4 = ⋅ + + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ (37) 

where, 

 pws = the water-vapor saturation pressure (atm), 

 TR = the dry-bulb temperature, (°R = °C *1.8 + 491.67), 

C1 = -10214.165, 

 C2 = -4.8932428, 

C3 = -0.0053765794, 

 C4 = -1.9202377 × 10-7, 

C5 = 3.5575832 × 10-10, 

 C6 = -9.0344688 × 10-14, and 

C7 = 4.1635019. 

For dewpoint range of 0 to 200 °C: 

( ) () [ ] pws C TR C C TR C TR C TR C TR ln 0.68 / 13 ln 3

12

2

8 9 10 11 = ⋅ + + ⋅ + ⋅ + ⋅ + ⋅ (38) 

where, 

 C8 = -10440.397, 

 C9 = -11.29465, 

C10 = -0.027022355, 

 C11 = -1.289036 × 10-5, 

C12 = -2.4780691 × 10-9, and 

 C13 = 6.5459673. 

After the water vapor saturation pressure is determined, the water vapor pressure of the moist air can be 

determined from the known relative humidity (RH), as shown in equation 39. 

pw = RH × pws

 (39) 

The information above provides all the information needed to determine the apparent atmospheric 

emissivity with the following variables: surface atmospheric pressure (atm), dry-bulb temperature (°C), 

relative humidity, and the ratio of carbon dioxide to water vapor. The atmosphere is divided into different 

layers, and by using a step-wise procedure, the emissivity can be accumulated from each layer. After the 

apparent emissivity (εapp) is determined, the intensity of atmospheric radiation (AR) can be determined in 

equation 40 (figure 5 above): 
59 

AR = εapp × σ ×Ta

4 (W/m2) 

 (40) 

Now with the intensity of atmospheric radiation determined, the apparent surrounding air temperature 

(T∞) can be solved from equation 41: 

T∞ = (AR / σ )

4 – 273 (°C) 

 (41) 

As the apparent surrounding air temperature is now determined, the Stefan-Boltzmann law can be used to 

determine the heat transfer by irradiation (equation 30). Figures 7 to 9 illustrate the sensitivity of the 

effective surrounding temperature to all the various input variables with the following parameters as 

baseline values for the analysis: atmospheric pressure = 750 millibars, dry-bulb temperature = 30 °C, 

relative humidity = 20 percent, ratio of carbon dioxide to water vapor = 1.0. Under the conditions 

investigated, there is a significant reduction in the apparent surrounding temperature associated with a 

decrease in total pressure and the relative humidity. A change in the carbon dioxide content seems to 

have a minimal impact on the apparent surrounding temperature, and a ratio of 0.1 should be sufficient for 

most conditions.(29)

-20

-10

0

10

20

30

40

0 10 20 30 40

Dry-bulb Temperature (°C)

Apparent Surrounding Temperature (°C)

Pz = 750 millibars

Pz = 1000 millibars

Pz = 500 millibars

Figure 7. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, 

atmospheric pressure. 
60 

-20

-10

0

10

20

30

40

0 10 20 30 40

Dry-bulb Temperature (°C)

Apparent Surrounding Temperature (°C)

RH = 20%

RH = 100%

RH = 60%

Figure 8. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, 

relative humidity. 

-20

-10

0

10

20

30

40

0 10 20 30 40

Dry-bulb Temperature (°C)

Apparent Surrounding Temperature (°C)

pc/pw = 1.0

pc/pw = 0.1

pc/pw = 0.5

Figure 9. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, 

ratio of carbon dioxide to water vapor. 

B.1.2.6 Prediction of Initial Pavement Temperature Profile 

Although the initial temperature of the mix and temperature of the subbase are required inputs in 

HIPERPAV II, the finite-difference temperature model used in HIPERPAV II requires as an input the 

complete temperature profile including depths beyond the subbase. For this purpose, HIPERPAV II uses 

a simple closed form solution for prediction of pavement temperatures.(31) The 24-hour periodic 

temperature, T, at a given depth, x, can be predicted as in equation 42:(31) 

( ) ) 12 sin( 2 2 C H

C

t x C arcTan

H C C

H e T T T

x C

M V + ⋅ − ⋅ −

+ +

⋅ = +

− ⋅ π

 (42) 
61 

where, 

 T = 24-hour periodic temperature of the mass, oC, 

 TM = mean effective air temperature, oC, 

 TV = maximum variation in temperature from the effective mean, oC, 

 t = time from beginning of cycle (one cycle = 24 h), 

 x = depth below surface, m, 

 H = h/k, where h is the surface convection coefficient, W/m2

/oC, and k is the 

conductivity, W/m2

/oC/m, and 

C = (0.131/c)

0.5, where diffusivity c = k/(sw), s is specific heat in J/kg/oC, and w is 

density in kg/m3

. 

As can be observed, the above model considers the climatic conditions and thermal properties of the 

materials for prediction of pavement temperature. To provide for temperature equilibrium with the 

environment, pavement temperatures are predicted for a total of 96 hours in advance up to the time of 

construction. 

B.1.3 Shrinkage 

HIPERPAV II has been updated to include the prediction of autogenous shrinkage as well as drying 

shrinkage. The chosen autogenous shrinkage model was developed by Jonasson and Hedlund.(32) 

Likewise, the drying shrinkage model in HIPERPAV II has been updated from the RILEM B3 model 

previously used in HIPERPAV I to the Baźant-Panula model.(33) Now, shrinkage modeling is subdivided 

into two cases, when the w/cm is less than 0.40, and when it is greater than or equal to 0.40. 

B.1.3.1 Autogenous Shrinkage and Drying Shrinkage for w/cm < 0.40 

Autogenous shrinkage is defined by the Japanese Committee on Autogenous Shrinkage as “The 

macroscopic volume reduction of cementitious materials when cement hydrates after initial setting. 

Autogenous shrinkage does not include the volume change due to loss or ingress of substances, 

temperature variation, the application of an external force, and restraint.”(34) (p. 54). The magnitude of 

autogenous shrinkage depends on the w/cm in the concrete. The lower the w/cm, the greater the 

importance of autogenous shrinkage, as compared to drying shrinkage. From a practical viewpoint, 

Aїtcin recommends that when w/cm < 0.40, autogenous shrinkage cannot be neglected.(34) For a w/cm of 

0.30, the autogenous shrinkage can represent 50 percent of the total shrinkage, with total shrinkage 

equaling drying shrinkage plus autogenous shrinkage. 

The shrinkage model selected for incorporation in HIPERPAV II was developed by Jonasson and 

Hedlund. In developing this mechanistic-empirical model, experimental test data for high-performance 

concrete (HPC) with a w/cm < 0.40 and 28-day compressive strength of equal to or greater than 80 MPa 

was used. The total shrinkage strain—autogenous shrinkage for the whole system plus drying shrinkage 

due to drying and wetting deformation at the surface—for the concrete’s cross section is expressed in 

equation 43 as:(32) 

εcs (t) = εcs0 (t) εcsd (t) < 0

 (43) 
62 

where, 

 t = time after casting (days), 

εcs (t) = total external shrinkage strain (×106 με), 

εcs0 (t) = autogenous shrinkage under sealed conditions (see equation 44), and 

εcsd (t) = additional strain due to drying/wetting caused by humidity change with the 

environment (see equation 45). 

Autogenous shrinkage is modeled as: 

εcs0 (t) = εs0∞ βs0(t)

 (44) 

where, 

βs0 (t) = time distribution of autogenous shrinkage (equation 45) and 

 εs0∞ = final value of autogenous shrinkage (equation 46). 

Autogenous shrinkage measurements were initiated 24 hours after casting. The authors state that, prior to 

24 hours, the concrete is plastic, but assume that the stresses and deformations begin after this time 

period. This expression for the time distribution of autogenous shrinkage starts at zero, 24 hours after 

casting. 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎥

⎦

⎤ ⎢

⎣

⎡

− = −

0.3

0

0 ( ) exp

start

s

s t t

t β t

 (45) 

where, 

 ts0 = 5 days (constant for HPC) and 

tstart = 1 day (start time of autogenous shrinkage). 

The time distribution of autogenous shrinkage is not a function of the concrete’s w/cm. Instead w/cm is 

incorporated into the ultimate autogenous shrinkage. It is expressed in the following empirical equation 

as: 

3

0 0.65 1.3 10−∞ ⎟⋅

⎠

⎞ ⎜

⎝

⎛ = − +

B

w s ε

 (46) 

where, 

 w = water content (kg/m3

) and 

B = cement content + silica fume content (kg/m3

). 

Drying shrinkage is a surface concept. The external humidity exchange occurs only in the outer shell of 

the structural member, called “surface layer drying.” The portion of the cross section affected by surface 

layer drying, αsd (figure 10), is assumed to be constant with time and is calculated using equation 47: 
63 

= ≤1

c

sd

sd A

ul

α

 (47) 

where, 

 u = perimeter of the cross section in contact with environmental humidity, 

Ac = cross section perpendicular to water flow, and 

lsd = typical length of surface for water exchange, given by equation 48: 

B

w

l

l sd ref

sd

−

=

0.5

,

 (48) 

where, 

 lsd,ref = 0.0045 m, the reference depth of surface layer drying for HPC. 

This term tends to infinity when the w/B ratio is 0.5. It can only be used when w/B < 0.50, which is one 

of the constraints of using this model. 

Figure 10. Surface layer zone subjected to drying shrinkage for a slip-formed pavement. 

There are two cases, when αsd = 1 and when αsd < 1, as shown for typical pavement cross sections, 

αsd < 1. However, for some cylinders, αsd = 1, for example, for cylinders with diameters of 100 mm and 

w/B = 0.32. 

Case I (equation 49): αsd = 1. 

εsd,all (t) = εsd,tot βsd (t) βsd,RH

(49) 

where, 

 εsd,all (t) = drying shrinkage (plus autogenous shrinkage) when the whole specimen is 

affected by drying, 

εsd,tot = final drying shrinkage (see equation 51), 

βsd,RH = coefficient depending on relative humidity (see equation 56), and 

βsd (t) = time development of drying shrinkage, expressed by equation 50: 

l

sd αsd
64 

0.5

( ) ⎥

⎦

⎤ ⎢

⎣

⎡

+ −

− =

sd s

s

sd t t t

t t β t

 (50) 

where, 

 t – ts = time after start of drying and wetting (days), 

ts = age of concrete at start of drying and wetting (≥ 1 day), and 

tsd = 200 days, time reflecting the typical rate of humidity exchange. 

This total shrinkage εsd,tot is the same order of magnitude for HPC as for normal strength concrete. The 

empirical relationship is: 

3

, 0.1 0.8 10− ⎟⋅

⎠

⎞ ⎜

⎝

⎛ = − − B

w

sd tot ε (51) 

Case II (equation 52): αsd < 1. 

When αsd is less than 1, a moisture exchange is taking place between the surface of the structural layer 

and the environment, and there is an inner part that is affected only by self-desiccation. Using a force 

balance and assuming that plane sections remain plane (equation 52), 

εcsd (t) = αsd εsd,all (t) 

(52) 

Combining with equation 49, equation 53 results, 

εcsd (t) = αsd εsd,tot βsd (t) βsd,RH

(53) 

setting equation 54, 

 sd sd sd ,tot ε =α ε ∞ (54) 

yields equation 55, 

εcsd (t) = εsd∞ βsd (t) βsd,RH

(55) 

where, 

 εcsd (t) = additional strain due to drying/wetting of the concrete with the environment, 

εsd∞ = final external strain due to drying shrinkage (see equation 54), 

βsd (t) = time development of drying shrinkage (see equation 50), and 

βsd,RH = coefficient depending on relative humidity (see equation 56). 
65 

To describe the shrinkage of HPC as a function of relative humidity: 

0

0

,

RH RH

RH RH

ref

sd RH

−

− β =

 (56) 

where, 

 RH = actual environmental relative humidity, 

RH0 = relative humidity at sealed conditions (80 percent for w/cm ≤ 0.4), and 

RHref = chosen relative humidity at a typical indoors environment (60 percent when 

w/cm ≤ 0.4). 

In addition, it has been found for normal strength concrete, and can be applied to HPC, that when the 

relative humidity is less than the reference relative humidity, it can be assumed that drying shrinkage is 

not affected by relative humidity, as seen in equation 57. 

sd RH RH RHref β , = 1 for ≤

 (57) 

The effect of changing the w/c on the total shrinkage according to the Jonasson model is shown in figure 

11. The lower w/c, the higher the total shrinkage. 

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70

Time (h)

Total Shrinkage (με)

w/c = 0.2, 0.25, 0.3, 0.35, 0.399

Jonasson Model

Figure 11. Influence of w/cm on total shrinkage predicted by the Jonasson model. 

B.1.3.2 Autogenous Shrinkage and Drying Shrinkage for w/cm ≥ 0.40 

The Baźant-Panula shrinkage model was selected to model the concrete when its w/cm ≥ 0.40. It models 

total shrinkage, which is autogenous shrinkage plus drying shrinkage, and it takes into account the 

composition of the mix and other empirical dependences.(35) It was also found to match the experimental 

drying shrinkage data better than the B3 model previously used in HIPERPAV I as described in section 

D.3.2. 
66 

The drying shrinkage strain is expressed by equation 58:(35)

(t t ) k S(t) sh sh h ˆ, ˆ 0 = ∞ ε ε (58) 

where, 

 εsh = shrinkage strain (με), 

t = time (days), 

t0 = age when drying begins (days), assumed to be the concrete’s set time, 

t

ˆ = duration of drying (days), 0 t

ˆ = t −t , 

εsh∞ = ultimate shrinkage strain (με) (see equation 63), 

kh = humidity dependence (see equation 65), and 

S(t

ˆ) = time dependence (see equation 59). 

The time dependence is shown in equation 59: 

( ) t

t S t

sh ˆ

ˆ ˆ + = τ (59) 

where, 

 τsh = shrinkage half-time (equation 60). 

The size dependence of the diffusion type is: 

( ) 1 0

1

2

150

600

C t

C D k ref

s

sh ⎟

⎠

⎞ ⎜

⎝

⎛

τ =

 (60) 

where, 

 ks = shape factor, ks = 1 for infinite slab, 1.15 for infinite cylinder, 1.25 for infinite 

square prism, 1.30 for sphere and 1.55 for cube (If the length of a cylinder or 

prism is 3 times its width, then it can be assumed to be infinitely long. For a 

finite length cylinder less than 3 times its width, its ks can be determined by 

linearly interpolating between the ks value for a sphere or prism and its 

corresponding ks for an infinitely long member), 

D = effective cross section thickness (mm), = 2 v/s, with v = volume and s = surface 

area, (D is thickness/2 based on calibrations using the HIPERPAV I field sites 

(see section D.3.2). The same calibration factor was also reported by 

Persson.(36)), 

C1

ref = 10 mm2

/day, and 

C1(t0) = age dependence (mm2

/day), given by equation 61: 

C (t) C k ( t) T 0.05 6.3/ '

1 = 7 + (61) 
67 

where, 

 C7 = empirical reference diffusivity at 7 days (mm2

/day) (see equation 66) and 

k'T = temperature dependence coefficient, given by equation 62: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − T T T

T kT

5000 5000

exp

0 0

'

 (62) 

where, 

 T = temperature (Kelvin) and 

T0 = reference temperature 23 °C (in Kelvin). 

This model was calibrated using laboratory data. Since it will be used to model drying shrinkage that 

occurs in the field at temperatures that are not found in the laboratory, the effect of k'T will be neglected. 

T will be set to 23 °C in the modeling. 

Ultimate shrinkage is given by equation 63: 

( )

( ) sh

sh s E t

E

τ

ε ε

+

+ ∞ = ∞

0

7 600

 (63) 

where, 

 εs∞ = empirical shrinkage given in equation 67. 

() ( ) t

t E t E

4 0.85

28

+ =

 (64) 

where, 

 E(28) = 28-day modulus of elasticity. 

Humidity dependence is the same as it is in the B3 model, as shown in equation 65: 

⎪

⎪

⎪

⎩

⎪

⎪

⎪

⎨

⎧

≤ ≤

− =

− ≤

=

interpolation 0.98 1

0.2 1

1 0.98 3

linear for h

for h

h for h

k

h

 (65) 

where, 

 h = relative humidity (0 ≤ h ≤ 1). 

The empirical dependences of drying shrinkage on concrete strength and composition of the mix are 

defined in the following equations. The reference diffusivity C7 (mm2

/day) is shown in equation 66: 
68 

C7 = 1/8 w/c c – 12 (66) 

if C7 < 7, C7 = 7, and if C7 > 21, C7 = 21. 

Final shrinkage εs∞ (10-6) is defined as shown in equation 67: 

y ε s∞ =1210 −880 (67) 

where, as shown in equations 68 and 69, 

 ( ) 1 4 390 1 − − y = z + (68) 

0.145 12 0

/

1 / 1.25 / 0.5 '

2 1/ 3

− ≥ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ ⋅ ⎠

⎞ ⎜

⎝

⎛ +

×

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ = + f if z

w c

s c

s

g

z a c c

 (69) 

else z = 0, with, 

 c = cement content (kg/m3

), 

w/c = w/c by weight, or w/cm, 

a/c = total aggregate (coarse + fine)-to-cement ratio by weight, 

g/s = coarse aggregate-to-fine aggregate ratio by weight, 

s/c = sand-to-cement ratio by weight, and 

f'c = 28-day compressive strength (MPa). 

Brooks investigated the effect of admixtures on shrinkage.(37) He found that shrinkage was not greatly 

affected by fly ash, GGBF slag, or silica fume (5–15 percent). As a result, these additives will not be 

added to the cementitious materials content when calculating the drying shrinkage with the Baźant-Panula 

model. 

The Baźant-Panula model does not take into account the cement type (α1) and the specimen curing (α2) 

factors that were included in the B3 model. They were added to equation 67, as shown in equation 70: 

( y) s 1210 880 ε ∞ =α1

α 2 − (70) 

where, as shown in equations 71 and 72, 

⎪

⎪

⎪

⎩

⎪

⎪

⎪

⎨

⎧

=

for Type III cement

for Type II cement

for Type I cement

1.1

0.85

1.0

α1

 (71) 
69 

and 

⎪

⎪

⎪

⎩

⎪

⎪

⎪

⎨

⎧

=

for sealed specimens

for water cured specimens

for steam cured specimens

1.2

1.0

0.75

α 2

 (72) 

As shown in figure 12, increasing the w/c causes the total shrinkage to increase, as predicted by the 

Baźant-Panula model. 

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70

Time (h)

Total Shrinkage (με)

w/c = 0.4, 0.5, 0.6 

Baźant-Panula Model

Figure 12. Effect of w/c on total shrinkage predicted by the Baźant-Panula model. 

B.1.3.3 Comparison Between the Shrinkage Models 

It is necessary to investigate the difference in the Baźant-Panula and Jonasson-Hedlund models when the 

w/cm is at and below 0.4. This is shown in figure 13. It is apparent that the shrinkage predicted by the 

Baźant-Panula model is greater, in some cases by 140 με. After experimental data is collected for 

pavement mixes with w/cm < 0.40, the Jonasson-Hedlund model can be calibrated. 
70 

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 70

Time (h)

Total Shrinkage (με)

Baźant-Panula Model w/c = 0.4

Jonasson w/c = 0.399, ts = 1

Jonasson w/c = 0.399, ts = set time

Figure 13. Comparison of the Baźant-Panula and Jonasson-Hedlund shrinkage models. 

The influence of the start time on the Jonasson-Hedlund also was investigated. Changing tstart (equation 

45) and ts (equation 50) to the set time allows the model to predict shrinkage at times less than 24 hours. 

This modification was made for HIPERPAV II predictions, since autogenous shrinkage has been 

documented to begin at times less than 24 hours.(34)

In this new approach, the predicted total shrinkage in HIPERPAV II is the greater of the shrinkage 

predicted by the Jonasson-Hedlund and the Baźant-Panula models. 

B.1.4 Nonlinear Restraint Model 

Recognizing the nonlinear restraint effect imposed by some subbases, such as hot-mix asphalt (HMA) 

subbases, a nonlinear model was included in HIPERPAV II in addition to the current linear one to 

provide for the characterization of such behavior. The nonlinear model is of the following form, shown in 

equation 73: 

n

f

c

f

u C

1

2 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

τ =

 (73) 

where, 

 τf = friction stress (kPa), 

uc = PCC axial displacement (m), 

δf = axial displacement at sliding (m), 

C2 = maximum friction stress (kPa), and

n = nonlinear power coefficient (dimensionless). 

Typical values of the above coefficients can be obtained by performing friction tests. The procedure for 

these tests is described elsewhere. (See references 38, 39, 40, and 41.) 
71 

B.1.5 Nonlinear Thermal Gradient Model 

Recognizing that thermal gradients through the slab depth are nonlinear for the most part, the model 

developed by Mohamed and Hansen is used in HIPERPAV II to determine an equivalent linear gradient 

as a function of a nonlinear one as follows in equation 74:(42)

2

* 12

h

M Teq α

Δ = −

 (74) 

where, 

 ΔTeq = equivalent linear temperature gradient, oC, 

 h = slab thickness, m, 

 α = PCC CTE, m/m/oC, and 

 M* = constant dependent on the temperature distribution expressed as shown in 

equation 75: 

∫

−

=

/ 2

/ 2

* ( )

h

h

M ε z zdz

 (75) 

where, 

 z = distance from slab midplane (z is positive downward), m, and 

 ε(z) = strain profile, m/m. 

The equivalent linear gradient from top to bottom of the slab determined with the above model was 

developed with the objective of producing the same curvature as the Westergaard and Bradbury linear 

gradient solution.(42)

In HIPERPAV II, the strain profile is determined as shown in equation 76: 

( ) ( ) Tz Tz,set ε z =α − (76) 

where, 

 Tz = current temperature at slab depth z, oC, and 

 Tz,set = temperature at slab depth z, at time of set, oC. 

B.1.6 Creep Model 

The creep model described below was not incorporated in HIPERPAV II due to lack of data for 

validation. However, it is presented here because researchers in this project made major efforts that could 

make incorporating the creep model relatively easy in the future when enough data for validation is 

available. 

When load is applied to a concrete member, it responds with an immediate elastic deformation (εel), 

followed by a time-dependent creep response (εcr), which is shown in figure 14. This time-dependent 
72 

response is best modeled by viscoelastic theory.(43) To obtain a reasonably accurate estimate of the 

stresses at early ages, the amount of creep must be taken into account. 

ε cr(t,t0) = φ(t,t0) ε el(t0)

Applied Stress, 

σ Strain, 

ε

Time

σ(t0)

Creep Strain

Instantaneous 

Elastic Strain

t0

t0 t

ε el(t0) = σ(t0)/E(t0)

Time

J(t,t0)⋅σ(t0) cr 0) = 

0)

0

0 

) = 

ε cr(t,t0) = φ(t,t0) ε el(t0)

Applied Stress, 

σ Strain, 

ε

Time

σ(t0)

Creep Strain

Instantaneous 

Elastic Strain

t0

t0 t

ε el(t0) = σ(t0)/E(t0)

Time

J(t,t0)⋅σ(t0) cr 0) = 

0)

0

0 

) = 

Figure 14. Time-dependent deformation at time t, for a loading at time t0.

(43)

In modeling of time-dependent deformation, creep compliance formulation is generally the preferred 

method. In this method, the total linear time-dependent deformation, ε(t), is expressed as mathematically 

as shown in equation 77 below and illustrated in figure 14 above. 

( ) ( , ) ( ) 0 0 ε t = J t t ⋅σ t (77) 

where, 

 J(t,t0) = creep compliance defined as the response at time t after loading at time t0 and 

σ(t0) = applied stress at time t0. 

The instantaneous and time-dependent components of the total deformation can be separated as shown in 

equation 78: 

Eeff E t

t t J t t

1

( )

1 ( , ) ( , )

0

0

0 = + = φ

 (78) 

where, 

 E(t0) = the instantaneous modulus of elasticity at time t0, 

φ(t,t0) = the creep coefficient (ratio of creep to elastic strain), and 

 Eeff = the effective modulus of elasticity at time t. 
73 

B.1.6.1 Creep Model Identified—Extended Triple Power Law 

Few models are available to model the time-dependent deformation and creep compliance of concrete at 

early ages. The Extended Triple Power Law model is developed from the Double Power Law and the 

Triple Power Law.(35,44) The Double Power Law is perhaps the most well known compliance function, 

and has been used by many authors because it is based on extensive laboratory test results. The Triple 

Power Law was developed to provide a more accurate description of the long-term creep. As is 

commonly done, it will also be assumed that the creep response in tension is equal to the creep in 

compression. 

Neither the Double nor the Triple Power Laws were calibrated for loading at early ages, and they were 

not intended to predict creep for young concrete.(45) Westman estimated that the Double and Triple Power 

Laws are only valid for loading ages larger than about 2 days.(43) Therefore, the Triple Power Law was 

adjusted first by Emborg(45) and then by Westman(43) to account for loading at ages less than about 2 days. 

The Extended Triple Power Law, as documented by Westman, provides good agreement with early-age 

test data, and accounts for all the factors that could influence the time-dependent deformation, such as: 

• Concrete age at setting. 

• Concrete age at loading (which is most important). 

• Applied stress level. 

• The influence of varying temperature. 

B.1.6.2 Creep Model Definition 

In 1989, Emborg extended the Triple Power Law with two additional functions, which Westman(43)

modified in 1999. For loading ages less than about 2 days, the function Ψ1(t0) models the age dependence 

of the instantaneous deformation, and Ψ2(t,t0) models the increase of creep when the load has been 

applied. The purpose of the two new terms, Ψ1(t0) and Ψ2(t,t0), are shown schematically in figure 15. 

The creep compliance according to the Extended Triple Power Law is as shown in equations 79 through 

90: 

( )[()( )]

0

2 0

0

1 0

0 0 0

0

1

0

0

( ) ( , ) , ;

1 ( , ) E

t t

E

t

t t t B t t n

E E

J t t m n Ψ

+

Ψ = + + − − + − α

φ

 (79)

where, 

 t = concrete age, 

 t0 = equivalent age when the load is applied (days), 

 E0 = negative asymptotic modulus of elasticity at time t0 (psi), (1 psi = 6.89 kPa) 

 (E0 may be determined from the 28-day modulus, E0 ≈1.5⋅E28), 

α = 1/40(w/c) (80) 

 w/c = water-to-cement ratio, 

Φ1 = 103n/2(28-m + α) (81) 
74 

m = 0.28 + (0.145 · f′

c)

-2

 (82) 

 f’c = 28-day cylinder compressive strength (MPa), 

n = 0.12 + ((0.07 · x6)/(5130 + x6)) if x > 4; and n = 0.12 if x ≤ 4 (83) 

( )

( ) 0.1( ) ( )( ) / / 4

/

/ 2.1

1

' 1.5 1/ 3 2.2

1.4 ⎥⋅ −

⎦

⎤ ⎢

⎣

⎡ = + f w c a g a

s c

a c

x c

 (84) 

where, 

 a/c = total aggregate/cement ratio, 

 s/c = sand/cement ratio, 

 a/g = coarse aggregate/cement ratio, and 

 a1 = 1.00 for Type I or II cement, 

 0.93 for Type III cement, and 

 1.03 for Type IV cement. 

B(t,t0;n) is a binomial integral and may be evaluated by the following power series (equations 85 and 86): 

( ) ( )( ) ⎥

⎦

⎤ ⎢

⎣

⎡ ∑ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − − −

− + + − − = ⋅ ∞

=

−

−

−

1

1

0 0

1 1 ln 1 1 , ;

k

k n k

k

k

n

n

n k k

n

n

B t t n n t β β β β

 (85) 

with 

β = t0/t and k = summation time step 

 (86) 

Furthermore, if t0 ≤ t1, 

1

1

1 0

1 0 1 ( )

a

s t t

t t

t ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

− Ψ =γ ⋅

 (87) 

if t0 > t1 , 

Ψ1 (t0 )=0 (88) 
75 

and if t0 ≤ t3, 

2 3

1

1 0

2

0

2 0 2 ( , ) 1 exp

a

s

a

t t

t t

t

t t

t t ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

−

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − Ψ =γ ⋅ − −

 (89) 

If t0 > t3 , 

Ψ2 (t,t0 )=0 (90) 

where, 

 ts = the apparent setting time of the concrete (days), 

 t1 , t3 = time limits for adjustment at early ages (days), 

 t2 , a2 = parameter for the development of the time function (days), 

γ1 = initial value of function Ψ1(t0) at t0 = ts, 

γ2 = initial value of function Ψ2(t,t0). at t0 = ts, 

 a1 = parameter modifying the shape of Ψ1(t0), and 

 a3 = parameter modifying the end value of Ψ2(t,t0). 

ψ2(t,t0)

ψ1(t0)

E0

E0

J(t,t0)

t

1 t

0

Time

ψ2(t,t0)

ψ1(t0)

E0

E0

J(t,t0)

t

1 t

0

Time

Figure 15. A schematic of the additional Ψ1(t0) and Ψ2(t,t0) functions to extend the Triple Power 

Law for the early-age creep response.(43)

The dependence of creep on different curing temperatures that are constant for the time of interest may be 

modeled with the coefficients nT and φT instead of n and φ1, as shown in equations 91 through 97:(35) 

nT = β T⋅n

 (91) 

where, 
76 

( ) 1

1 74/( 253.2)

0.25

7 +

+ − = T β T

, (T measured in Kelvin), and (92) 

( ) φ T =φ1 1+CT (93) 

where, 

CT = CT1⋅τT⋅C0

 (94) 

( ) 1

1 100/( 253.2)

0.25

1 3.5 − + − = T

CT

 (95) 

( ) 0.78

1 60/

1

0.69 +

+ =

oT

T

t

τ

 (96) 

1

2

0 C =0.125⋅(w/ c) (a / c)⋅a (97) 

 

where, 

 toT = age of the concrete when the temperature T is applied. 

The age of the concrete at time of loading, t0, is here expressed as shown in equation 98: 

= = ∫ ( ) ' ' ' ' " " t

e o T t t β t dt (98) 

where, 

 t'e = equivalent hydration period, and equation 99, 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − T T T

4000 4000 ' exp

0

β

 (99) 

where, 

 T0 = the reference temperature (293 oK). 
77 

In the documentation provided by Westman, the necessary values for each of the parameters listed in this 

section are provided to allow the implementation of this model.(43) Based on the characteristics of the 

different mixtures tested by Westman, the mixture corresponding to a typical pavement mixture was 

selected. The characteristics of this mix is as follows: w/c = 0.40, 330 kg/m3

 cement, 5.6 percent air 

content, and a 28-day compressive strength of about 47.2 MPa. Based on the test results with this mixture 

design, it is recommended that the following parameters for the Extended Triple Power Law be used: 

t1 = 1.5 days γ1 = 10 

t3 = 1.5 days γ2 = 18 

t2 = 0.02 days a1 = 5 

a2 = 0.2 a3 = 5 

To obtain a reasonably accurate estimate of the stresses at early ages, the amount of relaxation that occurs 

must be taken into account. It is recommended that the Extended Triple Power Law be used to determine 

the creep compliance at early ages, as this model has been developed to characterize early-age response. 

B.1.6.3 Implementation of Creep Model 

In the implementation of creep compliance formulation, there are two possible approaches, and both 

methods have their advantages and disadvantages. The methods can briefly be described as follows: 

• The simplest method “... is to assume the stress history is a series of sudden (discontinuous) 

stress increments and then solve the algebraic equations resulting from the superposition of 

creep responses due to all the individual stress increments.”(46) (pp. 135 and 136) The error 

involved with this numerical procedure is of the second time step, however, the result 

obtained by Emborg(45) and others show good agreement with test data. The disadvantage of 

this method is that large storage space could be required to store the complete history of 

stresses for all the elements in the structure. However, it is believed that this problem is 

insignificant for early-age analyses, as few elements are considered in the finite-element 

analysis (FEA), and a period of only 72 hours typically is considered. 

• The second method requires converting the creep compliance values into relaxation values. 

For this process, the Maxwell chain model is used most often in the conversion process. This 

procedure requires good selection of parameters for the Maxwell elements, and in some 

instances, convergence of the conversion could require user intervention. It is also reported 

that for very long load durations, negative relaxation values could develop, and adjustments 

of the creep curves are necessary to prevent this problem from occurring.(43) After the 

relaxation values are determined, further curve fitting also is required to obtain a smooth 

representation of the concretes behavior. 

If this model is incorporated in future versions of HIPERPAV, it is recommended that the first method be 

used, since the approach is less likely to produce conversion problems during analysis. The following 

sections will provide further details on the solution to this procedure. 

B.1.6.4 Algorithm for the Relaxation Formulation of Creep Deformations Based on the Principle of 

Superposition 

Using the principle of superposition, the strain history ε(t) caused by an arbitrary history of applied stress 

σ(t) can be determined by assuming the stress history is composed of infinitesimal step functions as 
78 

shown in figure 16.(46) The total strain can be calculated as shown in equation 100.(45,46) This equation is 

a general uniaxial constitutive relation defining concrete as an aging viscoelastic material. 

( ) ( , ) ( ) ( ) 0 0

0

0 t J t t d t t

t

ε = ⋅ σ + ε ∫

 (100) 

where, 

 J(t,t0) = creep compliance defined as the response at time t after loading at time t0, 

 dσ(t0) = stress increment at time t0, and

 ε0 (t) = stress-independent strain increment at time t. 

Time, t

Stress, 

σ

t0

dσ(t0)

Time, t

Stress, 

σ

t0

dσ(t0)

Figure 16. Decomposition of stress history into stress steps. 

When the history of strain is prescribed, equation 100 can be solved by a step-by-step numerical solution, 

where time is subdivided into discrete time steps, tr (r = 0,1,2, ... n) with time steps, Δtr = tr – tr-1.

(46) A 

schematic for the numerical solution is shown in figure 17, and the steps for the algorithm are as follows: 

Step 1: At time tr, determine the equivalent age ter, and the change in equivalent age as: Δter = ter – ter-1. 

Step 2: Determine the applied strain, εr , and calculate the change in strain as: Δεr = εr – εr-1.

Step 3: Determine the incremental elastic modulus, E′′r = 1/ J(r,r – 1⁄2). Subscript r, refer to the discrete 

time ter, and J(r,r – 1⁄2) may be interpreted as J(ter,ter – Δter/2).

Step 4: Determine the incremental strain, Δε′′r, as shown in equation 101. 

0

1

1

" r s r

r

s

r Δε = ∑ΔJ ⋅Δσ + Δε

−

= (101) 

where, 

 Δσs = σs – σs-1, Δε0

r = ε

0

r – ε

0

r-1, and 

 ΔJr = J(r,s – 1⁄2) – J(r – 1,s – 1⁄2). 

Step 5: Finally, the stress increment (Δσr) for the time step, Δtr can be determined as shown in equation 

102: 

Δσr = E′′r · (Δεr – Δε′′r)

 (102) 
79 

NOTE: Due to the nature of the summation required in equation 101, and the fact that the value J(x,x) is 

not singular, the start of the numerical iteration (r = 0, and r = 1) requires some initial calculations other 

than those presented above. Iteration interval r = 0, should be taken to occur at time, t = t0, and r = 1 

should be taken to occur at time, t = to + 0.01 (hours). The following calculations are necessary for r = 0 

and r = 1 (equations 103 and 104, respectively): 

At r = 0: 

Δσr = 0, and t = t0 (days) 

 (103) 

At r = 1: 

Δε′′r = 0, t = (t0 + 0.01)/24 (days), E′′r = 1/J(r,r – 0.1), and Δσr = E′′r ·(Δεr) 

 (104) 

Strain, ε

Time, t t

0

r = 0,1 2 3 4 5 6 ... n

Δεr

Time, t

Stress, 

σ

t

0

r = 0,1 2 3 4 5 6 ... n

Δσr (from equation 6)

Δt

r

Strain, ε

Time, t t

0

r = 0,1 2 3 4 5 6 ... n

Δεr

Time, t

Stress, 

σ

t

0

r = 0,1 2 3 4 5 6 ... n

Δσr (from equation 6)

Δt

r

Figure 17. Discreet subdivision of time for numerical creep analysis. 

 

Figures 18–20 show a schematic of how strains could be superimposed to model strain levels of varying 

intensities. Creep recovery at unloading could be overestimated by this principle, as the plastic flow 

component of the irrecoverable time-dependent deformation is not taken into accounted.(43)

Based on typical inputs, and the strains that were calculated with the HIPERPAV I program, the 

numerical procedure outlined above was programmed into mathcadTM to verify the results of the models. 

The results are shown in figure 21. With no relaxation modeled, the strains and the stresses cross the 

zero-stress level at the same time (approximately 22 hours). However, when the effects of relaxation are 

accounted for, the stress at ages less than 22 hours are significantly less, and the zero-stress level occurs 

earlier at an age of about 19 hours. Because much of the early tension has been relaxed, the magnitude of 

compressive forces between ages of 19 and 32 hours also is increased. 
80 

Time, t

ε 1

(t0)r = 4

r = 0,1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... n

Δεr = 4

Figure 18. Superposition of various strains intensities: Loading. 

ε2

r = 0,1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... n Time, t

Δεr = 12

(t0)r = 12

Figure 19. Superposition of various strains intensities: Unloading. 

εT

=

ε1 −

ε2

(t

0)r = 4 (t0)r = 12

r = 0,1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... n

Figure 20. Superposition of various strains intensities: Net applied strains. 
81 

-3

-2

-1

0

1

2

3

0 12 24 36 48

Concrete Age (h)

Total Stress (MPa)

-400

-300

-200

-100

0

100

200

300

400

Bazant and Westman

Total Strain (Microstrain)

No relaxation

Strain

Figure 21. Comparison of the results of the relaxation model and model without relaxation. 

B.1.6.5 Summary and Recommendations 

To obtain a reasonably accurate estimate of the stresses at early ages, the amount of relaxation that occurs 

must be taken into account. It is recommended that the Extended Triple Power Law be used to determine 

the creep compliance at early ages, as this model has been developed extensively to characterize early-age 

response. A numerical technique to model the time-dependent response for concrete at early ages is also 

presented. The principle of superposition is used, where the strain history ε(t) caused by an arbitrary 

history of applied stress σ(t), is determined by assuming the stress history is composed of infinitesimal 

step functions.(46) 

B.2 JPCP PERFORMANCE MODELS 

A brief description of the primary JPCP long-term performance models incorporated in HIPERPAV II is 

provided in the following sections. These models are divided in the following categories: 

• Environmental models. 

• Long-term materials properties models. 

• Structural models. 

• Distress models. 

Environmental models are used to predict the temperature and moisture gradient through the pavement 

structure. Long-term materials properties models are used to predict the development of strength and 

stiffness at ages beyond 28 days. Structural models are used to predict the pavement behavior in terms of 

stress, strain, and deflection due to environmental and traffic loadings. Finally, distress models are used 

to predict the distress progression as a function of environmental and traffic loads. 
82 

B.2.1 Environmental Models 

B.2.1.1 Long-Term PCC Temperature Prediction Model 

As stated in section B.1.2, the finite-difference method is used for prediction of long-term concrete 

temperatures in HIPERPAV II. A detailed description of this model is presented in that section. 

However, because pavement temperatures undergo seasonal changes in the long term, and because 

HIPERPAV II predicts PCC temperatures only at isolated periods of time for every season, the initial 

pavement temperature profile is required as an input in the finite-difference method for predicting the 

subsequent PCC temperatures for that season. HIPERPAV II uses the closed form solution developed by 

Barber described in section B.1.2.6 for this purpose. 

B.2.1.2 Subgrade Moisture Model 

This section summarizes the assumptions and limitations of the moisture model incorporated in 

HIPERPAV II. The model provides a simple method to predict the average monthly moisture content in 

pavement base materials using site-dependent climate conditions, soil data, and some pavement 

geometry.(18)

B.2.1.2.1 Inputs

The required inputs for the model are given below. 

• Percent clay, %Clay, defined as the percent passing the #200 sieve. 

• Saturation water content, wsat.

• Plastic limit, PL. 

• Liquid limit, LL.

• Plasticity index, PI.

• Difference in water content between the plastic limit and saturation, wsat – PL.

• Suction at the plastic limit, SucPL.

• Monthly rainfall, rainmo.

• Specific gravity of solids, Gs.

• Existence of paved shoulders. 

• Thornthwaite moisture index (THMI).

The THMI is a correlation between rainfall and the potential for water loss through evaporation and 

transpiration. 

High rainfall totals do not necessarily equate to a high THMI values because climatic conditions may 

dictate that the moisture is lost before it is absorbed into the soil.(47) A current practice is to group climate 

types according to moisture and winter temperature.(48) Table 14 gives a range of THMI values for 

specific locations in each of these climate types. 
83 

Table 14. Thornthwaite moisture index values. 

City THMI Moisture Winter Temperature 

Chicago, IL 30 Wet Cold

Fargo, ND −5 Moderate Cold

Reno, NV −40 Dry Cold

Washington, DC 60 Wet Moderate

Oklahoma City, OK 0 Moderate Moderate

Las Vegas, NV −42 Dry Moderate

Atlanta, GA 55 Wet Warm

Dallas, TX 0 Moderate Warm

San Antonio, TX −18 Dry Warm

Default soil characteristics that provided values for lesser known parameters were included with the 

model. Table 15 gives these values. 

Table 15. Default soil characteristics. 

USC %Clay wsat – PL SucPL Gs

CH 70 26.2 3.5 2.68

CL 40 8.4 3.2 2.7

MH 30 5.3 3 2.7

ML 20 2.2 2.8 2.71

SC 30 4.4 2.9 2.65

SM 25 2.4 2.7 2.65

SP–SC 12 1.5 2.6 2.65

SW–SC 12 1.5 2.6 2.65

SP–SM 10 0.5 2.4 2.65

SW–SM 10 0.5 2.4 2.65

SP 5 0.3 2.4 2.64

SW 5 0.3 2.4 2.66

GW–GC 12 1.1 2.2 2.65

GP–GC 12 1.1 2.2 2.65

GW–GM 10 0.6 2 2.65

GP–GM 10 0.6 2 2.65

GP 5 0.2 1.8 2.65

GW 5 0.2 1.8 2.65

B.2.1.2.2 Calculations

The model makes a series of four calculations to predict the average monthly moisture content. 

• Reference Suction: The reference suction, Sucref, is based on the %Clay and THMI. The 

magnitude of reference suction is determined as shown in equations 105 through 110: 
84 

If %Clay ≤ 6 percent: 

 

THMI ≥ -12.5 Sucref = 1.86 

 (105) 

THMI < -12.5 Sucref = -0.0141 * THMI + 1.69 

 (106) 

If 6 percent < %Clay < 40 percent: 

THMI ≤ -0.5 Sucref = -0.0251 * THMI + 2.5 

 (107) 

THMI > -0.5 Sucref = -0.0062 * THMI + 2.46 

 (108) 

If %Clay ≥ 40 percent: 

THMI ≤ -5.98 Sucref = -0.043 * THMI + 3.23 

 (109) 

THMI > -5.98 Sucref = -0.0118 * THMI + 3.4 

 (110) 

• Average Monthly Rainfall: The average monthly rainfall, rainavg, is calculated by taking the 

average of the maximum, rainmax, and minimum, rainmin, monthly rainfall totals for the design 

year (equation 111). 

rainavg = (rainmax + rainmin)/2 

 (111) 

• Suction Variation: The following steps in equations 112 through 114 are made to calculate 

the monthly soil suction, Sucmo: 

If rainmo > rainavg Sucmo = Sucref – ((rainmo – rainavg)/(rainmax – rainavg)) * ∆

 (112)

If rainmo < rainavg Sucmo = Sucref + ((rainavg – rainmo)/(rainavg – rainmin)) * ∆

 (113)
85 

If rainmo = rainavg Sucmo = Sucref

 (114) 

where, 

 Δ = 0.25 for paved shoulders and 

 Δ = 0.50 for unpaved shoulders. 

 

• Calculation of Moisture Content: The final step in the model is to correlate the monthly 

suction value to moisture content, as shown in equations 115 through 117. 

 If Sucmo ≥ SucPL: 

 (115) 

 If Sucmo < SucPL: 

wsat < LL wmo = PL + ((Sucmo – SucPL)/(1.0 – SucPL)) * PI

 (116) 

wsat ≥ LL wmo = PL + ((Sucmo – SucPL)/(1.0 – SucPL)) * (wsat – PL)

 (117) 

B.2.1.2.3 Sensitivity Analysis

A sensitivity analysis was performed on the continuity of the reference suction calculations and the 

influence of climate and rainfall. 

B.2.1.2.3.1 Reference Suction 

A quick analysis on the continuity of the reference suction calculation was performed by choosing values 

just above and below the calculation thresholds. This analysis is not included, but it indicated that the 

reference suction calculation is continuous. Six sets of values for %Clay and THMI were used to evaluate 

the six possible reference suction calculations. The effect of paved shoulders was also examined for each 

scenario. Constant monthly rainfall totals were used during this portion of the sensitivity analysis even 

though the THMI varied between runs. Table 16 shows the factorial for this portion of the experiment. 

The following sections summarize the results according to soil classification. 

wmo = ((Sucmo – 5.5)/(SucPL – 5.5)) * PL
86 

Table 16. Factorial for reference suction sensitivity analysis. 

 Scenarios

Variables 1 2 3 4 5 6 7 8 9 10 11 12

Thornthwaite −15 −15 10 10 −15 −15 10 10 −15 −15 −10 −10

Soil class CL CL CL CL GW- GW- GW- GW- GW GW GW GW

%Clay 40 40 40 40 10 10 10 10 5 5 5 5

w(PL) – w(sat) 8.4 8.4 8.4 8.4 0.6 0.6 0.6 0.6 0.2 0.2 0.2 0.2

w(sat) 23.4 23.4 23.4 23.4 15.6 15.6 15.6 15.6 10.2 10.2 10.2 10.2

Plastic limit 15 15 15 15 15 15 15 15 10 10 10 10

Liquid limit 40 40 40 40 21 21 21 21 15 15 15 15

Plasticity index 25 25 25 25 6 6 6 6 5 5 5 5

Suction(PL) 3.2 3.2 3.2 3.2 2 2 2 2 1.8 1.8 1.8 1.8

Paved shoulder Y N Y N Y N Y N Y N Y N

Lean Clay (CL): Results for the CL soil are presented in figure 22 and table 17. Table 17 reports the 

monthly moisture content for scenarios 1–4 as outlined in table 15. The fifth (1–2) and sixth (3–4) 

columns examine the effect of paved shoulders on moisture content. The final two columns (1–3 and 2–

4) examine the effect of changing the formula for reference suction calculation by a change in the THMI. 

The average and standard deviation for the effects of these changes are also given. Figure 22 shows the 

monthly variation in moisture content. The THMI value appears to control the general vertical location in 

this figure, while rainfall and paved/unpaved shoulders control variability. The presence of a paved 

shoulder appears to reduce moisture content variation throughout the year. 

Table 17. Moisture contents for lean clay (CL) in scenarios 1–4. 

 Scenario

Month Rain (mm) 1 2 3 4 1–2 3–4 1–3 2–4

Jan 81 10.31 10.02 14.18 13.89 0.29 0.29 3.87 3.87

Feb 93 10.56 10.53 14.43 14.39 0.04 0.04 3.87 3.87

Mar 64 9.95 9.31 13.82 13.18 0.64 0.64 3.87 3.87

Apr 89 10.49 10.37 14.35 14.24 0.11 0.11 3.87 3.87

May 173 12.23 13.86 16.91 19.75 1.63 2.84 4.68 5.89

Jun 59 9.85 9.10 13.72 12.97 0.75 0.75 3.87 3.87

Jul 155 11.85 13.11 16.26 18.45 1.26 2.19 4.40 5.34

Aug 108 10.87 11.14 14.74 15.01 0.27 0.27 3.87 3.87

Sep 17 8.97 7.34 12.83 11.20 1.63 1.63 3.87 3.87

Oct 129 11.30 12.00 15.29 16.51 0.70 1.22 3.99 4.51

Nov 168 12.12 13.65 16.72 19.38 1.52 2.66 4.60 5.73

Dec 83 10.35 10.11 14.22 13.98 0.25 0.25 3.87 3.87

 Average 0.76 1.07 4.05 4.37

 Std. Dev 0.61 1.02 0.32 0.81
87 

6

8

10

12

14

16

18

20

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Moisture Content (%)

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Figure 22. Monthly moisture content variation for lean clay (CL), scenarios 1–4. 

 

Well-Graded Silty Gravel (GW–GM): Results for the GW–GM soil are presented in figure 23 and table 

18. These scenarios also show that the moisture content value is dictated by the THMI, but the variability 

is dictated by rainfall and shoulder conditions. The variability of the GW–GM soil is noticeably less than 

the CL soil. This shows that the model accounts for changes in particle size, which directly affects the 

suction parameters used in the moisture content calculations. Smaller particle sizes or higher %Clay

typically mean that the soil does not drain as well and is more susceptible to moisture content variation. 

As shown in figure 23 and in the previous section, the model predicts that a paved shoulder lessens the 

variability of moisture content throughout the year. 

Table 18. Moisture contents for well-graded silty gravel (GW–GM) in scenarios 5–8. 

 Scenario

Month Rain (mm) 5 6 7 8 5–6 7–8 5–7 6–8

Jan 81 11.05 10.86 13.10 12.91 0.19 0.19 2.05 2.05

Feb 93 11.22 11.20 13.27 13.25 0.02 0.02 2.05 2.05

Mar 64 10.82 10.40 12.87 12.45 0.42 0.42 2.05 2.05

Apr 89 11.17 11.10 13.22 13.15 0.07 0.07 2.05 2.05

May 173 12.32 13.39 14.37 15.60 1.07 1.23 2.05 2.21

Jun 59 10.75 10.26 12.80 12.31 0.49 0.49 2.05 2.05

Jul 155 12.07 12.90 14.12 14.95 0.83 0.83 2.05 2.05

Aug 108 11.42 11.60 13.47 13.65 0.18 0.18 2.05 2.05

Sep 17 10.17 9.10 12.22 11.15 1.07 1.07 2.05 2.05

Oct 129 11.70 12.16 13.75 14.21 0.46 0.46 2.05 2.05

Nov 168 12.25 13.25 14.30 15.42 1.00 1.12 2.05 2.17

Dec 83 11.08 10.92 13.13 12.97 0.16 0.16 2.05 2.05

 Average 0.50 0.52 2.05 2.07

 Std. Dev 0.40 0.44 0.00 0.06
88 

6

8

10

12

14

16

18

20

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Moisture Content (%)

Scenario 5

Scenario 6

Scenario 7

Scenario 8

Figure 23. Monthly moisture content variation for well-graded silty gravel (GW–GM), scenarios 5–8. 

Well-Graded Gravel (GW): Results for the GW soil are presented in figure 24 and table 19. The effects 

of THMI, paved shoulders, and rainfall are less pronounced for the GW soil. THMI changes did not alter 

the vertical placement in figure 24 as in the previous scenarios, which caused all four moisture contents to 

be in the same ranges throughout the design year. One explanation is that the model the GW soil contains 

only 5 percent clay and drains freely. Therefore, the evaporation and transpiration accounted for by the 

THMI does not have as great an affect as for soils with higher percentages of clay. In these scenarios, the 

presence of a paved shoulder reduces the moisture content variability, but not in the same range as in the 

previous scenarios. 

Table 19. Moisture contents for well-graded gravel (GW) in scenarios 9–12. 

 Scenario

Month Rain (mm) 9 10 11 12 9–10 11–12 9–11 10–12

Jan 81 9.61 9.49 9.72 9.60 0.12 0.12 0.11 0.11

Feb 93 9.71 9.70 9.82 9.81 0.01 0.01 0.11 0.11

Mar 64 9.46 9.19 9.57 9.30 0.27 0.27 0.11 0.11

Apr 89 9.68 9.63 9.79 9.74 0.05 0.05 0.11 0.11

May 173 10.20 10.20 10.20 10.20 0.00 0.00 0.00 0.00

Jun 59 9.42 9.11 9.53 9.22 0.31 0.31 0.11 0.11

Jul 155 10.20 10.20 10.20 10.20 0.00 0.00 0.00 0.00

Aug 108 9.84 9.95 9.95 10.14 0.11 0.19 0.11 0.19

Sep 17 9.05 8.37 9.16 8.49 0.68 0.68 0.11 0.11

Oct 129 10.04 10.20 10.20 10.20 0.16 0.00 0.16 0.00

Nov 168 10.20 10.20 10.20 10.20 0.00 0.00 0.00 0.00

Dec 83 9.62 9.52 9.74 9.63 0.10 0.10 0.11 0.11

 Average 0.15 0.14 0.09 0.08

 Std. Dev 0.19 0.20 0.06 0.06
89 

6

8

10

12

14

16

18

20

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Moisture Content (%)

Scenario 9

Scenario 10

Scenario 11

Scenario 12

Figure 24. Monthly variation for well-graded gravel (GW), scenarios 9–12. 

B.2.1.2.3.2 Climate and Rainfall 

The second part of the sensitivity analysis evaluated two specific soils at five locations. The soil 

parameters used in this analysis were derived from Lytton’s default values for CL and GW–GM soil 

types.(48) THMI and monthly rainfall values for each location were identified using historical climate data 

from the National Climate Data Center (NCDC).(49) Table 20 shows the factorial used for this aspect of 

the analysis. 

Table 20. Factorial for climate and rainfall variation. 

Location City THMI Moisture Winter Temperature 

1 Chicago, IL 30 Wet Cold 

2 San Antonio, TX −18 Dry Warm 

3 Oklahoma City, OK 0 Moderate Moderate 

4 Atlanta, GA 55 Wet Warm 

5 Reno, NV −40 Dry Cold 

Table 21 gives the soil data for the CL and GW–GM soils used in the analysis. 
90 

Table 21. Soil data for climate and rainfall variation analysis. 

Property Soil 1 Soil 2

Soil class CL GW–GM

%Clay 40 10

w(PL) – w(sat) 8.4 0.6

w(sat) 26.4 15.6

Plastic limit 18 15

Liquid limit 38 21

Plasticity index 20 6

Suction(PL) 3.2 2

Gs 2.7 2.65

Table 22 gives the monthly rainfall totals for each of the five locations. Notice that the THMI value does 

not depend directly upon rainfall. 

Table 22. Monthly rainfall totals for locations in the U.S in millimeters.(49)

Month Chicago, IL San Antonio, TX Oklahoma City, OK Atlanta, GA Reno, NV

Jan 36.6 43.4 28.7 120.4 27.2

Feb 32.5 46.0 39.6 121.9 25.1

Mar 63.8 38.6 68.8 146.6 18.0

Apr 89.4 63.5 70.4 108.2 9.7

May 79.8 107.2 132.8 109.0 17.5

Jun 92.5 96.8 109.5 90.4 11.7

Jul 89.4 54.9 66.3 127.3 7.1

Aug 105.9 64.5 66.0 93.0 8.1

Sep 87.4 86.6 97.5 86.9 9.9

Oct 58.4 80.5 82.0 77.5 9.7

Nov 72.6 66.5 50.3 98.0 22.1

Dec 61.5 38.4 35.6 110.0 25.1

Total 869.7 787.1 847.1 1289.1 191.0

Lean Clay (CL): The results from the CL soil are given in table 23 and figure 25. This soil showed a 

large amount of variability between climate types. Atlanta, GA, and Chicago, IL, have the highest THMI 

values and have the highest predicted moisture contents. Reno, NV, has the lowest THMI and 

subsequently has the lowest predicted moisture content. These findings reinforce earlier observations that 

the vertical placement in figure 25 is directly related to THMI and the monthly variation is due to rainfall. 
91 

Table 23. Moisture contents for lean clay (CL) in five U.S. cities. 

Month Chicago, IL San Antonio, TX Oklahoma City, OK Atlanta, GA Reno, NV

Jan 17.46 10.04 14.48 22.64 6.26

Feb 17.25 10.20 14.89 22.73 5.84

Mar 19.06 9.77 15.99 24.35 4.47

Apr 20.64 11.19 16.04 21.83 2.82

May 20.05 13.66 18.45 21.87 4.34

Jun 20.84 13.08 17.52 20.66 3.20

Jul 20.65 10.69 15.89 23.08 2.35

Aug 21.67 11.25 15.88 20.82 2.53

Sep 20.52 12.51 17.06 20.43 2.86

Oct 18.73 12.16 16.49 19.81 2.83

Nov 19.61 11.36 15.29 21.16 5.28

Dec 18.92 9.75 14.73 21.94 5.85

Average 19.62 11.30 16.06 21.78 4.05

Std. Dev. 1.37 1.31 1.18 1.29 1.46

0

5

10

15

20

25

30

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Moisture Content (%)

Chicago

San Antonio

Oklahoma City

Atlanta

Reno

Figure 25. Monthly variation for lean clay (CL) in five U.S. cities. 

Well-Graded Silty Gravel (GW–GM): The results from the analysis of the GW–GM soil type are shown 

in table 24 and figure 26. The prediction for this soil shows less variation than the CL soil. This also 

reinforces earlier observations that the model assumes soils with higher clay contents will fluctuate more 

than granular soils that drain more freely. Even with less variation, the moisture contents varied 

according to the THMI value at each location. 
92 

Table 24. Moisture contents for well-graded silty gravel (GW–GM) in five U.S. cities. 

Month Chicago, IL San Antonio, TX Oklahoma City, OK Atlanta, GA Reno, NV

Jan 10.04 10.01 11.96 14.75 9.63

Feb 10.20 10.09 12.18 14.79 9.40

Mar 9.77 9.86 12.78 15.60 8.64

Apr 11.19 10.64 12.82 14.37 7.74

May 13.66 11.99 14.10 14.39 8.58

Jun 13.08 11.67 13.62 13.82 7.95

Jul 10.69 10.36 12.73 14.96 7.48

Aug 11.25 10.67 12.73 13.90 7.58

Sep 12.51 11.36 13.37 13.71 7.76

Oct 12.16 11.17 13.06 13.42 7.75

Nov 11.36 10.73 12.40 14.05 9.09

Dec 9.75 9.85 12.10 14.42 9.40

Average 11.30 10.70 12.82 14.35 8.42

Std. Dev. 1.31 0.72 0.64 0.61 0.80

0

5

10

15

20

25

30

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Moisture Content (%)

Chicago

San Antonio

Oklahoma City

Atlanta

Reno

Figure 26. Monthly variation for well-graded silty gravel (GW–GM) in five U.S. cities. 

B.2.1.2.4 AASHO Road Test

The model was evaluated using historical weather data from the NCDC and soil data from the American 

Association of State Highway Officials (AASHO) road test.(49,50,51) The pavement in loop 1 (untrafficked 

control lanes) was used for the analysis. Three layers of soil were compacted beneath the pavement. 

These are referred to as the embankment, subbase, and base layers. Published average spring and summer 
93 

moisture contents from the road test were compared to the results from the model.(51) Some problems 

may have occurred in estimating the parameters needed by the model from the given soil data. Table 25 

shows the gradation for each soil layer. 

Table 25. Gradation for AASHO road test soils.(50)

% Passing Embankment Subbase Base 

3.8 cm 100 100 100

2.5 cm 100 100 90

1.9 cm 100 96.9 81

1.3 cm 100 89.7 68

No. 4 99 71.2 48

No. 10 96.8 – 35

No. 40 91 27 20

No. 60 87.7 – –

No. 100 – – 13.5 

No. 200 80.6 7.5 10

To run the model, soil parameters were estimated from the gradation and other data included in the 

AASHO road test reports.(50,51) The gradation was used to determine the soil type and the corresponding 

default values included with the model were then used. Table 26 gives the actual values used in the 

model. 

Table 26. Soil parameters for AASHO road test soils. 

Property Embankment Subbase Base 

Soil class CL SW–SM GW–GM 

%Clay 81 7 10 

w(PL) – w(sat) 8.4 0.5 0.6 

w(sat) 24.9 7.5 7.6 

Plastic limit 16.5 7 7 

Liquid limit 29.4 10 9 

Plasticity index 13.6 3 2 

Suction(PL) 3.2 2.4 2 

Gs 2.71 2.65 2.65 

Paved shoulder (Y/N) YYY

Figure 27 compares the predicted moisture content using the aforementioned soil data and average rainfall 

totals from the NCDC and the measured values during the AASHO road test. The predicted 

measurements were typically within 2 to 3 percent in moisture content from the measured values. The 

lack of rainfall data from the time of measurement and error in the estimated soil properties could lead to 

deviation from the measured values. 
94 

0

2

4

6

8

10

12

14

16

18

20

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

Month

Moisture Content (%)

Embankment (Predicted)

Subbase (Predicted)

Base (Predicted)

Embankment (Measured) 

Base (Measured)

Subbase (Measured)

Figure 27. Comparison of predicted and measured values from the AASHO road test. 

B.2.1.2.5 LTPP Sites

The model also was evaluated using soil and weather data from DataPave 2.0, Beta Version (April 1999) 

and compared with moisture contents calculated in a FHWA time-domain reflectometry study.(52,53) The 

sites used for this purpose were in Texas (48–1068) and Maine (23–1026). Table 27 gives the climatic 

data for each site. 

Table 27. Climatic data for LTPP sites. 

Location THMI Moisture Winter Temperature

Texas 10 Moderate Warm

Maine 80 Wet Cold

As for the AASHO road test analysis, some soil properties had to be estimated from the given data. 

Missing soil data from the LTPP database had to be estimated to run the model. Soil types were recorded 

according to the AASHTO classification and had to be correlated to the Unified Soil Classification 

system to obtain certain properties. Figures 28 and 29 compare the predicted moisture contents and the 

values obtained from the FHWA study for the sites in Texas and Maine, respectively. The values from 

the FHWA study had to be estimated from charts and seemed to have questionable reliability. 
95 

0

5

10

15

20

25

30

Jan

Feb

Mar

Apr

May

June

JulyAugSep

Oct

NovDec

Month

Moisture Content (%)

Subgrade

Subbase

LTPP Value for Subbase

Figure 28. Texas LTPP site comparison. 

The subgrade for the Texas site is a lean clay (CL, A–7–6) and the subbase is a well-graded silty gravel 

(GW–GM, A–2–4). For this location, the moisture content prediction compared very well with the data 

from the FHWA study, although no data for the subgrade was found in the database. 

0

2

4

6

8

10

12

14

16

18

20

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

Month

Moisture Content (%)

Subgrade

Subbase

LTPP Values

Figure 29. Maine LTPP site comparison. 
96 

The Maine site has a lean silty soil (ML, A–4) in the subgrade and a well-graded silty gravel (GW–GM, 

A–1–A) in the subbase. The model predicted the subgrade to be saturated throughout the year and the 

subbase to be saturated from March to September. The saturated water content was an estimated 

parameter for these soils, which signals the need for quality soil property assumptions to ensure the 

reliability of the model. 

B.2.1.2.6 Summary and Conclusions

This model appears to be able to predict monthly moisture content based on a few simple assumptions 

regarding THMI, %Clay, and presence of paved shoulders. Since the model is fairly simple, estimated 

soil and weather parameters can directly affect the outcome and accuracy of the model, as indicated by 

the Maine LTPP site comparison. The following trends were noticed from evaluating the model and 

should be noted before the model is used further: 

• Changing reference suction procedures due to changes in THMI does not greatly affect the 

moisture content calculation. 

• Paved shoulders reduce variability in moisture content. 

• Moisture content variability is related to clay content and rainfall. 

• Average moisture content is related to THMI and rainfall. 

The following items are not included in the model and can affect the moisture conditions beneath 

pavements: 

• Surface infiltration through the pavement layers. 

• Varying drainage conditions. 

• Water table location. 

• Layer thicknesses. 

• Initial (compacted) moisture content. 

• Intensity of rainfall. 

• Horizontal and vertical variation of moisture content within layers. 

• Freezing and thawing. 

B.2.2 Long-Term Materials Properties Models 

B.2.2.1 PCC Strength and Stiffness 

Mechanical properties used in HIPERPAV II for long-term PCC characterization include modulus of 

elasticity and any of the following three strengths: tensile, flexural (modulus of rupture), or compressive. 

During the pavement life, the PCC slab is exposed to various stresses, such as curling and warping 

stresses, thermal axial stresses, and wheel load stresses. In the long term, one of the major failure modes 

is cracking due to fatigue. This generally has been found to be a function of the tensile stress to strength 

ratio at the bottom of the layer, implying that tensile strength is a significant characterization property. 

Unlike most concrete structures, JPCP does not rely on steel to withstand tensile stresses and is, therefore, 
97 

typically designed using a specified tensile strength. Because concrete is much weaker in tension than in 

compression, tensile strength is the most critical strength characteristic. 

The elastic modulus is an estimate of the slope of the stress-strain curve in the elastic region and a good 

indicator of the overall structural stiffness of the concrete. Because stresses and strains are related 

through the elastic modulus under assumptions of linear elasticity, it is important that this property be 

characterized. The model incorporated in HIPERPAV II is described in reference 54. 

The following test methods are used to characterize PCC strength and stiffness. 

• Splitting tensile strength (fST): ASTM C 496. 

• Modulus of rupture (fR) : ASTM C 78 (third point loading). 

• Compressive strength (fc): ASTM C 39. 

• Modulus of elasticity (Ec): ASTM C 469. 

B.2.2.1.1 Relationship between Modulus of Rupture (fR) and Splitting Tensile Strength (fST)

In this section, recommended relationships between the different PCC pavement (PCCP) strength test 

methods are presented. 

Melis et. al investigated the (fST/fR) ratio with different mix properties that are representative of concretes 

normally used in concrete pavements in Texas.(55) Altogether, 720 beams and 1260 cylinders were tested 

during this study. For this study, centerpoint loading according to ASTM C 293 was used to determine 

the rupture modulus of the concrete. Hence, all the correlations with regard to the flexural strength 

determined in this study will have to be converted to incorporate the loading configuration’s effect on the 

tested concrete strength. The correlation between the splitting tensile and flexural strengths were 

determined for different concrete mixes, and the following mix variables were investigated: 

• Cement factor: 279 kg/m3

, and 335 kg/m3. 

• Cement type: Type I, II, and III. 

• Air content: 1–3 percent, 4–6 percent, and 8–10 percent. 

• Coarse aggregate type: River gravel and limestone. 

• Coarse aggregate size: Grade Nos. 2 and 5. 

• Coarse aggregate factor: 0.65, 0.75, and 0.80. 

• Admixtures: Three combinations: None, water reducer and air entrainment, 

and accelerator and air entrainment. 

• w/c: 0.4, 0.5, and 0.554. 

• Curing age: 4, 7, 28, and 56 days. 

• Slump: 0–25 mm, 25–76 mm, and 127–178 mm. 

• Curing temperature: 10 °C, 24 °C, and 38 °C. 

 

Table 28 provides a summary of the test results achieved. Based on the results summarized in table 28, it 

was concluded that the transformation equation from the centerpoint loaded modulus of rupture (fRC) to 

the splitting tensile strength should be as shown in equation 118: 
98 

(fST/fRC) ratio = 0.62 

 (118) 

Table 28. Summary of strength test results obtained by Melis et. al.(55)

Splitting Tensile 

(152-mm x 305-mm Cylinder) Modulus of Rupture 

Average 

Strength 

(MPa) 

C.V. 

( % ) 

Average 

Strength 

(MPa) 

C.V. 

( % ) 

(fST/ fRC)

Ratio 

4 days 2.69 6 4.34 6 0.62 

7 days 2.86 6 4.62 6 0.62 

28 days 3.24 6 5.31 6 0.62 

56 days 3.52 6 5.38 5 0.66 

Average 2.86 6 4.59 6 0.62 

Melis et. al made the following final conclusions and recommendations based on their test results(55) (pp. 

75–76): 

• “The splitting tensile test is an effective test method for estimating the tensile strength of 

concrete. The cylinders associated with the splitting tensile test are easier to handle than 

those specimens used for the flexural beam test.” 

• “The variability and dispersion of the results from the 152-mm by 304-mm cylinder 

specimens tested by the splitting tensile test method did not differ significantly from the 

variability and dispersion of those from the flexural beam test method.” 

The recommendation from Melis et al. was based on centerpoint-loaded flexural beams, and to use their 

conversion formula, a conversion between the third point and centerpoint-loaded flexural specimens are 

required. Carrasquillo and Carrasquillo performed a study with more than 700 beam specimens cast from 

14 different mixes to investigate the use of centerpoint loading versus the third point loading in 

determining the flexural strength of concrete.(56)

The correlation between a specimen loaded at its center as opposed to its third point, for coarse aggregate 

sizes normally used in concrete pavement construction, were determined to be as shown in equation 119: 

fR = 0.864 x fRC

(119) 

The relationship found above is also of the same order of magnitude with earlier findings from 

Kellermann, which concluded that the third point loading strength of a beam is about 88 percent of that 

found when it is loaded at its centerpoint.(57) Based on the fact that the tests performed by Carrasquillo 

and Carrasquillo were done more recently on typical concrete mix designs used for concrete pavements, it 

is reasoned that their conversion between the two loading configurations should be used. 

Based on the results obtained by Carrasquillo and Carrasquillo, the conversion presented in equation 118 

can be modified to account for the reduced flexural strength obtained when the third point loading 

configuration is used as opposed to the centerpoint loading configuration. Using the conversion that the 
99 

third point flexural strength is 86.4 percent of the centerpoint loading, the following ratio (equation 120) 

between the splitting tensile strength and the third point-loaded modulus of rupture can be derived: 

(fST/fR) ratio = 0.72 

 (120) 

B.2.2.1.2 Relationship between Modulus of Rupture (fR) and Compressive Strength (fc)

The fairly common relationship, shown in equation 121, between the modulus of rupture and compressive 

strength recommended by ACI is:(58)

R c f = 0.7 f ' (in MPa) (121) 

However, it has been shown that the ACI equation provides a lower bound estimate (5th percentile) of the 

flexural strength; on the conservative side when designing reinforced concrete structures against cracking. 

It is not appropriate to use the ACI equation, therefore, when a conversion between average pavement 

strength is necessary. It also has been recommended that the relationship between the compressive 

strength and modulus of rupture is better predicted with expressions as a function of (f'c

2/3) as compared to 

those expressions as a function of (f′c

1/2).(59)

Raphael investigated the relationship between the flexural and compressive strength of concrete.(60) In 

this study, 12,000 individual test results gathered by 4 independent researches were investigated together 

with the authors’ own test results. The regression analysis that best fit the data can be seen in figure 30, 

and was determined to be, as shown in equation 122: 

( )( 2/ 3)

2.3 R C f = ⋅ f (in psi, 1 psi = 6.89 kPa) (122) 
100 

0 1000 2000 3000 4000 5000 6000 7000

900

800

700

600

500

400

300

200

100

0

Modulus of Rupture (psi)

Compressive Strength (psi) (MPa)

7 14 21 28 35 42 49

(MPa)

6.3

5.6

4.9

4.2

3.5

2.8

2.1

1.4

.7

0 1000 2000 3000 4000 5000 6000 7000

900

800

700

600

500

400

300

200

100

0

Modulus of Rupture (psi)

Compressive Strength (psi) (MPa)

7 14 21 28 35 42 49

(MPa)

6.3

5.6

4.9

4.2

3.5

2.8

2.1

1.4

.7

Figure 30. Comparison of test results with the correlation proposed in equation 122.(60) 

In Texas, 306 compressive and 306 flexural test were performed on concrete specimens made from 5 

different pavement mix designs. Two different aggregate types were used for these projects—limestone 

and river gravel. The relationship between the compressive and flexural strength as presented in equation 

123 was determined to provide the best fit, and a r2 value of 0.79 was obtained. 

( ) (2/ 3)

2.28 R C f = ⋅ f (in psi, 1 psi = 6.89 kPa) (123) 

Note that equations 122 and 123 are nearly identical and that they were developed from independent test 

results. Figure 31 shows the comparison of the equation developed by Raphael (equation 122) with 

regard to the test results measured in Texas. This figure demonstrates that Raphael’s equation provides a 

good fit for the test data. This figure further shows the conservative nature of the ACI equation with 

regard to estimating the concrete’s modulus of rupture. Based on the data presented in this section, it is 

recommended that equation 122 be used to describe the relationship between flexural and compressive 

strength. 
101 

0

100

200

300

400

500

600

700

800

900

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Compressive Strength (psi)

Modulus of Rupture (psi)

Raphael's Relationship

ACI Relationship

TxDOT QC/QA Projects

(MPa)

7 14 21 28 35 42 49 56 63 

(MPa)

6.3

5.6

4.9

4.2

3.5

2.8

2.1

1.4

.7

Figure 31. Modulus of rupture versus compressive strength for Texas data. 

B.2.2.1.3 Relationship between Modulus of Elasticity (Ec) and Compressive Strength (fc)

The well established relationship between modulus of elasticity (Ec) and compressive strength (fc) as 

recommended by the ACI will be used in this project. The conversion is shown in equation 124, and it 

can be seen that it is a function of the unit weight of the concrete. As the coarse aggregate accounts for 

50–70 percent of the concrete by volume, the unit weight of the mix is determined mostly by the type of 

aggregate used in the mix. 

1.5 '

c c 0.043 c E = w ⋅ f (124) 

where, 

 Ec = modulus of concrete in MPa and 

wc = unit weight of concrete in kg/m3

. 

Note that equation 124 is only valid for values of wc between 1500 to 2500 kg/m3

. To complete the 

conversion, the unit weight of the concrete must be determined. Popovics provides the following 

simplified equation (equation 125) to estimate the concrete unit weight.(61)

w =16.02⋅(SG(45 − 0.6Air)+ 33) c (125) 

where, 

 wc = unit weight of concrete in kg/m3

, 

SG = average specific gravity of aggregate, and 
102 

Air = percent air content. 

The average specific gravity of aggregate depends on the specific gravity of the mineral of which the 

aggregate is composed and also the amount of voids. The average specific gravity for different natural 

aggregates is presented in table 29.(62)

Table 29. Specific gravities for different aggregate types.(62)

Aggregate Type Specific Gravity 

Limestone 2.66 

Sandstone 2.69 

Granite 2.69 

River gravel 2.72 

Basalt 2.80 

Based on a typical air content of 4 percent and the specific gravities listed in table 29, the unit weights of 

the different aggregate types are as presented in table 30. 

Table 30. Specific unit weights for different aggregate types.(62) 

Aggregate Type Unit Weight (wc) (kg/m3) 

Limestone 2344 

Sandstone 2365 

Granite 2365 

River gravel 2385 

Basalt 2440 

B.2.2.1.4 Models for Characterization of Long-Term Concrete Properties

The long-term model forms recommended in the CEB-FIP Model Code 1990 are used HIPERPAV II.(54) 

The equations in the model apply to concrete with normal weight aggregates with no appreciable amount 

of entrapped air other than intentionally entrained air. 

The model calculates the values for strength and elastic modulus relative to the desired 28-day value. 

Application of the equations provides reasonable values for ages beyond 28 days. Figure 32 shows the 

curves for tensile strength and elastic modulus from 0 to 20,000 days (50 years) based on 28-day values 

of 700 psi for tensile strength and 4000 ksi for elastic modulus, reasonable 28-day values for a concrete 

pavement. Using the CEB-FIP model, there is a 23 percent gain in tensile strength from 28 days to 3 

years. Elastic modulus increases 11 percent during the same time period. After 50 years, the gains are 27 

percent and 13 percent for tensile strength and elastic modulus, respectively, over the 28-day values. 
103 

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1 10 100 1,000 10,000 100,000

Age of PCC (days)

Tensile Strength (MPa)

-

5,000

10,000

15,000

20,000

25,000

30,000

35,000

Elastic Modulus (MPa)

Tensile Strength

Modulus

Figure 32. Tensile strength and elastic modulus values calculated using the CEB-FIP equation. 

The development of strength with time depends on the type of cement, temperature, and curing 

conditions. The models assume a mean curing temperature of 20 oC and curing in accordance with 

International Organization for Standardization (ISO) 2736/2. Equation 126 is used: 

f (t) f (28) (t) t = t β (126) 

where, 

 ft(t) = the tensile strength at time t, 

ft(28) = the desired 28-day tensile strength, and, as shown in equation 127, 

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = −

1/ 2

1 /

28 ( ) exp 1

t t

β t s

 (127) 

where, 

 s = coefficient that depends on the type of cement, 

 0.20 for rapid hardening high strength cements, 

 0.25 for normal and rapid hardening cements, and 

 0.38 for slowly hardening cements, 

t = time in days, and 

t1 = 1 (for 1 day). 
104 

CEB-FIP recommends that the gain in other concrete properties, such as the modulus of rupture, 

compressive strength, and modulus of elasticity, be calculated using the same β(t) factor. This is the 

approach used in HIPERPAV II to determine the concrete properties at ages other than 28 days. 

The CEB-FIP model code provides general equations for concrete structures. The equations were 

developed from a compilation of available data and, as such, background and original references for the 

models are not provided in the CEB-FIP document. Although the equations are not specific to concrete 

pavements, they provide reasonable values for tensile strength and elastic modulus over the long term. 

However, the general nature of the equations dictates that the values calculated for curing times beyond 

28 days be considered as only approximations to actual values. 

The validation data for the tensile strength model was published in the ACI Materials Journal, by 

Ghafoori and Bucholc.(63) This validation shows an excellent correlation between the calculated and 

measured values with an r2 of 0.995. 

The validation data for the elastic modulus model was published in the ACI Materials Journal, by Khan, 

et al.(10) The measured values from the study at 14 different curing times during the first 100 days were 

compared to values calculated using the CEB-FIP model at the same ages and forced through the 

measured 28-day value. There was a good correlation between the calculated and measured values for 

most ages during the first 100 days of curing, with an overall r2 value of 0.92. Although there is not a 

strong correlation between the measured and calculated values for the first 10 days, HIPERPAV II uses a 

maturity-based model for this purpose.(1) 

B.2.3 Structural Models 

B.2.3.1 LTE and Midslab Stress and Deflection Models 

To predict the response of a rigid pavement due to external wheel loads accurately, a model is needed to 

assess the behavior of the pavement structure in the vicinity of discontinuities such as cracks and joints. 

This section describes the theoretical LTE model for both doweled and nondoweled JCP, and the midslab 

stress and deflection prediction models used along with the LTE model. These models were incorporated 

into HIPERPAV II. 

The transfer of a wheel load across joints must be considered when mechanistically modeling the 

performance of a JCP. The LTE characterizes how traffic wheel loading is transferred from one section 

of JCP to the adjacent section. For a nondoweled JCP joint, load transfer can be attributed solely to 

aggregate interlock. If dowels are used, then both the dowels and the aggregate interlock contribute to the 

LTE of the joint. The theoretical LTE model presented here characterizes the load transfer across a joint 

as either a deflection transfer (LTEδ), or as a stress transfer (LTEσ). 

If the deflection LTE of a joint is 100 percent efficient, both slabs will deflect the same amount. This is 

illustrated in figure 33, where both slabs deflect the same amount (δ/2). 
105 

δ/2 δ/2

JCP

Wheel

Dowel

Figure 33. Schematic of deflection load transfer (LTEδ) for a doweled JCP. 

For the stress LTE (LTEσ), the stress in the pavement due to wheel loading is transferred across the joint. 

The following sections present the theoretical equations that can be used to calculate LTE for doweled or 

nondoweled sections of JCP. The model is based primarily on work conducted by Westergaard.(64,65) 

This model calculates LTE immediately after construction. The effect of repetitive loading on the joint 

and how this influences the LTE with regard to wearout and dowel looseness is discussed in subsequent 

sections. 

B.2.3.1.1 Model Formulation

The following sections describe the detailed formulation of the LTE model. To present this formulation 

in a logical and straightforward manner, the model is divided into the following calculation components: 

• Dimensional parameters. 

• Dowel influence parameters. 

• Aggregate interlock parameters. 

• Joint stiffness parameters. 

• Free edge deflection. 

• Free edge stress. 

• Unloaded edge deflection. 

• Unloaded edge stress. 

• Loaded edge deflection and stress. 

• LTE parameters. 

The dimensional parameters affect all of these components directly, except for the loaded stress and 

deflection, and the LTE, which are affected indirectly by these parameters. The remaining nine 

components work linearly, as illustrated in figure 34. 
106 

Dowel

Influence

Aggregate

Interlock

Joint

Stiffness

Free Edge

Deflection

Free Edge

Stress

Unloaded Edge

Deflection

Unloaded Edge

Stress

Loaded Edge

Defl. and Stress

Load Transfer Efficiency 

(LTE)

Figure 34. Schematic of LTE model logic. 

B.2.3.1.2 Dimensional Parameters

These models identify dimensional parameters that are used in the majority of the remaining models. The 

first variable is the radius of the contact area (a). It is defined in equation 128 from basic geometry as:(64)

pt

P

a

π =

 (128) 

where, 

 a = radius of the contact area (m), 

P = wheel load (N), and 

pt = tire pressure (MPa). 

The radius of relative stiffness (l) of the pavement system is defined in equation 129 as follows:(64)

( ) 4 2

3

12 1 μ k

E h l

c

c

− =

 (129) 

where, 

 l = radius of relative stiffness (m), 

Ec = PCC elastic modulus (MPa), 

h = PCC slab thickness (m), 

μc = PCC Poisson’s ratio (unitless), and 

k = slab support reaction modulus (MPa/m). 

A number of the following formulae will use the dimensionless ratio of these two parameters. 

B.2.3.1.3 Dowel Influence Parameters

To determine the influence of dowels on the overall load transfer, a model based on the theory of 

Timoshenko and Lessels is used.(66) A summary of this theory can be found in a subsequent ACI 

publication.(67) 
107 

A number of variables are required for this characterization. The first is the bending moment of inertia 

(ID) of the dowel. This is defined in equation 130 as:(68)

64

4

D

DI πφ

=

 (130) 

where, 

 ID = bending moment of inertia of a circular dowel (m4

), and 

φD = diameter of the dowel (m). 

The cross-sectional area of a circular dowel (AD) is defined in equation 131 as:(68)

4

2

D AD

πφ

=

 (131) 

where, 

 AD = cross-sectional area of the dowel (m2). 

An adjustment is made of the cross-sectional area to account for its use in shear calculations.(69) The 

result is an effective cross-sectional area (ADz), defined in equation 132 as: 

ADz 9AD = 0. (132) 

where, 

 ADz = effective cross-sectional area of the dowel (m2), and 

AD = cross-sectional area of the dowel (m2) from equation 131. 

The shear modulus of the dowel bar (GD) can possibly be a user input. However, it is more practical to 

estimate this value based on the assumption that it is a homogeneous, isotropic material, as shown in 

equation 133:(68)

2(1 ) D

D

D

E G

+ μ =

 (133) 

where, 

 GD = shear modulus of the dowel (MPa), 

ED = elastic modulus of the dowel (MPa), and 

μD = Poisson’s ratio of the dowel (unitless). 

This formula should not be used when the dowels are constructed with anisotropic materials, such as 

fiberglass. 

To calculate the contribution of dowel stiffness to the LTE, five additional parameters must be calculated. 

The first is a correction factor for deep-beam shear deformation (φ), defined in equation 134 as:(69)

2

12

G A w

E I

D Dz

D D φ =

 (134) 
108 

where, 

 φ = deep-beam shear deformation correction factor (unitless), 

ID = bending moment of inertia of a circular dowel (m4

), from equation 130, 

GD = shear modulus of the dowel (MPa), from equation 133, 

ADz = effective cross-sectional area of the dowel (m2), from equation 132, and 

w = joint opening (m). 

Secondly, the relative stiffness (or characteristic) of the dowel-concrete system (β) is calculated in 

equation 135 as:(69)

4

4 D D

D D

E I

K φ β =

 (135) 

where, 

 β = characteristic of the dowel-concrete system (m-1), and 

KD = effective modulus of dowel support (MPa/m). 

The shear stiffness of the dowel (C) is then defined in equation 136 as:(69)

(1 ) 3 +φ = w

E I C D D

 (136) 

where, 

 C = dowel (beam) shear stiffness (N/m), and 

φ = deep-beam shear deformation correction factor (unitless), from equation 134. 

The dowel-concrete interaction parameter (DCI) is then calculated in equation 137 as:(69)

w

E I DCI D D

β

β

+ = 2

4 3

 (137) 

where, 

 DCI = dowel-concrete interaction parameter (N/m), and 

β = characteristic of the dowel-concrete system (m-1), from equation 135. 

Finally, the dowel shear stiffness (D′) is calculated in equation 138 as:(69)

DCI C

D

12

1 1

1

+

′ =

 (138) 

where, 

 D′ = dowel shear stiffness (N/m), 

DCI = dowel-concrete interaction parameter (N/m), from equation 137, and 

C = dowel (beam) shear stiffness (N/m), from equation 136. 
109 

B.2.3.1.4 Aggregate Interlock Parameters

To characterize the joint stiffness contribution due to aggregate interlock, a new model has been 

developed. This model is based on data collected by the Portland Cement Association (PCA) on a 

controlled load transfer experiment.(70) 

The LTE model described here was employed in developing the new aggregate interlock model. To 

accomplish this, the agg/kl parameter (to be described) was “solved” as an unknown variable. The 

remaining (known) variables first were fixed, and the agg/kl parameter was solved for a known (reported) 

joint transfer efficiency (JTE). The dowel and joint opening variables were not needed in this analysis, 

and the remaining known variables are given in table 31. 

Table 31. LTE model variables used in developing the aggregate interlock model.(70)

Variable Description Units Value(s) 

Ec PCC elastic modulus MPa 30,337 *1

μc PCC Poisson’s ratio none 0.15 *2

H PCC slab thickness mm 178 and 229 

tsaw Sawcut depth mm 0 

P Wheel load N 40,034 

pt Tire pressure MPa 0.31 *3

K Slab support reaction modulus MPa/m 24.2 (clay) 

39.4 (sand-gravel subbase) 

122.7 (cement-treated subbase)

Notes: 

*1 – PCC modulus estimated from given compressive strength of 41.4 MPa 

*2 – Assumed 

*3 – Calculated from given load radius of 203 mm 

JTE is a parameter that describes the percent of a load that is transferred from a loaded slab to an 

adjoining unloaded slab through load transfer. In the case of this experiment, aggregate interlock was the 

only mechanism. Additional information on this parameter will be given in a subsequent section. For the 

PCA experiment, JTE results for five combinations of the inputs in table 31 were reported. Within these 

five combinations, results for a number of crack openings were given. In total, 15 combinations of crack 

opening, slab thickness, and k-value were tested. From these combinations, agg/kl values were 

backcalculated using the LTE model. The results from these backcalculations are given in figure 35. 
110 

0.1

1

10

100

0 20 40 60 80 100

Joint Transfer Efficiency (%)

Dimensionless Aggregate Interlock (agg/kl ) Figure 35. Relationship between the calculated agg/kl and measured JTE. 

As can be seen from figure 35, the relationship between these two variables is quite pronounced. The 

next step in the development of an aggregate interlock characterization model was to identify a 

relationship between the backcalculated agg/kl values and the measured crack opening. Figure 36 

illustrates the results of this comparison. 

0.1

1

10

100

1000

0 0.5 1 1.5 2 2.5

Crack Opening (mm)

Dimensionless Aggregate Interlock (agg/kl)

229 mm data

178 mm data

229 mm model

178 mm model

Figure 36. Relationship between measured crack opening and the calculated agg/kl. 
111 

From figure 36, two distinct relationships were identified corresponding to the two slab thicknesses used 

in the experiment. On a semilog scale, the relationships appear to be linear, and the two trends appear to 

be roughly parallel. As a result, a simple model form was selected with an exponential base, a constant 

slope, and a variable intercept. The final model is of the form shown in equation 139: 

w e

kl

agg −1.5 = γ

 (139) 

where, 

 agg/kl = the dimensionless aggregate interlock parameter (unitless), 

γ = aggregate interlock model intercept (unitless), defined below, 

e = base of natural logarithm (≈ 2.71828...), and 

w = crack opening (mm). 

Through calibration, the aggregate interlock model intercept (γ from equation 139) for the two known 

thicknesses was found to be 122 for the 229-mm slabs, and 37 for the 178-mm slabs. Based on 

engineering judgment, it is assumed that this intercept value would yield zero agg/kl as the thickness 

decreased in an exponential form and would increase linearly after an effective slab thickness of 178 mm. 

As a result of this assumption, the equations 140 and 141 were derived for the prediction of the intercept 

value as a function of the intact slab thickness (defined as the slab thickness minus the sawcut depth): 

For h – tsaw < 178 mm: 

6 3.5309 1.388 10 ( ) saw = ⋅ h − t − γ (140) 

For h – tsaw > 178 mm: 

γ = 2.425⋅(h − tsaw ) − 309 (141) 

where, 

 γ = aggregate interlock model intercept (unitless), 

h = PCC slab thickness (mm), and 

tsaw = sawcut depth (mm). 

This model should be considered preliminary. One inherent deficiency in the model is the lack of a larger 

factorial of data for calibration. It is recommended that additional data be collected to conduct a more 

refined calibration. Subsequently, the model should be validated using an independent data set. 

Although not required in the subsequent formulation, the variable defining the aggregate interlock (agg) 

can be calculated from the agg/kl value by simply multiplying by the slab support modulus (k) and by the 

radius of relative stiffness (l) as shown in equation 142: 

kl

kl

agg agg =

 (142) 

where, 

 agg = aggregate interlock (MPa), 
112 

 agg/kl = the dimensionless aggregate interlock parameter (unitless), 

k = slab support reaction modulus (MPa/m), and 

l = radius of relative stiffness (m), from equation 129. 

B.2.3.1.5 Joint Stiffness Parameters

To derive a common method to include the impacts of both dowels and aggregate interlock, a joint 

stiffness parameter is calculated. The joint stiffness parameter, or J value, is employed directly in a 

continuation of Westergaard’s formulation for load transfer developed by Skarlatos, and reported 

subsequently by Ioannides and Hammons.(65,71,72) 

For purposes of this model, the contribution to joint stiffness due to the presence of dowels (JD) is defined 

in equation 143:(69)

s kl

D J

D

D

' =

 (143) 

where, 

 JD = dimensionless joint stiffness due to dowels (unitless), 

D′ = dowel shear stiffness (N/m), from equation 138, 

sD = dowel spacing (m), 

k = Slab support reaction modulus (MPa/m), and 

l = radius of relative stiffness (m), from equation 129. 

The contribution of aggregate interlock to joint stiffness is simply defined as agg/kl, defined previously in 

equation 139. For nomenclature purposes, this variable is redefined in equation 144: 

kl

agg J agg =

 (144) 

where, 

 Jagg = dimensionless joint stiffness due to aggregate interlock (unitless), and 

 agg/kl = the dimensionless aggregate interlock parameter (unitless), from equation 139. 

The sum of these two parameters is the overall joint stiffness (J), which is defined in equation 145: 

D agg J = J + J (145) 

where, 

 J = overall dimensionless joint stiffness (unitless), 

JD = dimensionless joint stiffness due to dowels (unitless), from equation 143, and 

Jagg = dimensionless joint stiffness due to aggregate interlock (unitless), from 

equation 144. 

B.2.3.1.6 Free Edge Deflection 

The free edge deflection for a JCP is defined as the critical concrete deflection induced by a wheel load 

when applied on a theoretically long pavement edge with no adjoining slab. This is illustrated graphically 

in figure 37. This stress is commonly calculated using Westergaard’s classical formulation.(65) For 
113 

purposes of this model, a modified form is adopted here that has been enhanced by Ioannides and 

Hammons.(72) These authors have revisited the Westergaard solutions for pavement deflections and 

stresses, and have enhanced them using sophisticated numerical methods that were not available when the 

original solutions were developed. 

Free Edge

δf

Figure 37. Free edge loading of JCP. 

For edge deflections, a dimensionless free edge deflection ( * δ f ) is calculated as shown in equation 146: 

2

3 4 5

* 0.5 ⎟

⎠

⎞ ⎜

⎝

⎛ = − +

l

a B

l

a δ f B B

 (146) 

where, 

 * δ f = dimensionless free edge deflection (unitless), 

B3,B4,B5 = Westergaard coefficients for free edge deflection (unitless), defined below, 

a = radius of the contact area (m), from equation 128, and 

l = radius of relative stiffness (m), from equation 129. 

The three Westergaard coefficients (B3, B4, and B5) are defined in equations 147, 148, and 149: 

( ) 2 312 1

2 1.2

c

c B

μ

μ

−

+ =

 (147) 

( ) B B 4μ c 0.76 0. 4 = 3 + (148) 

3

2

4

5 2B

B B =

 (149) 

where, 

 B3,B4,B5 = Westergaard coefficients for free edge deflection (unitless), and 

μc = Poisson’s ratio of the PCC. 

The free edge deflection (δf) can then be calculated from the dimensionless free edge deflection ( * δ f ) as 

shown in equation 150: 
114 

2

*

kl

f P

f

δ

δ =

 (150) 

where, 

 δf = free edge deflection (m), 

* δ f = dimensionless free edge deflection (unitless), from equation 146, 

P = wheel load (m), 

k = slab support reaction modulus (MPa/m), and 

l = radius of relative stiffness (m), from equation 129. 

B.2.3.1.7 Free Edge Stress

The free edge stress is calculated in a manner similar to that of the free edge deflection. A dimensionless 

free edge stress ( * σ f ) is first calculated in equation 151 as the sum of two components: 

* * * σ f = σ +σ c (151) 

where, 

 * σ f = dimensionless free edge stress (unitless), 

* σ = first component of the dimensionless free edge stress (unitless), defined below, 

and * σ c = second component of the dimensionless free edge stress (unitless), defined 

below. 

The two components of the dimensionless stress function are calculated in equations 152 and 153: 

( )

( ) ⎥

⎦

⎤ ⎢

⎣

⎡ − ⎟ +

⎠

⎞ ⎜

⎝

⎛ − +

+ = 8

1 0.1159 ln

3

* 12 1 c

c

c

l

a μ

π μ

μ σ

 (152) 

( )

( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ + ⎥

⎦

⎤ ⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ − + −

+

+ =

2

* 0.9544 0.3822 1.30259 2.98398

4

3

3

12 1

l

a

l

c a

c

c

c

μ

π μ

μ σ

 (153) 

where, 

 * σ = first component of the dimensionless free edge stress (unitless), 

* σ c = second component of the dimensionless free edge stress (unitless), 

μc = Poisson’s ratio of the PCC (unitless), 

a = radius of the contact area (m), from equation 128, and 

l = radius of relative stiffness (m), from equation 129. 

The constants employed in equation 153 are based on the assumption that the Poisson’s ratio of the PCC 

is equal to 0.15. As a future enhancement to this model, it may be possible to rederive these constants for 
115 

other values of Poisson’s ratio. However, due to the overall sensitivity of this parameter, this exercise 

may be of secondary importance. 

Based on the dimensionless free edge stress, the actual free edge stress can be calculated in equation 154: 

2

*

h

f P

f

σ

σ =

 (154) 

where, 

 σf = free edge stress (MPa), 

* σ f = dimensionless free edge stress (unitless), from equation 151, 

P = wheel load (N), and 

h = PCC slab thickness (m). 

B.2.3.1.8 Unloaded Edge Deflection

The unloaded edge deflection is based on the same derivations previously described for the free edge 

deflection. In the case of the unloaded edge deflection, the value is equal to the deflection of the 

unloaded side of two adjoining slabs. Figure 38 illustrates this, where the unloaded and loaded edge 

deflections are defined graphically. 

Loaded

Deflection

δl

Unloaded

Deflection

δu

Load

Figure 38. Loaded and unloaded deflections of a JCP. 

The dimensionless unloaded edge deflection is given in equation 155: 

[ ] ( ) J

l

a

l

a u B B 10

2

3 4

* 0.008 ⎟ 1+ log ⎠

⎞ ⎜

⎝

⎛ δ = ′ − ′ +

 (155) 

where, 

 * δ u = dimensionless unloaded edge deflection (unitless), 

B′3,B′4 = Westergaard coefficients for unloaded edge deflection (unitless), defined 

below, 

a = radius of the contact area (m), from equation 128, 

l = radius of relative stiffness (m) – from equation 129, and 
116 

J = overall dimensionless joint stiffness (unitless), defined in equation 145. 

The Westergaard coefficients for this equation are defined in equations 156 and 157: 

( )

4.6516 1.8210

0.6367 log10 1

3 +

− + ′ = J

J J B

 (156) 

[ ( ) ] 0.24 B4

′ = B3′ 0.6984 + 0.0441log10 1+ J − 0.00655J (157) 

where, 

 B′3,B′4 = Westergaard coefficients for unloaded edge deflection (unitless). 

The unloaded edge deflection (δu) can then be calculated from the dimensionless unloaded edge 

deflection ( * δ u ) in equation 158: 

2

*

kl

uP u

δ δ =

 (158) 

where, 

 δu = unloaded edge deflection (m), 

* δ u = dimensionless unloaded edge deflection (unitless), from equation 155, 

P = wheel load (N), 

k = slab support reaction modulus (MPa/m), and 

l = radius of relative stiffness (m), from equation 129. 

B.2.3.1.9 Unloaded Edge Stress

The dimensionless unloaded edge stress can be calculated in equation 159: 

( )

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ ⎟ + ′ ⎠

⎞ ⎜

⎝

⎛ ′ − ′ − =

2

1 2 9

2

* 0.5 24 1

l

a B

l

a B B c

u π

μ σ

 (159) 

where, 

 * σ u = dimensionless free edge stress (unitless), 

B′1,B′2,B′9 = Westergaard coefficients for unloaded edge stress (unitless), 

μc = Poisson’s ratio of the PCC (unitless), 

a = radius of the contact area (m), from equation 128, and 

l = radius of relative stiffness (m), from equation 129. 

The Westergaard coefficients for this equation are defined in equations 160, 161, and 162: 

( ) 1

0.00773 0.03360 0.03316 0.07205log 1 1 10 +

− ′ = + + +

J

J B J

 (160) 
117 

4.209

1

2 1

0.000149 0.08281 0.4790 ⎟

⎠

⎞ ⎜

⎝

⎛ ′ = ′ + − J

B B J

 (161) 

[ () () J J ] B e 2 10 10 5.0908 2.2805log 0.1577 log

9

− + − ′ = (162) 

where, 

 B′1,B′2,B′9 = Westergaard coefficients for unloaded edge stress (unitless), and 

J = overall dimensionless joint stiffness (unitless), defined in equation 145. 

Based on the dimensionless unloaded edge stress, the actual unloaded edge stress can be calculated as 

shown in equation 163: 

2

*

h

uP u

σ

σ =

 (163) 

where, 

 σu = unloaded edge stress (MPa), 

* σ u = dimensionless unloaded edge stress (unitless), from equation 159, 

P = wheel load (N), and 

h = PCC slab thickness (m). 

B.2.3.1.10 Loaded Edge Deflection and Stress

The loaded edge deflection and stress can easily be derived based on the corresponding free and unloaded 

edge responses. The loaded edge deflection can be calculated as shown in equation 164: 

δ l = δ f − δ u (164) 

where, 

 δl = loaded edge deflection (m), 

δf = free edge deflection (m), from equation 150, and 

δu = unloaded edge deflection (m), from equation 158. 

The loaded edge stress can similarly be calculated as shown in equation 165: 

σ l = σ f −σ u (165) 

where, 

 σl = loaded edge stress (MPa), 

σf = free edge stress (MPa), from equation 154, and 

σu = unloaded edge stress (MPa), from equation 163. 

B.2.3.1.11 LTE Parameters

Three LTE responses can be derived from the above referenced formulation: JTE, deflection LTE, and 

stress LTE. 
118 

JTE is defined as the percent of a load that is transmitted across a discontinuity (joint) due to the load 

transfer mechanisms present. Using the derived parameters, this can be calculated in equation 166: 

l u

u JTE

δ δ

δ

+ = 2

 (166) 

where, 

 JTE = joint transfer efficiency (often reported as a percent), 

δu = unloaded edge deflection (m), from equation 158, and 

δl = loaded edge deflection (m), from equation 164. 

The JTE is the value that was reported by the PCA in the aggregate interlock experiment for which the 

new aggregate interlock model is presented.(70)

Deflection LTE (LTEδ) is the ratio of the deflections of the unloaded to the loaded slabs. It is defined 

mathematically in equation 167: 

l

u LTE

δ

δ

δ =

 (167) 

where, 

 LTEδ = deflection LTE (often reported as a percent). 

Finally, the stress LTE is similarly calculated and is defined as the ratio of the stress induced in the 

unloaded slab to the stress in the loaded slab (equation 168): 

l

u LTE

σ

σ σ =

 (168) 

where, 

 LTEσ = stress LTE (often reported as a percent), 

σu = unloaded edge stress (MPa), from equation 163, and 

σl = loaded edge stress (MPa), from equation 165. 

The relationship between the various LTE indicators is of interest. For example, it can be demonstrated 

in equation 169 that the relationship between JTE and LTEδ is: 

JTE

JTE LTE

1 0.5

0.5

− δ =

 (169) 

where, 

 LTEδ = deflection LTE (often reported as a percent), from equation 167, and 

 JTE = joint transfer efficiency (often reported as a percent), from equation 166. 

Figure 39 illustrates this relationship. It can be seen, that the relationship does falls below the line of 

equity, demonstrating the nonlinear relationship in equation 169. 
119 

0

20

40

60

80

100

0 20 40 60 80 100

Joint Transfer Efficiency (%)

Deflection Load Transfer Efficiency (%)

Line of Equality

 -

Figure 39. Relationship between JTE and LTEδ. 

As expected, the relationship between LTEδ and LTEσ is more complex. This is due to the complex 

nature of the formulation previously described. However, figure 40 illustrates that the relationship 

between these two parameters is a function of the a/l ratio, defined previously in equation 159. 

0

20

40

60

80

100

0 20 40 60 80 100

Stress Load Transfer Efficiency (%)

Deflection Load Transfer Efficiency (%)

a/l = 0.02

a/l = 0.05

a/l = 0.1

a/l = 0.2

a/l = 0.5

a/l = 1.0

Figure 40. Relationship between LTEσ and LTEδ. 
120 

B.2.3.1.12 LTE Wearout Model

The wearout model takes into account the effect of traffic loading on LTE. The wearout model is based 

on experimental deflection testing evaluation of laboratory controlled slabs subjected to loading at a joint 

capable of transferring load through aggregate interlock only.(70) 

Equation 139 models aggregate interlock at the beginning of the loading period. The LTE model depends 

on δu and δl that, in turn, depend on the joint stiffness for aggregate interlock.(73) 

Figure 41 shows the JTE results obtained from the experimental work performed by Colley and 

Humphrey as a function of loading cycles of a 4086-kg load.(70) 

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

- 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,00

0

Loading Cycles

Effectiveness (%)

Joint opening 0.6 mm

Joint opening 0.9 mm

Joint opening 1.1 mm

Joint opening 1.7 mm

Joint opening 2.2 mm

Figure 41. JTE results obtained from the experimental work performed by Colley and Humphrey 

as a function of loading cycles of a 4086-kg load.(70)

The initial JTE at the beginning of the loading period is modeled with the initial aggregate interlock 

previously developed. To model JTE as a function of loading cycles, an exponential function was fitted 

to the backcalculated agg/kl obtained for each one of the curves shown in figures 42 and 43. The 

resulting model for wearout is of the form shown in equation 170: 

N s

wear asymp init

e

kl

agg

kl

agg

kl

agg − / ⎟

⎠

⎞ ⎜

⎝

⎛ = +

 (170) 

where, 

 agg/klwear = Dimensionless aggregate interlock parameter at N loadings, 
121 

 agg/klasymptote = Dimensionless aggregate interlock parameter at an infinite number of 

loading cycles, 

 agg/klinit = Dimensionless aggregate interlock parameter at the beginning of the 

loading period, 

N = Noncalibrated cumulative traffic loading, and 

s = Shape parameter, approximately 44,000 for the 229-mm slab and 

91,000 for the 178-mm slab, on average. 

To use the above model practically, the agg/klasymptote parameter was estimated based on the 

backcalculated agg/kl values at the end of the experimental loading period from reference 70. Figure 44 

shows the resulting agg/ klasymptote as a function of joint opening for the two slab thicknesses evaluated. 

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

- 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,00

0

Loading Cycles

Effectiveness (%)

Joint opening 0.6 mm

Joint opening 0.9 mm

Joint opening 1.1 mm

Joint opening 1.7 mm

Joint opening 2.2 mm

Figure 42. Influence of joint opening on JTE, 229-mm concrete slab, 152-mm gravel subbase.(70)
122 

0

10

20

30

40

50

60

70

80

90

100

- 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000

Loading Cycles

Effectiveness, (%)

Joint opening 0.4 mm

Joint opening 0.6 mm

Joint opening 0.9 mm

Joint opening 1.1 mm

Joint opening 1.7 mm

Figure 43. Influence of joint opening on JTE, 178-mm concrete slab, 152-mm gravel subbase.(70)

0.01

0.10

1.00

10.00

100.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0

1/ Joint Opening (1/mm)

agg/kl

agg/kl asymptote (229 mm)

agg/kl asymptote (178 mm)

Exponential (agg/kl asymptote (229mm)

Exponential (agg/kl asymptote (178 mm)

Figure 44. Asymptote dimensionless joint stiffness as a function of joint opening. 

From the above data, a simple model was developed to predict the agg/klasymptote parameter as a function 

of joint opening as shown in figure 171: 
123 

w

asymptote

e

kl

agg 3.63 = ξ

 (171) 

where, 

 ξ = aggregate interlock asymptote model intercept (unitless), and 

w = joint opening (mm). 

The ξ intercept was found to depend on the slab effective thickness. The model was calibrated to have the 

same slope for both known thicknesses. This slope was assumed to have an exponential trend for h – tsaw

≤ 178 mm and increase linearly thereafter. The resulting model for the ξ intercept is shown in equations 

172 and 173: 

For h – tsaw ≤ 178 mm: 

( ) 8 6.9814 1.935 10 saw = x h − t − ξ (172) 

For h – tsaw > 178 mm: 

ξ = 0.01533(h −tsaw )− 0.092 (173) 

The data used to develop the above wearout model is based on laboratory controlled testing of 

experimental slabs. The following limitations are encountered in the application of the above model: 

• Laboratory testing subjected the slabs to more severe conditions than normally encountered 

in the field. Higher deflections were observed for the laboratory experiment than for 

pavements evaluated in the field. In addition, while the support characteristics and joint 

opening were kept constant for the loading experiment, these conditions change in the field 

with time of day and season.(70)

• Only two thicknesses were investigated. 

• The joint effectiveness results were not reported individually for the shape or hardness of the 

aggregates for the repetitive loading experiment. It is expected that differences in behavior 

would be observed for concrete with different aggregate properties as reported by Nowlen.(74)

It is therefore recognized that, although the above model provides a reasonable approach to characterizing 

LTE as a function of traffic loading and joint opening, investigation of a larger factorial of thicknesses, 

materials, and environmental conditions is required. 

B.2.4 Distress Models 

Several selection criteria were considered in selecting each individual JPCP distress model. One criterion 

included the preference for mechanistic models. Another selection criterion was that the model had been 

previously validated. Finally, the most important criterion (with respect to the HIPERPAV II effort), was 

that the model take into account early-age indicators for distress prediction such as joint opening, built-in 

curling, and/or delamination. 
124 

B.2.4.1 Faulting Without Dowels 

The faulting model for JCPs without dowels at the joints incorporated into HIPERPAV II, was developed 

using the combined Concrete Pavement Evaluation System (COPES) and Performance/Rehabilitation of 

Rigid Pavements (RIPPER) databases.(75) The pavements are subdivided by their environmental regions 

of origin in the United States (wet-freeze, wet-no freeze, dry-freeze, and dry-no freeze) and by their 

design features in table 32. 

Table 32. Distribution of pavement sections used in nondoweled faulting model.(75)

Climatic 

Region None/AGG CTB/ATB LCB PERM 

Wet-freeze 5 5 2 2 

Wet-no freeze 14 82 – – 

Dry-freeze 2 86 – – 

Dry-no freeze 3 127 14 – 

NOTE: None: no base, AGG: aggregate, ATB: asphalt-treated base, CTB: cement-treated base, 

LCB: lean concrete base and PERM: permeable stabilized or permeable nonstabilized base. 

A mechanistic-empirical faulting model has been developed for nondoweled JCPs. The faulting equation 

is provided in equation 174: 

() ()

⎥

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎢

⎣

⎡

− ⋅

⎟ + ⋅ − ⋅ − ⋅ ⎠

⎞ ⎜

⎝

⎛ +

+ ⋅ + ⋅

=

DRAIN

BTERM EDGESUP STYPE FI

OPENING DEFLAMI

FAULT ESAL

0.00891

0.00565 0.00770 0.00263

1000

0.0400

0.000038 0.01830 100 0.000619 100

*

1.9840

0.5585 1.7229

0.2500

(174) 

where, 

 FAULT = mean faulting across the transverse joint (inches), The primary reference is 

not clear in defining mean faulting across the transverse joint. However, 

because the Distress Identification Manual for the Long-Term Pavement 

Performance Project was used for performing the condition surveys in that 

study, mean faulting is understood as the average faulting for a pavement 

section at the transverse joints after a given number of ESALs,(15,72)

 ESAL = cumulative 18,000-lb equivalent single-axle loads in traffic lane (millions), 

 OPENING = average transverse joint opening of the analysis pavement section, 

computed for the maximum climatic temperature drop throughout the year 

(inches), and 

 DEFLAMI = Ioannides’ pavement corner deflection (inches) = equation 175: 

2

0.88 1.4142 1.2

l

l

⋅

⎟

⎠

⎞ ⎜

⎝

⎛ ⋅ ⋅ −

KSTAT

a

P

 (175) 

where, 

 l = radius of relative stiffness (inches), 

 P = applied wheel load (~9000 lb), 

 a = radius of applied load (~5.64 inches, assuming a tire pressure of 90 psi), 
125 

 KSTAT = modulus of subgrade reaction on top of base (psi/inch), 

FI = freezing index (degree-days), and 

 BTERM = base type factor, which equals equation 176: 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− ⋅ − ⋅

+ ⋅ + ⋅ + ⋅

OGB LCB

GB CTB ATB

ESAL

0.003714 0.006441

0.045456 0.05115 0.007279 0.003183

10 0.2076

 (176) 

where, 

 GB = variable for dense-graded aggregate base (1 if aggregate base, else 0), 

 CTB = variable for dense-graded cement-treated base (1 if cement-treated base, else 

0), 

 ATB = variable for dense-graded asphalt-treated base (1 if asphalt-treated base, else 0), 

 OGB = variable for open-graded aggregate or asphalt-treated base (1 if open-graded 

base, else 0), 

 LCB = variable for lean concrete base (1 if lean concrete base, else 0), 

 EDGESUP = index for edge support (0 if no edge support exists, else 1), 

 STYPE = index for AASHTO subgrade soil classification (0 if A–4 to A–7 or 1 if A–1 to 

A–3), and 

 DRAIN = index for drainage condition (0 if no edge subdrain exists, else 1). 

(1 inch = 25.4 mm, 1 lb = 0.454 kg, 1 psi = 6.894 KPa) 

The r2 statistic for this model is 0.81, and 398 slabs were used in its development. 

Although this model is not truly mechanistic, it does contain a number of fundamental input parameters. 

In addition, the selected model has been validated using an extensive data set. Finally, the use of joint 

opening in this model, which is considered to be an important early-age indicator for distress prediction, 

was one of the primary factors for its selection. 

B.2.4.2 Faulting of Doweled Pavements 

The faulting model for JCPs with dowels incorporated in HIPERPAV II was also developed using the 

combined COPES and RIPPER databases.(75) The distribution of these pavement sections throughout the 

United States by climatic region and by subbase type is shown in table 33. 

Table 33. Distribution of doweled pavement sections.(75) 

Climatic 

Region None/AGG CTB/ATB LCB PERM 

Wet-freeze 257 44 – 5 

Wet-no freeze 11 35 4 – 

Dry-freeze 141 10 – 1 

Dry-no freeze – – 1 1 

NOTE: None: no base course, AGG: aggregate, ATB: asphalt-treated base, CTB: cement-treated base, 

LCB: lean concrete base and PERM: permeable stabilized or permeable nonstabilized base. 

The erosion of concrete from around dowels through repeated loading contributes to faulting in doweled 

pavements. In addition, pavement curling and warping increases deflection at the joint, further stressing 
126 

the dowels. It has been recommended that the bearing stresses at the joint be less than 10.4 MPa to limit 

faulting.(64) The mechanistic-empirical faulting equation (equation 177) is given as: 

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎟ − ⋅ − ⋅ − ⋅ ⎠

⎞ ⎜

⎝

⎛

⎟ − ⋅ ⎠

⎞ ⎜

⎝

⎛ ⎟ + ⎠

⎞ ⎜

⎝

⎛ +

=

DRAIN EDGESUP STYPE KSTAT

BSTRESS AVJSPACE

FAULT ESAL

0.01868 0.00879 0.00959

100

0.1492

10

0.007353

1000

0.1204 0.04048

* 0.05911

0.3388 0.6725

0.5280

 (177) 

where, 

 FAULT = mean transverse joint faulting (inches), 

ESAL = cumulative equivalent 18,000-lb single axle loads in lane (millions), and 

BSTRESS = maximum dowel bearing stress on concrete using closed form solution (psi), 

shown in equation 178: 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⋅ ⋅

+ ⋅ ⋅ ⋅ 3 4

2

E I BETA

BETA OPENING f P T K

s

d d

 (178) 

where, 

 BETA = relative stiffness of the dowel-concrete system, 

 df = a distribution factor (included in reference 75), 

 P = applied wheel load (~9000 lb), 

 T = percent transferred load (set to 0.45), 

 I = moment of inertia of dowel bar cross section (inches4

), 

 Kd = modulus of dowel support (~1,500,000 psi/inch), 

 OPENING = average transverse joint opening (inches), 

 ES = modulus of elasticity of the dowel bar (set to 29,000,000 psi), 

 AVJSPACE = average pavement joint spacing, 

 KSTAT = effective modulus of subgrade reaction on top of the base (psi/inch), 

 DRAIN = index for drainage condition (0 if no edge subdrain exists, else 1), 

 EDGESUP = index for edge support (0 if no edge support exists, else 1), and 

 STYPE = index for AASHTO subgrade soil classification (0 if A–4 to A–7, else 1 if A–1 

to A–3). 

(1 in = 25.4 mm, 1 lb = 0.454 kg, 1 psi = 6.894 KPa) 

The r2 statistic for this model is 0.67, and 559 slabs were used in its development. 

For the case of faulting with dowels, the use of bearing stress (related to joint opening) in the above 

model was one of the primary factors for its selection. In addition, although this model is not truly 

mechanistic, it contains a number of fundamental input parameters. Another factor influencing the 

selection of this model is that it has been validated using an extensive data set. 
127 

B.2.4.3 Joint Opening Model 

The faulting models incorporated in HIPERPAV II (for both doweled and nondoweled JPCP) include 

inputs for joint opening. However, these faulting models were originally developed and calibrated based 

on a unique definition of joint opening. 

The joint opening prediction made by HIPERPAV II is based on a different approach than the FHWA 

model. The FHWA model is closed form and rather simple prediction, while the HIPERPAV II model is 

based on a more sophisticated finite-difference-based analysis. Therefore, to use the joint prediction made 

by HIPERPAV II in predicting long-term faulting, a submodel was developed to convert from the 

HIPERPAV II-predicted joint opening to the joint opening parameter used in the FHWA faulting 

model.(75) 

A parametric sensitivity analysis was performed on both the doweled and nondoweled faulting models. 

For the sensitivity analysis, joint opening was varied from 0.1 mm to 12.7 mm, and traffic loading from 0 

to 50 million 80 KN ESALs. Plots of the results are in figures 45 and 46. As expected, these figures 

show that sensitivity to the faulting prediction exists as a function of both joint opening and traffic 

loading. 

Figure 45. Sensitivity of faulting to joint opening and cumulative traffic loading for nondoweled 

JPCP (MESAL = 1,000,000 ESAL). 

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30 35 40 45 50

MESALs

Faulting (mm)

0.1 mm

0.3 mm

0.5 mm

1.3 mm

2.5 mm

5.1 mm

12.7 mm
128 

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 5 10 15 20 25 30 35 40 45 50

MESALs

Faulting (mm)

0.1 mm

0.3 mm

0.5 mm

1.3 mm

2.5 mm

5.1 mm

12.7 mm

Figure 46. Sensitivity of faulting to joint opening and cumulative traffic loading for doweled JPCP 

(MESAL = 1,000,000 ESAL). 

In the original FHWA report, joint opening is defined as in equation 179:(75)

⎟

⎠

⎞ ⎜

⎝

⎛ + ⋅ = ⋅ ⋅ ε

2

12 ALPHA TRANGE OPENING CON AVJSPACE

 (179) 

where, 

 OPENING = joint opening, in inches (1 inch = 25.4 mm), 

CON = frictional restraint adjustment factor (unitless) (0.65 for stabilized subbases, 

0.80 for aggregate subbases), 

AVJSPACE = average joint spacing in feet, (1 ft = 0.3048 m), 

ALPHA = PCC CTE in inch/inch/°F, (1 inch/inch/degree Fahrenheit (°F) = 0.56 m/m/oC ), 

TRANGE = annual temperature range in °F, (1 °F = 0.56 oC ), and 

ε = PCC drying shrinkage coefficient (in microstrains). 

Since the free strain of the PCC is defined in the last term, equation 179 can be simplified into equation 

180: 

OPENING CON AVJSPACE free = ⋅ ⋅12 ⋅ ε (180) 

The slab-base restraint model in HIPERPAV II is based on a finite-difference solution of the axial 

movement-restraint phenomenon.(1) It is currently one of the key models in predicting the critical stress in 

the concrete during the early-age period. However, this same model also can be used to predict the joint 

opening as a function of a number of variables, including those listed in table 34. 
129 

Table 34. HIPERPAV slab-base restraint model variables. 

Variable Definition Typical Value 

h PCC slab thickness 305 mm 

L Average joint spacing 4.6 m 

Ec PCC elastic modulus 27,579 MPa 

εfree Free strain 300 × 10-6 m/m 

δcrit Movement at maximum friction 0.5 mm 

Fmax Maximum friction force 27.6 KPa 

The calculation of the joint opening in HIPERPAV II is not a closed form, as is that in the FHWA model 

(shown in equations 179 and 180), therefore the formulae for its calculation are not given here for 

brevity.(1) 

Before even a cursory comparison of these two models for the prediction of joint opening, selecting 

“equivalent” inputs for the degree of slab-base restraint is required. The FHWA model includes a CON 

variable that is assigned a value of either 0.65 or 0.8, depending on the subbase type. The HIPERPAV II 

model is more sophisticated; it requires two parameters that define a bilinear relationship between the slab 

movement and corresponding force required for the movement. The intersection of the bilinear 

relationship is how the two parameters are defined. Extensive documentation on various subbase types 

was drawn upon to define equivalent values of subbase restraint that correspond to the two CON values 

given in the FHWA report. The final selection of these values, used in this analysis, is given in table 35. 

Table 35. Definition of equivalent slab-base restraint values for joint opening models. 

Subbase Type CON Value for

FHWA Model 

δcrit Value for 

HIPERPAV Model

Fmax Value for 

HIPERPAV Model

Stabilized base 0.65 0.254 mm 55.2 KPa 

Aggregate base or 

LCB with bond breaker 0.80 0.508 mm 27.6 KPa 

To compare the predictive ability of the joint opening models, a factorial was established that consisted of 

1920 combinations of the various model inputs. The variables and the ranges selected for this factorial 

are included in table 36. 

Table 36. Factorial of joint opening model inputs. 

Variable Minimum Value Maximum Value 

Slab thickness 50.8 mm 406 mm 

Average joint spacing 0.9 m 12.2 m 

PCC elastic modulus 20,700 MPa 41,400 MPa 

Free strain 50 με 2000 με

Slab-subbase restraint CON = 0.65 

δcrit = 0.254 mm 

Fmax = 55.2 KPa 

CON = 0.80 

δcrit = 0.508 mm 

Fmax = 27.6 KPa 
130 

The joint openings, using both the FHWA and the HIPERPAV II models, then were calculated for each of 

the factorial combinations. The results are given in figure 47. As can be seen in the figure, the 

predictions using the two models do not coincide. In all cases, the HIPERPAV II model predicts a greater 

joint opening than does the FHWA model. However, this is not surprising, due to the fundamental 

differences in the predictive methodology. 

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0

FHWA Model Joint Opening (mm)

HIPERPAV Model Joint Opening (mm)

Figure 47. Relationship between joint opening model predictions. 

Because the FHWA faulting model has been developed and calibrated based on a unique definition of 

joint opening, it is critical to the proper use of the model to find a relationship that can convert the 

HIPERPAV II prediction to the FHWA prediction. 

It was decided that the most practical means of implementing a submodel to convert the HIPERPAV II 

joint opening to the FHWA joint opening is by calculating a ratio between the two. A nonlinear 

regression analysis was performed on the 1920 combinations given in the last section to predict the ratio 

of the FHWA to the HIPERPAV II joint opening. The result of this regression analysis is as shown in 

equation 181: 

HP crit c

FHWA

E

F

OPENING h

OPENING 57923. 2.3010 10 0.018459 0.84241 4 max +⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − − × −

δ (181) 

Equation 181 has an r2 of 0.926 and a Standard Error of the Estimate (SEE) of 0.020. Using this 

equation, the HIPERPAV II joint openings in figure 47 were converted to their equivalent HIPERPAV II 

joint opening predictions. The results are illustrated in figure 48. 
131 

0.0

5.0

10.0

15.0

20.0

25.0

0.0 5.0 10.0 15.0 20.0 25.0

FHWA Model Joint Opening (mm)

Revised HIPERPAV Model Joint Opening (mm)

Figure 48. Relationship between revised joint opening model predictions. 

B.2.4.4 Midslab Cracking Models 

This section describes models for accumulating damage and models for predicting cracking in PCCP 

slabs. A short description also is given of three other models considered by the research team responsible 

for reference 76 in choosing appropriate fatigue damage and slab cracking models. 

B.2.4.4.1 Fatigue Damage Model

The first type of model is concrete fatigue damage resulting from load applications that induce stresses in 

the pavement slab. The four proposed models in reference 76 regarding concrete fatigue damage are 

(references 77, 78, 79, and 80 are the original sources for each of these models): 

Corps of Engineers and ERES Consultants, Inc. (ERES/COE) Model (equation 182):(77)

 

log N = 2.13 • SR-1.2

 (182) 

NCHRP 1–26 Model (equation 183):(78)

 

0.2276 5.367

0.0032

log(1 ) log

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡− − =

− SR P N

 (183) 
132 

Zero-Maintenance Model (equation 184):(79)

 

log N = 17.61 – 17.61 · SR

 (184) 

Austin Research Engineers, Inc. (ARE) Model (equation 185):(80)

N = 23,440 • SR-3.21

 (185) 

where, 

 N = number of allowable load applications, 

 SR = stress-to-strength ratio (σ/MR), 

 σ = adjusted Westergaard critical stress in psi (1 psi = 6.89 KPa), 

 MR = PCC modulus of rupture in psi (1 psi = 6.89 KPa), and 

 P = probability of failure. 

Figure 49 shows the four models’ prediction of allowable loads as a function of stress-to-strength ratio. 

The figure shows the four models above, and includes the NCHRP 1–26 model based on both 50 percent 

and 5 percent probability of failure. The comparison in reference 76 fixed the probability term in the 

NCHRP 1–26 model at 50 percent. 

The evaluation of the four models in reference 76 determined that the ERES/COE model was the best 

candidate, so it was chosen for use in the HIPERPAV II damage and cracking model. It should be noted, 

however, that the NCHRP 1–26 model is virtually identical to the chosen model when the probability 

term is set at 15 percent chance of failure, or an 85 percent reliability level. 

1.E-02

1.E+02

1.E+06

1.E+10

1.E+14

1.E+18

1.E+22

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Stress-Strength Ratio

Allowable Load Applications

ERES/COE

NCHRP 1-26 at 50 percent failure

NCHRP 1-26 at 5 percent failure

ARE: FHWA-RD-77-67

Zero-maintenance

Figure 49. Allowable loads versus stress-to-strength ratio. 
133 

The following paragraphs are taken from the discussion and critique of models in reference 76. 

ERES/COE model—this model was developed from U.S. Army Corps of Engineers data from 51 fullscale field sections. The edge load stress was calculated using H–51 program (computerized Pickett and 

Ray charts) and multiplied by 0.75 to account for the edge support in the sections. 

NCHRP 1–26 model—this model was developed using the COE and AASHO road test data. This model 

is also based on edge load stress. 

Zero-Maintenance model—this model is based on laboratory testing results of 140 beams. 

ARE model—this model was developed based on the AASHO road test data. The actual loads were 

converted to 18-kip ESALs, and the maximum midslab stresses were calculated using elastic layer theory. 

Yu et al. recognize that the first two models (ERES/COE and NCHRP 1–26) are very similar in form and 

that they give similar results at specific values of the probability term.(76) The report stated that the ZeroMaintenance model gave the most scatter, and that the ARE model gave the narrowest range of damage 

values but does not show a logical trend. Later, the report selects the ERES/COE model, stating that the 

damage results of the NCHRP 1–26 model were shifted to the left of the ERES/COE model by one 

magnitude. Results from the ERES/COE model are in a more conventional range (about 50 percent 

cracking at fatigue damage of 1.0). 

The ERES/COE model was incorporated in HIPERPAV II. This model could be changed in the future as 

new developments (such as those under the NCHRP 1–37a study) become available. 

B.2.4.4.2 Slab Cracking Model

The second model discussed in this section is the slab cracking model. Yu et al. developed a percent 

cracking model based on the accumulated damage.(76) This model was incorporated in HIPERPAV II and 

is given as equation 186: 

100

Percent Cracking =

1 + 1.41 · FD-1.66

 (186) 

where, 

 FD = accumulated fatigue damage. As shown in equation 187, 

= ∑

i

i

N

n

FD

 (187) 

where, 

 n = actual number of loads for load group i, and 

N = allowable number of loads for load group i. 
134 

In the classic damage model form, using Miner’s law, damage from individual loads is accumulated to 

produce an aggregate damage value with which the level of cracking is predicted. 

Figure 50 shows the fit of the data to the model in equation 186. As can be seen in the figure, when 

accumulated damage equals 1, the slab cracking approaches 40 percent. This is one of the reasons Yu et 

al. selected the model.(76) 

Figure 50. Fatigue cracking model with associated data.(76) 

B.2.4.4.2.1 Assumptions 

The form of the model was selected because it represents the theoretical characteristics of cracking 

progression in a PCC pavement section. Two theoretical boundary conditions are: 1) there will be 0 

percent cracking when fatigue damage = 0, and 2) 100 percent of the slabs will be cracked as fatigue 

damage approaches infinity. This form of the model and the given boundary conditions ignore the 

possibility of environment-related cracking before any traffic-related fatigue damage, and the fact that 

100 percent of the slabs may crack at a finite level of damage. 

A good aspect of the model is that it seems to have been developed using sections both with and without 

cracked slabs. Some models can only consider sections with at least some cracking, and thus do not 

properly represent all possible data points in a set of data. 

Other assumptions include the aggregate effects of curling and loading stresses and ability of the 

researchers to calculate stresses and fatigue damage accurately. The latter will be discussed in greater 

detail in the “Limitations” section below. The stress induced by traffic loads is adjusted for thermal 

curling, but other conditions such as drying shrinkage and other sources of curling and warping are not 

considered. Yu et al. state that climate can have a significant effect on cracking prediction due to the 

thermal and moisture gradients to which the slab is subjected.(76) The report references these effects, but 

other than the difference between temperature in the slab top and bottom, there is no way to account for 

these conditions. 
135 

B.2.4.4.2.2 Limitations 

There are several limitations on this model, including the use of reliability, the necessity of calculating of 

fatigue damage rather than directly measuring it, the use of regression models rather than mechanisticempirical models, and the use of the model without the curling component. 

The first limitation mentioned above, the fact that reliability is not considered directly, is a drawback that 

the NCHRP 1–26 model does not have. In that model, as mentioned previously, the probability of failure 

is specifically included. This probability of failure can be considered analogous to the inverse of the 

probability of success. Given a 50 percent probability of failure, as the one considered in reference 76, 

the model also predicts a 50 percent probability of success. Given a 15 percent probability of failure, an 

85 percent probability of success is implied (which is more reasonable for pavements on less important 

facilities). For this reason, the NCHRP 1–26 model was seriously considered for this project. 

The need to calculate rather than measure fatigue damage directly is a limitation of this and any model. 

To validate a model, predictions of stress and accumulated damage must be made by other means. 

Perhaps a more reliable method of validating a combination of damage and cracking models could be 

made by comparing the inputs to the stress model described in the following section to the level of 

cracking predicted and observed. In that way, the entire stress-damage-cracking model system can be 

evaluated and validated. 

A third limitation is the use of regression models. Although it is recognized that mechanistic models are 

much more difficult to develop, validate, and calibrate, new research should advance the state of the art so 

that such models are more reliable and accurate. As new models become available, the project team will 

evaluated them, and those that improve the predictive capability of the computer guidelines will be 

adopted. 

The fourth limitation listed at the beginning of this section is the statement in reference 76 that “(w)hen 

this model is used without considering the built-in upward curling of slabs, the model is likely to predict 

an excessively high amount of cracking.” (p. 78) Although it is not expected that this will be the case, it 

is a limitation of the model that should be considered. 

B.2.4.4.3 Midslab Stress Adjustment Model

This section describes the model incorporated for midslab cracking prediction in HIPERPAV II. The 

model’s background, characteristics, assumptions, and limitations, and a description of the validation 

efforts are included here. 

B.2.4.4.3.1 Model Identification 

The edge stress adjustment model is taken from a combination of papers submitted to TRB, ASCE, and 

the 6th International Conference of Concrete Pavements. (See references 81, 82, 83, and 84.) Each of the 

papers discussed in this section are based on the same principles, but contain different aspects of stress 

adjustment that the overall model addresses. This section combines the concepts and components of the 

various papers and demonstrates how they are all used together to modify the Westergaard free edge 

stress. 
136 

B.2.4.4.3.2 Model Characteristics 

The model was derived from multiple runs of the ILLISLAB FEA program. The basis for this approach 

is that FEA can consider the effects of finite slab size and the possible loss of support due to linear 

temperature differentials. Theoretical (Westergaard) solutions that are based on infinite slab and full 

contact assumptions cannot consider the reality of slab size and temperature and moisture differentials. 

The models presented in these papers were developed using multiple FEA runs with varying pavement 

designs and conditions. The resulting stresses predicted by the FEA were compared to the theoretical 

Westergaard solutions using the same conditions. Adjustment factors were developed to account for the 

differences in the two sets of solutions. In this way, a closed form solution was developed to represent 

the results of the FEA. 

The papers claim that the models developed have been carefully validated and are readily implementable 

in spreadsheets or computer programs. They claim that the models are properly formulated to satisfy 

applicable engineering boundary conditions and that they are simple, easy to comprehend, and 

dimensionally correct. They further claim that the models can be extrapolated to wider ranges of input 

parameters. 

One of the papers is an attempt to revise the PCA thickness design methodology and maintains 

adjustment factors for the placement of truck loads relative to the slab edge, and for the concrete’s 

increased strength beyond 28 days.(82) Since HIPERPAV II includes strength gain prediction models 

beyond 28 days, this factor was omitted from this model. HIPERPAV II predicts this strength, 

eliminating the need to adjust the stress to account for increased strength. 

The model developers reduced the Westergaard edge loading and deflection solutions to three 

dimensionless terms given by equations 188, 189, and 190:(81) 

P

h2

σ ⋅

 (188) 

P

k 2 δ ⋅ ⋅ l

 (189) 

P

q

2 ⋅ l

 (190) 

where, 

 σ = Westergaard’s edge stress, FL-2, 

δ = Westergaard’s edge deflection, L, 

q = subgrade vertical stress, FL-2, 

h = slab thickness, L, 
137 

P = single wheel load, F, 

k = modulus of subgrade reaction, FL-3, and 

l = radius of relative stiffness of the slab-subgrade system, L. 

The three dimensionless terms all depend on the normalized load radius a/l, assuming a constant 

Poisson’s ratio of 0.15. Indeed, virtually all the models developed for these papers include an a/l term 

and other terms normalizing length dimensions to the radius of relative stiffness, such as W/l (slab width), 

L/l (slab length), and Do/l (distance of wheel load to slab edge). 

B.2.4.4.3.3 Logic 

The term σeq, or equivalent stress, means the Westergaard edge stress adjusted for the specific design and 

conditions relating to the pavement in question. This stress is determined by equation 191: 

( ) 1 2 3 4 5 1 R R R R R R f e we ce T σ = σ ⋅ ⋅ ⋅ ⋅ ⋅ +σ ⋅ ⋅ (191) 

where, 

 σe = equivalent edge stress prediction, FL-2, 

σwe = Westergaard edge stress, FL-2, 

σce = Westergaard/Bradbury edge curling stress, FL-2, 

R1 = wheel configuration factor (single or dual tire and single, tandem, or tridem 

axle), 

R2 = finite slab length and width factor, 

R3 = tied concrete shoulder factor, 

R4 = widened outer lane factor, 

R5 = bonded or unbonded second layer factor, 

RT = adjustment factor for the combined effect of loading and thermal curling, and 

f1 = PCA adjustment factors for the effect of truck placement on the edge (see table 

37). 

Table 37. PCA edge adjustment factors. 

Percent Trucks at Edge Adjustment Factor f1

1 0.825 

2 0.855 

3 0.870 

4 0.880 

5 0.890 

6 0.894 

7 0.901 

 

The Westergaard closed form edge stress equation is given as equation 192, and the 

Westergaard/Bradbury curling stress equation is given in equation 193. 
138 

( )

( ) ( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ + − + − + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

+ = la

ka

Eh

h

P w e μ μ μ

π μ

μ σ 1.18 1 2

2

1

3

4 1.84

100

log

3

3 1

4

3

2

 (192) 

where, 

 μ = concrete Poisson’s ratio, 

E = concrete elastic modulus, FL-2, and 

a = radius of the applied load, L. 

2

CE T c

Δ = α

σ

 (193) 

where, 

α = concrete CTE, T-1, 

ΔT = temperature differential through slab thickness, T, 

C = curling stress coefficient, which equals the formula shown in equation 194: 

( )⎥

⎦

⎤ ⎢

⎣

⎡ − tan( ) + tanh( ) sin(2 )sinh(2 )

2cos( ) cosh( ) 1 λ λ

λ λ

λ λ

 (194) 

 λ = the formula shown in equation 195: 

l 8

W

 (195) 

 W = slab width, L. 

These equations are used to determine a free edge stress, which is later modified by factors developed 

through the FEA performed by the authors of the referenced papers. (See references 81, 82, 83, and 84). 

The researchers identified several dimensionless mechanistic variables with which they performed 

regression analysis on the ILLISLAB FEA results. The sets of variables are different under the loadingonly condition and the loading-plus-thermal-curling analysis. The following variables (shown in 

equations 196 and 197) were identified: 

Loading-only condition: 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ 2

, , , , , , , h

h

k

a L W s t D AGG f o eff

l l l l l l l

 (196) 
139 

Loading-plus-thermal-curling analysis: 

 ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

Δ 2 4

2

, , , , , l l l l kl

Ph

k

h T a L W f γ α

 (197) 

where, 

 s = transverse wheel spacing, L, 

t = longitudinal axle spacing, L, 

 Do = offset distance between the outer face of the wheel and the slab edge, L, 

 AGG = aggregate interlock factor, FL-2, 

 heff = effective thickness of two unbonded layers, L, which equals the formula shown 

in equation 198: 

( )

( ) 1 1

2 2 2

2

2

1 E h

E h h h ⋅⋅ +

 (198) 

 h1 = thickness of top slab, m, (also signified as h), 

 h2 = thickness of second concrete slab, m, 

 E1 = concrete elastic modulus of top slab, MPa, (also signified as E), and 

 E2 = concrete modulus of second slab, MPa. 

For the midslab (edge) stress, the daytime curling condition is critical. An early version of the model was 

developed to account for the edge stress under nighttime curling conditions, where the curling counteracts 

the effect of traffic loading.(81) However, the most recent version of the model omits the nighttime 

condition. Models for adjustment factors considering both conditions are included in reference 84. The 

model also includes equations for curling-only conditions. These components are not for use in a fatigue 

cracking model, but were developed for validation purposes. They are included in this section to maintain 

the integrity of the model as it appeared in the references. 

B.2.4.4.3.4 Assumptions 

The papers and models presented in this section take the original Westergaard stress equations, along with 

their assumptions of infinite slab size and medium slab thickness, and compare their results to stresses 

predicted by ILLISLAB, an FEA computer program. The FEAs were performed under various load 

configurations, slab sizes, and other conditions that alter the configurations assumed by Westergaard in 

his original work. The resulting stresses predicted by ILLISLAB were then compared to the Westergaard 

stresses, and appropriate adjustment factors were developed by the authors. A basic assumption the 

authors made is that of a constant concrete Poisson’s ratio of μ = 0.15, which greatly simplified the model 

development. 

By using the FEA, the authors were able to eliminate the Westergaard assumption of full contact between 

the pavement slab and the subgrade. An important assumption in doing this, however, and one that is not 

mentioned by the authors of references 81 through 84 is that the nature of the stress model may change 

when a slab lifts off the subgrade, or when a void is otherwise present under the slab. The authors simply 

predict the adjustment factor for those conditions. This may be appropriate, but an addition to the model 
140 

may be necessary to predict slab liftoff and then calculate the stresses in a different way, possibly using 

beam theory or further FEA. 

B.2.4.4.3.5 Limitations 

These models have several limitations that are not discussed by the authors, but these may impact the 

models’ validity. The first and easiest to correct is that many typographical errors were found in the 

presentation of these models in the various publications. In fact, each publication in which the models 

were presented has at least some errors that were identified, but it is not known if other errors exist in the 

presentation of the models and their coefficients. Another limitation is that some of the models in the 

different publications have entirely different coefficients or have differences in their construction. This 

means, for example, that the model for adjusting Westergaard edge stresses affected by the presence of a 

tandem axle (single wheel) configuration was changed after it was originally published in Transportation 

Research Record No. 1568 to when it was published in the 6th International Conference of Concrete 

Pavement proceedings.(82,84) No explanation was given for this and other change, while other models in 

the same group were not changed. 

Another limitation of these models is that each one has limits on the dimensions or configuration that can 

be analyzed with them. For example, the ratio of dual wheel spacing to radius of relative stiffness (l) 

cannot be less than 0.2 nor greater than 4.0. Similar restrictions are placed on slab length to l, axle 

spacing to l, etc. The restrictions arise from the limitations on the model development, but the authors 

seem to indicate that the models can be extrapolated beyond these limits.(81) It is not difficult to construct 

a set of conditions that violate the restrictions placed on the individual models, increasing the probability 

that the user of a design procedure may violate those same restrictions with a normal design problem. 

Further investigation should be made to determine the extent to which the restrictions may be violated 

safely. 

A limitation on the validity of the entire set of models is maintained by the fact that the models were 

developed using ILLISLAB and that the same finite-element program was used to validate the models. 

The paper in reference 81 indicates that a series of ILLISLAB runs was performed to validate the models. 

It states that factorial runs were totally independent of previous modeling processes. It seems, however, 

that to use the same methods for model development and validation necessarily introduces bias in the 

results of the validation. To verify and validate these models further, the project team has performed 

FEAs by using LS-DYNA. The models have been compared to the results from LS-DYNA which, 

together with the ILLISLAB validation, have provided some confidence in the validation claims of the 

authors. 

B.2.4.4.3.6 Slab Stress, Damage, and Cracking Model Integration 

This section describes the integration of the midslab and corner stress adjustment models (section 

B.2.4.4.3) with the PCC fatigue damage and cracking model (sections B.2.4.4.1 and B.2.4.4.2) and with 

the overall long-term performance analysis module in HIPERPAV II. In general, the cracking module 

contains four embedded loops. The first two loops are for the time of day and the season of the year. 

Within these two loops a third loop over each axle configuration, from which the Westergaard free edge 

and free corner stresses are computed. The fourth loop adjusts the load group. For each combination, the 

edge and corner stresses are adjusted, midslab and corner fatigue damage is accumulated, and then 

cracking for each case is determined. 

The stress and damage integration module is essentially a damage accumulation model. The appropriate 

damage for individual load groups, axle configurations, seasons, and times of day are accumulated, and at 

the end of each season, the total damage is used to calculate the level of cracking from the date of 

construction to the current time. 
141 

For midslab cracking, the stress adjustments are determined, as described in section B.2.4.4.3. The 

Westergaard stresses are determined for both the longitudinal and transverse free edge, given other 

conditions such as load, slab thickness, concrete elastic modulus, and the modulus of subgrade support. 

The stresses are then modified to account for load transfer to adjacent slabs (section B.2.3.1) and by 

applying the adjustment factors. Then, for each combination of season, time of day, axle, and load, the 

fatigue damage for both longitudinal and transverse cracking is accumulated. At the end of each season, 

the accumulated fatigue damage is used in the cracking model described above to predict the accumulated 

level of cracking, both in the transverse and longitudinal directions. 

Figure 51 shows a flowchart describing the stress-fatigue-cracking integration module. The flowchart 

applies to each season for which the analysis is performed. For each season, the analysis is performed 

two times a day to capture the effects of upward and downward curling. Within each of the two times, the 

analysis loops over the axle and load groups, as described above. The total accumulated fatigue damage 

and percent slab cracking values are then returned to the main analysis routine. 
142 

For Each of Four Seasons per Year

Loop over two times of day

Loop over six axle groups

Calculate transverse edge stress adjustment

Calculate longitudinal corner stress adjustment

Loop over 45 load groups

Calculate Westergaard transverse edge stress

Calculate Westergaard longitudinal edge stress

Adjust Westergaard stresses

Calculate midslab fatigue

Accumulate midslab damage

Have all load groups

been processed?

No

Yes

Have all axle groups

been processed?

No

Yes

Have all times of day

been processed?

No

Yes

Compute cracking for season

For Each of Four Seasons per Year

Loop over two times of day

Loop over six axle groups

Calculate transverse edge stress adjustment

Calculate longitudinal corner stress adjustment

Loop over 45 load groups

Calculate Westergaard transverse edge stress

Calculate Westergaard longitudinal edge stress

Adjust Westergaard stresses

Calculate midslab fatigue

Accumulate midslab damage

Have all load groups

been processed?

No

Yes

Have all axle groups

been processed?

No

Yes

Have all times of day

been processed?

No

Yes

Compute cracking for season

Figure 51. Flowchart of stress, damage, and cracking module. 
143 

The values that will be calculated and returned by this routine include the accumulated and incremental 

damage as well as the total cracking for the current season. 

B.2.4.5 Roughness Model 

Measuring the roughness of pavements is one of the most economical methods used to predict pavement 

serviceability. Two common roughness indicators are the present serviceability index (PSI) and the IRI. 

An evaluation of PSI and IRI models available in the literature and the models incorporated in 

HIPERPAV are presented in the following sections. 

B.2.4.5.1 Present Serviceability Index 

Present serviceability is defined as the ability of a specific section of pavement to serve high-speed, highvolume, mixed traffic in its existing condition.(64) The PSI originally was developed at the AASHO road 

test in 1960. PSI is a rating scale from 0 to 5, where 4 to 5 represent very good pavement, 3 to 4 is good, 

2 to 3 is fair, 1 to 2 poor, and 0 to 1 is very poor. This rating is a function of the pavement’s physical 

measurements of roughness and distress (e.g., cracking, faulting, patching). It depends on the pavement’s 

longitudinal profile, where cracking, patching, and faulting are likely to contribute. The longitudinal 

profile can be expressed as the mean slope variance (deviation of the record from a baseline). These 

measurements are combined to formulate PSI. 

The original equation (equation 199) for the PSI of rigid pavements is based on 49 rigid sections:(64) 

PSI = 5.41−1.71log(1+ SV) − 0.09 C + P (199) 

where, 

PSI = present serviceability index, 

SV = slope variance measured using a profiler (10-6 rad), 

C = cracking in ft/1,000 ft2

 (1 ft = 0.3048 m), and 

P = patching (ft2

/1,000 ft2). 

The influence of faulting and spalling were also measured, but these did not have a statistically significant 

influence on the pavement serviceability. The r2 for this model is 0.92. 

This equation contains several limitations: 

• The profiler that measured slope variance is no longer in use. 

• Riders’ perceptions of road serviceability have changed over the past 30 years because 

vehicles, highway characteristics, and speeds have changed. 

• The rideability equation includes surface defects. Roughness and surface distresses do not 

necessarily correlate, because they are physically different attributes of the pavement 

condition.(64) 

A 1990 study to predict PSI in JPCPs developed the following regression model, shown in equation 

200:(85) 
144 

PSI = 4.536 − 0.0182( ) TFAULT − 0.00313(SPALL)− 0.00162(TCRKS ) () − 0.00317 FDR (200) 

where, 

TFAULT = cumulative transverse joint faulting in inches per mile (1 inch per mile 

(inch/mi) = 15.8 mm/km), 

SPALL = number of deteriorated (medium and high severity) transverse joints per mile 

(1 mi = 1.609 km), 

TCRKS = number of transverse cracks (all severities) per mile (1 mi = 1.609 km), and 

FDR = number of full depth repairs per mile. 

For this model, the r2 is 0.58 using 282 pavements. This model is a linear regression of multiple variables 

collected according to the Distress Identification Manual for the Long-Term Pavement Performance 

Project.(86) The intercept (4.536) is the maximum PSI allowed when all distresses equal zero. As the 

distresses accumulate, PSI decreases. Since the model sensitivity to FDR is relatively small and difficult 

to model, it can be omitted. The model incorporated in HIPERPAV II is shown in equation 201: 

PSI = 4.536 − 0.0182( ) TFAULT − 0.00313(SPALL)− 0.00162(TCRKS ) (201) 

This model has some limitations, including: 

• A longitudinal roughness term is not included in the model. Therefore, it does not account 

for long wavelength roughness due to subbase and subgrade settlement and heave. The 

distresses included only account for short wavelength roughness. 

• The model cannot account for differences in construction quality, which can affect initial 

roughness. 

• The model can output negative PSI. An error catcher is needed so that the minimum PSI 

output is 0. 

• Care must be taken to ensure that the data input to the model is collected according to the 

LTPP distress manual regulations.(87) 

Using the model presented in equation 201, the model’s sensitivity to the faulting, spalling, and transverse 

cracking input parameters was assessed. An analysis was completed to calculate how each distress 

influences the PSI. To reduce PSI to 2.0 from the initial 4.536, each distress was increased while the 

other two distresses were kept at zero. As seen in figure 52, faulting has the greatest influence on PSI, 

spalling next, followed by transverse cracks. PSI depends on faulting 6 times more than spalling, and 

almost 12 times more than transverse cracking. 
145 

0

500

1000

1500

2000

2500

TFAULT SPALL TCRKS 

JCP Distresses

Faulting (mm/km), Spalls (no./km), 

and Transverse Cracks (no./km)

Figure 52. Amount of each individual distress required to reach a PSI of 2.0. 

B.2.4.5.2 International Roughness Index

The IRI was developed at the International Road Roughness Experiment held in Brazil in 1982.(64) It is 

currently the standard for the FHWA Highway Performance Monitoring System database.(64) IRI 

describes the longitudinal surface profile in the wheel path, and it is defined as the average rectified slope 

(ratio of the accumulated suspension motion to the distance traveled) obtained from a mathematical model 

of a standard quarter car traversing a measured profile at a speed of 80 km/h. It is computed from surface 

elevation data collected by a topographical survey or mechanical profiler. The measurements should be 

calibrated to the measurement standard because roughness is sensitive to tire type, tire pressure, load, 

vehicle suspension system, and vehicle speed. 

IRI can be estimated as a function of the PSI. Using linear regression, a contractor developed an IRI 

model using the LTPP GPS–3 sections. IRI is correlated to PSI as shown in equation 202. 

IRI(m/ km) =1.0602(5 − PSI) (202) 

The r2 is 0.76 for 3199 pavement sections. This equation only depends on PSI, so a sensitivity analysis is 

not needed. A plot of IRI versus PSI is shown in figure 53. 
146 

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

PSI

IRI (m/km)

Figure 53. Shape of IRI versus PSI curve. 

It may be necessary to develop a more sophisticated model that includes pavement design and location 

features in a later IRI calculation, as shown in equation 203. 

IRI = (PSI, Joint Spacing, Season, Location) 

 (203) 

The initial roughness (IRIo) also can be incorporated into the relationship as shown in equation 204: 

IRI = IRIo + ∆IRI

 (204) 

where, 

 ΔIRI = the change in IRI due to traffic loading and weather conditions. 

B.2.4.5.3 Other IRI Relationships

Other relationships have been developed for IRI that use the JCP distress data as input. This section will 

compare these relationships, documented in FHWA–RD–97–147, FHWA–RD–00–130 and in the Guide 

for Mechanistic Design of Pavements developed under NCHRP study 1-37A to the one developed by the 

contractor, described above.(88,89,90) 

B.2.4.5.3.1 FHWA–RD–97–147 

For nondoweled JCP in the LTPP database, IRI is related to faulting as shown in equation 205.(88) 

IRI(m / km) = 0.0098*TFAULT +1.268 (205) 

where, 

 TFAULT = total faulting (mm) per LTPP section. 

This equation has an r2 of 0.48 for 51 sections and is plotted in figure 54. 
147 

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 50 100 150 200

Total Faulting per Section (mm)

IRI (m/km)

Figure 54. Effect of faulting on IRI. 

B.2.4.5.3.2 FHWA–RD–00–130 

This IRI model was developed to improve the prediction models for PCC pavement performance-related 

specifications.(89) This IRI model is based on pavement distresses and also a site parameter that accounts 

for climate, age, and other factors that influence IRI, as shown in equation 206. 

IRI = IRI0 + 0.013 * %CRACKED + 0.007 * %SPALL + 0.001 * TFAULT + 0.03 * SITE

 (206) 

where, 

 IRI = smoothness (m/km), 

 IRI0 = initial smoothness measured as IRI (m/km), 

 %CRACKED = percent slabs with transverse cracking and corner cracks (all severities) 

(0–100 percent), 

 %SPALL = percent joints with spalling (medium and high severity) (0–100 percent), 

 TFAULT = total joint faulting cumulated per km (mm), 

 SITE = site factor, as shown in equation 207: 

SITE = AGE * (1 + FI)

1.5 * (1 + P0.075) * 10-6

 (207) 

 AGE = pavement age, 

 FI = freezing index (°C-days), and 

 P0.075 = percent subgrade material passing 0.075 mm (No. 200) sieve (0–100 percent). 

The statistics for this model are N = 183, r2 = 0.70 and SEE = 0.35 m/km. This model is compared to the 

others in figures 55 to 57. 
148 

B.2.4.5.3.3 1-37A Guide for Mechanistic Design of Pavements—TRB 2000 Presentation 

An IRI model was presented at the 2000 TRB session for the 1-37A Guide for Mechanistic Design of 

Pavements.

(90) It is given in equation 208: 

IRI = IRI0 + 0.0337 * TransCk + 0.0083 * JtSPALL

+ 0.0997 * PATCH + 0.062 * CorBreak + 0.01255 * 

AGE + 0.001547 * TotFAULT (208) 

where, 

 IRI = smoothness (m/km), 

 IRI0 = initial IRI (m/km), 

 TransCk = transverse cracking (all severities) (assumed to be 0–100 percent), 

 JtSPALL = percent joints with spalling (all severities) (0–100 percent), 

 PATCH = percent of area with flexible or rigid patching (all severities) (assumed to be 0–

100 percent), 

 CorBreak = percent joints with corner breaks (all severities), 

 AGE = pavement age (years), and 

 TFAULT = total joint faulting (mm/km). 

No information on the modeling statistics (i.e., N and r2) was provided. 

B.2.4.5.3.4 1–37A Guide for Mechanistic Pavement Design—TRB Presentation in 2001 

In the 2001 TRB conference, the IRI (smoothness) model was modified from its past version presented at 

the 2000 TRB conference.(91) It more closely resembles the FHWA–RD–00–130 model, but it contains a 

term for patching. The general form of the equation is shown in equation in 209: 

S(t) = S0 + A1 D(t)1 +......+ An D(t)n + B SF + Cj Mj

(209) 

where, 

 S(t) = pavement smoothness, 

 S0 = initial IRI, 

 D(t) = distress, 

 SF = site factor to address site conditions, 

 M = maintenance activities, and 

 A, B, C = regression coefficients. 

The model regression coefficients are as shown in equation 210: 

IRI = IRIi + 0.0137 CRK + 0.07 SPALL + 0.005 PATCH 

+ 0.0015 TFAULT + 0.04 SF (210) 
149 

where, 

 IRI = pavement smoothness (m/km), 

 IRIi = initial IRI (m/km), 

 CRK = percent slabs with cracking (all severities transverse and corner breaks), 

 SPALL = percent of joints with spalling (medium and high severities), 

 PATCH = area with flexible or rigid patching (all severities) (m2

), 

 SF = site factor, as shown in equation 211: 

SITE = AGE * (1 + FI)

1.5 * (1 + P0.075) * 10-6

 (211) 

 AGE = pavement age (years), 

 FI = freezing index (°C-days), 

 P0.075 = percent subgrade material passing 0.075-mm sieve, and 

 TFAULT = total joint faulting (mm/km). 

No information on the modeling statistics (i.e., N and r2) was provided. 

B.2.4.5.4 IRI Model Comparison

The five models are summarized below in table 38. The units and dependent variables included in the 

models are listed. In the following parametric studies, only the distress variables for faulting, cracking, 

spalling, patching, and the initial IRI0 will be examined. The other variables will be held constant. 

Table 38. Comparison between IRI models. 

IRI Models FHWA–

RD–97–147 

FHWA–

RD–00–130 

1–37A 

Guide 

(2000 TRB) 

1–37A 

Guide 

(2001 TRB) 

Contractor

Units inches/mi m/km m/km m/km m/km and 

inches/mi 

Initial IRI: IRI0 Constant Variable Variable Variable Constant 

TFAULT TFAULT TFAULT TFAULT TFAULT 

– Spalls Spalls Spalls Spalls 

– Cracks Cracks Cracks Cracks 

– – Corner 

Breaks 

– – 

Distress 

Variables 

– – PATCH PATCH – 

– AGE AGE AGE – 

Other Variables – FI – FI – 

– P0.075 – P0.075 – 

To perform the comparison, control variables for the models have been chosen. Because model FHWA–

RD–97–147 only has a faulting term, faulting will first be varied in all four models between 0 to 1200 

mm. For both the FHWA–RD–00–130 and 1–37A models, IRI0 of 0.5 m/km is assumed, as is AGE of 10 

years. Likewise, a freezing index of 300 °C-days and percent subgrade materials passing the No. 200 

sieve of 40 percent are assumed. These are the control variables used in the model reference.(89) To 

convert the number of distresses per mile in the contractor’s model to a percentage, an average joint 
150 

spacing of 5.1 m is used. This is the average joint spacing for all the GPS–3 sections in the LTPP 

database. The comparison is shown graphically in figure 55. 

As can be seen in figure 55, the slope of the IRI versus faulting models tend to be similar for all the 

prediction equations. One of the major distinctions is the high initial IRI0 of the FHWA–RD–97–147 

model. The FHWA–RD–00–130 model and the contractor’s model are very similar, as are the two 

1–37A models. 

0

0.5

1

1.5

2

2.5

3

3.5

0 200 400 600 800 1000 1200

Faulting (mm)

IRI (m/km)

97-147

00-130

2002/2000

2002/2001

Contractor

Figure 55. Comparison of faulting influence between the various IRI models. 

Now the influence of cracking and spalling will be assessed using the IRI models. The FHWA–RD–97–

147 model will not be included because it is dependent only on faulting. By varying the percent cracking 

between 0 percent and 100 percent, the plots for IRI versus percent cracking can be produced (figure 56). 

Similarly, the influence of spalling will be assessed; this is shown in figure 57. For both of these plots, 

the level of faulting is assumed to be 600 mm. 

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90 100

Cracking (%)

IRI (m/km)

00-130

2002/2000

2002/2001

Contractor

Figure 56. Effect of percent cracked slabs on FHWA–RD–00–130, 1–37A Guide, and contractor 

IRI models. 
151 

Increasing percent cracked slabs in figure 56 causes a marked increase in IRI according to the 1–37A 

model presented in 2000 at TRB. Its effect on the other three models is not as severe. 

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60 70 80 90 100

Spalling (%)

IRI (m/km)

00-130

2002/2000

2002/2001

Contractor

Figure 57. Effect of percent spalling on FHWA–RD–00–130, 1–37A Guide, 

and contractor IRI models. 

Increasing the percent spalling causes a slight increase in IRI for all four models. The slopes of the 

FHWA–RD–00–130 and 1–37A IRI models are approximately the same. 

Patching is only a factor in the 1–37A models. The other models do not account for it. Its influence on 

IRI is shown below in figure 58. The 1–37A model presented in 2000 is more sensitive to patching than 

is the one presented in 2001. 

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7 8 9 10

Patching (%)

IRI (m/km)

2002/2000

2002/2001

Figure 58. Effect of percent patching on IRI for the 1–37A models. 
152 

To assess the influence of initial roughness on the IRI models, IRI0 is varied in the FHWA–RD–00–130 

and 1–37A models in figure 59. It is apparent that the slopes of all the models are the same. This is 

expected because IRI0 is an additive term. The contractor model cannot account for initial IRI, but it can 

be modified to do so in the future. In these modeling predictions, percent spalling and cracking are 

assumed to be 30 percent, and faulting is assumed to be 600 mm. 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9

Initial IRI (m/km)

IRI (m/km)

00-130

2002/2000

2002/2001

Contractor

Figure 59. Effect of initial IRI0 on FHWA–RD–00–130, 1–37A, and contractor IRI models. 

It appears, based on the parametric analysis, that the FHWA–RD–00–130 and the 1–37A models are the 

most versatile. They account for the pavement distresses and also allow for an initial roughness (IRI0). 

The simpler model by the contractor does not include an initial IRI0 term. The two models that are the 

most similar are the FHWA–RD–00–130 model and the 1–37A model presented in 2001. Because 

documentation on the development of the latter model was scarce when the HIPERPAV II was 

developed, the IRI model described in FHWA–RD–00–130 was incorporated into HIPERPAV II for its 

versatility and validation. 

B.2.5 Long-Term JPCP Model Assumptions and Limitations 

The long-term JPCP module of the HIPERPAV II system was developed to optimize early-age strategies 

based on how they perform in the long term. With this objective in mind, two early-age strategies can be 

analyzed in the long term under the same long-term environmental and traffic conditions. 

Accurate predictions of long-term performance require accurate and detailed information on pavement 

structural factors, materials characterization, environmental conditions, and traffic data. Because the 

HIPERPAV II long-term module is intended to help the user optimize early-age strategies rather than 

serve as a tool for pavement design, a number of considerations were made to simplify the data entry. 

B.2.5.1 Pavement Support 

No long-term input of seasonal adjustment factors for the k-value is required. The k-value used in the 

long-term module is the k-value input from the early-age analysis. This k-value represents the subgrade 

support conditions during construction. The k-value varies seasonally as a function of soil moisture and 

temperature, among other factors, and this may have a significant effect on pavement performance. 
153 

Loss of support is an important factor that affects the performance of the pavement. Loss of support 

depends highly on the erodibility of the subbase materials, presence of water, slab deflection, and 

magnitude and amount of traffic loads.(64) Available loss of support (pumping) models have limited 

applicability to mechanistic models such as the one used in HIPERPAV II to predict midslab cracking. 

For example, pumping models developed during the AASHO road test account for subbase materials 

highly susceptible to erosion and are thus not currently used. COPES models do not consider the subbase 

type as a factor.(64) Given the lack of a sound loss-of-support model, and considering that the HIPERPAV 

II long-term analyses are made to compare early-age factors, no loss-of-support model was incorporated. 

It is therefore important to emphasize that the effect of the structural support provided by the subbase 

must be evaluated with a pavement design procedure such as the one developed by the NCHRP 1–37A 

study. 

Also, to minimize the number of inputs, no input for soil type is required. The soil type input required for 

the faulting prediction model has been hard coded to AASHTO classification A–2–6. Although the effect 

of soil type on faulting prediction for JPCP with no dowels is minimal, a significant effect on the faulting 

prediction for JPCP with dowels is observed. Given that the comparisons of early-age strategies are made 

under the same conditions of LTE in the long term, the results of the comparative analysis should be 

unaffected by this factor. 

B.2.5.2 Structural Response 

Loading position for analysis of longitudinal cracking is assumed at midslab along the transverse joint as 

required by the Westergaard stress model. No stress adjustment is made to account for the fact that the 

loading position rather than at midslab occurs at the wheel path. 

No lift-off of the concrete slab from the subbase due to curling is considered, and the bond between the 

PCC slab and subbase layer is not taken into account. 

B.2.5.3 Drainage 

The model that is used to predict average monthly moisture content in the pavement layers underneath the 

slab is rather simplistic. This model uses site-dependent climatic conditions, soil data, and some 

pavement geometry, but does not consider information on the drainage system. 

The faulting prediction models require input on whether edge subdrains are used. The condition for no 

subdrains is hard coded for this model. 

B.2.5.4 Traffic 

Input of accurate load spectra information requires of significant data entry time. To ease entry of traffic 

inputs, a number of assumptions are made: 

• Daily and seasonal distributions are hard coded to be constant (no daily or seasonal variations 

in traffic are considered). 

• Conversion from ESALs to traffic load spectra is based on findings from the NCHRP 1–37A 

study.(92) Load spectra is backcalculated based on an average load distribution per axle type. 

The percentage of single, tandem, and tridem axles is based on a weighted average of axles 

per truck for an average vehicle class distribution on rural and urban highways. 
154 

Early-age strategies are compared under the same traffic conditions in the long term. Therefore, it is 

assumed that the effect of traffic distribution on these comparisons is minimal. 

B.2.5.5 Distress Models 

A spalling model was not included in the long-term prediction module because of the complexity required 

to account for all possible factors that affect spalling distress. These include the moisture state in the 

pavement slab, concrete evaporation, sawcutting procedures, and dowel bearing stresses, among other 

factors. 

Because no spalling distresses are predicted, serviceability and IRI may be underpredicted, as they are a 

function of the level of distresses present. 

B.3 CRCP EARLY-AGE MODELS 

The selected model for prediction of CRCP early-age behavior in HIPERPAV II is the CRCP–8 model 

developed by the CTR of the University of Texas at Austin, TX. CRCP–8 is a mechanistic model based 

on equilibrium of internal forces in the reinforced concrete for predicting concrete and steel stresses as a 

function of the concrete mechanical properties, temperature development, and restraint imposed by the 

subbase and the steel. Similar to the JPCP module in HIPERPAV II, stresses in the concrete are 

compared to the strength development at any time step for prediction of crack formation. 

B.3.1 CRCP Stress Prediction 

Figure 60 shows a schematic representation of the one-dimensional model for analysis of concrete and 

steel stresses in a CRCP basic analysis unit bounded by two adjacent transverse cracks and longitudinal 

joints.(93)

dx

Free Body Diagram:

Crack Crack

Fs Fs+dFs

Fs = Force in the Steel

Fi

dx Fi = Friction Force

f

b

fb = Bond Stress

Fc Fc+dFc

Fc = Force in the Concrete

Fc Fc+dFc

dx

Free Body Diagram:

Crack Crack

Fs Fs+dFs

Fs = Force in the Steel

Fi

dx Fi = Friction Force

f

b

fb = Bond Stress

Fc Fc+dFc

Fc = Force in the Concrete

Fc Fc+dFc

Figure 60. Schematic representation of analysis of concrete and steel stresses in CRCP–8. 
155 

The complete model derivation is described in detail in reference 93; only the primary governing 

equations are presented here. For derivation of the governing equations of the CRCP system, a number of 

assumptions are made: 

• Concrete and steel properties are linearly elastic. 

• Temperature variations and drying shrinkage are uniformly distributed throughout the slab 

depth. 

• Friction at the slab-subbase interface is considered elastic. 

• The effect of creep and warping are neglected. 

Since concrete stress is zero at cracks, considering that the steel stresses that develop at the crack location 

must be in equilibrium with the subbase restraint and the stresses in the concrete at any point in the slab, 

the following relationship is derived in equation 212:(93)

+ − − = 0

∫

p D

F dx

p s

L

x

i

sc

s

cx

sx σ

σ

σ

 (212) 

where, 

 x = coordinate distance from midslab, 

σsx = stress in the steel at location x, 

σcx = stress in the concrete at location x, 

ps = ratio of cross sectional area of steel (As) to area of concrete (Ac), 

σsc = stress in the steel at a crack, 

L = one-half of the slab segment length, 

Fi = friction force per unit length along the slab, and 

D = thickness of the concrete slab. 

Equation 213 is used to determine the stresses in the concrete at any location along the slab. 

[ ] ( ) c c s sh

sx

cx E T

n

α α ε

σ

σ = + − Δ +

 (213) 

where, 

 Ec = modulus of elasticity of the concrete, 

n = Ec/Es, 

Es = modulus of elasticity of the steel, 

αc = thermal coefficient of expansion of the concrete, 

αs = thermal coefficient of expansion of the steel, 

ΔT = temperature change, and 

εsh = drying shrinkage of the concrete. 

Steel stress at the crack is determined as shown in equation 214: 
156 

[ ] ( )

p D

Fdx

T

p

Ec

np s

L

x

i

c s sh

s

sx

s

∫

+ − Δ + − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

σ = + σ α α ε

1 1 sc

 (214) 

with terms as previously defined. 

Depending on the relative displacements between the steel and the concrete, two zones are identified: 1) a 

fully bonded zone at the middle of the geometric model where concrete and steel displacement are zero, 

and 2) a bond development zone, in proximity to the cracks, where steel displacement is zero, but 

concrete displacement occurs, and is a function of the material properties and environmental conditions. 

With the above conditions, for the fully bonded zone, the rate of steel and concrete stress is primarily a 

function of subbase restraint as shown in equations 215 and 216. For the bond development zone, the rate 

of steel and concrete stress is primarily a function of the bond stress as shown in equations 217 and 218. 

⎟

⎠

⎞ ⎜

⎝

⎛ −

− =

n

D p

d F

s

i

dx 1

σ sx

 (215) 

 

⎟

⎠

⎞ ⎜

⎝

⎛ +

− =

n

nD p

d F

s

i

dx 1

σ cx

 (216) 

φ

σ 4 ( )

dx

sx d f x b =

 (217) 

where, 

 fb(x) = bond stress at location x along the steel-concrete interface and 

 φ = diameter of steel bar. 

D

d f x p F

b s i = − − φ

σ 4 ( )

dx

cx

 (218) 

To solve the above system of equations, it is necessary to define a boundary condition for the steel stress 

at the crack location. It is assumed that the steel stress at cracks is the same regardless of the slab length. 

The steel stress is determined for a slab length with a mean crack spacing, Xbar, as shown in equation 219: 
157 

∫ = ⋅ ⋅Δ ⋅

X

sxdx Es s T Xbar

0

σ α

 (219) 

In addition to the above boundary condition, relationships for the bond stress and bond development 

length are derived as a function of the steel stress at the crack location. A simplified coordinate system 

with origin at the location where bond slippage begins is used, as shown in figure 61, to derive the bond 

stress and bond development length relationships in equations 220–222. 

-a b

x

Crack

Bond Slippage 

Begins

Fully Bonded Zone

Bond Development 

Zone

0

s

Midslab

Figure 61. Simplified coordinate system for development of bond stress distribution functions. 

 (220) 

where, 

 s = coordinate distance from the location where bond slippage begins, 

K = bond stiffness (bond stress per unit slip), 

W(s) = bond slip at location s, 

C,D,E = constants that are functions of the boundary conditions (derived in reference 

93), and 

b = bond development length. 

 (221) 

where, 

 c = b(aK)

0.5, 

β = θ/(EcD), 

θ = slope of the subbase frictional stress distribution, 

A = constant that is a function of the boundary conditions (derived in reference 93), 

and 

a = distance from the location where bond slippage begins to midslab. 

⎟

⎠

⎞ ⎜

⎝

⎛ = + + +

b

s fb s Kw s Cs D E

2 ( ) ( ) cos 2 π

K

s a

b

s

b

K

E D

K

C Cs

K

w s Ae Be b

cs

b

cs

α

π β

π

α

α

α

( )

2

cos

4

1 2 ( )

2

2

2 + ⎟ −

⎠

⎞ ⎜

⎝

⎛

+

⎟ −

⎠

⎞ ⎜

⎝

⎛ = + − + +

−
158 

∫∫

−

− = − Δ

b

a

b

x

fb s dsdx σ scL Esα s TL

φ ( ) 4

 (222) 

A second relationship between the steel stress at a crack and the bond development length is derived as 

shown in equations 223–225: 

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎟

⎟

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎜

⎝

⎛

⎟

⎠

⎞ ⎜

⎝

⎛ +

+ − + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = −

∫ ∫ − −

n

D p

Fdx

p DC

Fdx

C

C

C

b

s

a

i

s

b

a

i

sc 1

1 1

4(266)

0

1 1

2

1

σ φ

 (223) 

where, 

nps

C 1

1 =1+

 (224) 

[ ] ( ) c s sh

s

c T

p

E C = α −α Δ + ε 2

 (225) 

An iterative process is used to solve equations 222 and 223 that provides the same bond development 

length for a given σsc. With the bond development length and steel stress at the crack, concrete and steel 

stresses along the slab length are computed with the above relationships for both the fully bonded zone 

and the bond development zone. Initially, no subbase restraint is assumed, and an iterative process is 

used to solve for it. The subbase restraint stress distribution is approximated by a linear function of the 

distance from midslab. 

B.3.2 CRCP Strength Prediction 

In CRCP–8, the Monte Carlo method is used to simulate the PCC strength variability. By assuming a 

normal distribution for the PCC tensile strength, the Monte Carlo method is used to probabilistically 

assign different values of tensile strength along the pavement length. A comparison of the concrete stress 

and the simulated concrete tensile strength at any point is performed for prediction of crack formation. In 

this fashion, crack spacing is predicted with an inherent variability.(93) 

As an enhancement to the CRCP–8 model, in this study, similar to the strength prediction for JPCP, the 

maturity method is used in the CRCP HIPERPAV II module to predict the early-age strength. 
159 

B.3.3 CRCP Temperature Prediction 

In CRCP–8, the minimum and maximum PCC temperatures are an input for the days after construction 

until concrete reaches full strength (assumed to be 28 days) and for the coldest time of the year. As an 

enhancement to the CRCP–8 model, in this study the required PCC temperatures are predicted with the 

finite-difference temperature model described in section B.1.2. 

B.3.4 CRCP Model Limitations 

The CRCP model used in HIPERPAV II is a one-dimensional mechanistic model with the following 

limitations: 

• No curling effects are considered. Although it has been hypothesized that, due to the short 

slab lengths in CRCP, curling is not a significant factor, new findings suggest that curling 

may lead to horizontal cracking due to the restraint imposed by the steel. 

• The CRCP model does not account for creep-relaxation effects. Although creep-relaxation 

models are used in HIPERPAV for JPCP, no attempt to include this model in the CRCP 

module was made, because this could nullify the previous validation efforts made to this 

model. 

• Because of the one-dimensional characteristics of the CRCP model, the steel is assumed to be 

at middepth. The effect of bar mats at different depths cannot be modeled. 

• As identified from the validation results, the bond-slip relationships used have limited 

validity and may not predict properly the transfer of stresses from the concrete to the steel, 

possibly affecting the crack width predictions. 

• Time of crack formation is not taken into account. This factor is believed to be of significant 

importance in determining crack width properly, since crack width is a function of the drying 

shrinkage and relaxation characteristics after cracks occur, among other factors. 

B.4 MODELS USED IN THE COMET MODULE 

Selection of the FHWA mix optimization study was described in Volume I of this report series. This 

study was incorporated in the HIPERAPV II system in the form of a module termed Concrete 

Optimization, Management, Engineering, and Testing (COMET). COMET is a simplified derivation of 

the Concrete Optimization Software Tool (COST) software originally developed by FHWA and the 

National Institute of Standards and Technology. A two-stage analysis process is involved. 

Stage I: Trial Batches 

A limited number of factors (or decision variables) are determined by providing bound values and a 

midpoint value. Specific gravity and unit cost of the constituents (e.g., cement, admixture, aggregate) are 

defined by the user. Desirability curves for responses or objective functions (e.g., cost, 28-day strength) 

are defined. 

Trial batches, whose number is based on the number of factors plus replicates, then are generated. The 

predicted responses are obtained from default predictive models. However, the predicted responses may 

be overwritten using actual trial batch test results. 
160 

Stage II: Virtual Batches 

A full quadratic model is fitted for each response based on the responses from the trial batches. Virtual 

mixes are then generated using a finer grid (i.e., adding more combinations within the operability region 

of the variable space). The responses of virtual mixes are subsequently predicted by the fitted quadratic 

models. Scores for all virtual mixes are calculated and ranked. The top N virtual mixes are then 

recommended as optimized mixes, where N is defined by the user. 

B.4.1 Comments on COMET Features and Implementations 

Since COMET is a simplified version of the FHWA COST software, its usability is enhanced while 

hiding the inherent complexity of the analysis. (See references 94, 95, 96, and 97.) This is not to deter 

users who have limited statistical backgrounds. However, flexibility and detailed statistical reports for all 

analysis stages are not available, nor is the more robust analysis that is provided by COST. 

COMET uses FORTRAN in the back-end coding while it uses Microsoft® Visual Basic®/HTML in the 

front-end coding. COMET uses four fixed factors: percent coarse aggregate of total aggregate weight, 

cementitious content, percent pozzolan of total cementitious, and w/c. COMET uses three fixed 

responses: cost, early-age strength, and 28-day strength. Property desirability curves (with six data 

points) are user-defined for each response. 

 Face-centered design methodology is used to generate 29 trial mixes based on equation 226: 

NB k x FP AP CP k = 2 + 2× + = + + (226) 

where, 

 k = number of factors (four in this case), 

 x = number of centerpoints (five in this case), 

 NB = number of trial batches, 

 AP = number of axial points, 

 CP = number of central points, and 

 FP = number of factorial points. 

The trial batches may be increased if number of factors is increased. The current version of COMET 

utilizes eight evenly spaced design points between the limits of each factor. This generates a combination 

of 4096 virtual mixes (i.e., 84

). A full quadratic model is used in model fitting. Fifteen terms are 

contained in this model. The 29 face-centered design points are used for model fitting, with predicted 

responses calculated for each of the 4096 points. 

The central composite design (CCD) is a very efficient experiment design technique to fit second-order 

response models. It uses a two-level factorial or fraction combined with axial and centerpoints. The 

factorial points describe “a variance-optimal design for a first-order model or a first-order + two-factor 

interaction model”.(98) (p. 322) The centerpoints capture the curvature in the system. If curvature exists, 

axial points will help in the approximation of quadratic terms efficiently. In summary, CCD is very 

efficient at providing information on variable effects and overall experimental error while minimizing the 

number of required runs. 
161 

B.4.2 Concrete Compressive Strength Model 

To calculate concrete compressive strength as a function of w/c, Abrams’ equation is used.(61) The most 

basic form of this equation (equation 227) relates compressive strength directly to w/c. 

w c A

A

A

c C

B

A f = + /

 (227) 

where, 

 fc = compressive strength, in KPa, 

 w/c = water-to-cement ratio, and 

 AA, BA, and CA = empirical coefficients that are independent of strength and w/c. CA

commonly is set to zero. 

The empirical coefficients depend on the units, materials, test method used, age of testing, and the 

conditions of validity for Abrams’ rule. Abrams’ rule states that: 

• Compressive strengths are lower with higher w/c’s, 

• Compressive strengths are higher with lower w/c’s, and 

• Compressive strengths are identical with the same w/c. 

The strengths of comparable concrete depend solely on their w/c’s regardless of their compositions. 

Abrams’ rule is valid, provided that the following 10 assumptions hold: 

1. The strength-developing capabilities of the cements used are identical. 

2. The quantities and strength influencing effects of the admixtures used are identical. 

3. The concrete specimens are prepared, cured, and tested under the same conditions. 

4. The concrete ingredients are distributed evenly. 

5. Air contents are the same, air voids are distributed uniformly, and none of the voids are too 

large for the specimen size. 

6. Aggregate particles are stronger than the matrix. 

7. The bonds between aggregate surfaces and the matrix are strong. The bond can transfer the 

stresses to the aggregate before loading crushes the matrix. 

8. The strength affecting physical and chemical processes (drying, aggregate reactivity) are the 

same and are not overwhelming (hydration). 

9. The composite nature of the concrete affects the strength of the compared concretes to the 

same extent. 

10. The contribution of the aggregate skeleton is the same in the various concretes. 

B.4.3 Development of the Compressive Strength Prediction Model Based on Mix Design 

The compressive strength prediction model formulated for COMET must account for the influence of 

w/c, pozzolans, and aggregate contents, in addition to concrete age. The relationships between these 

inputs and compressive strength are listed below. 

B.4.3.1 Effect of Water-to-Cement Ratio 

A basic model for compressive strength at 28 days is given in equation 228: (61) 
162 

 

c day w c f ksi 28 / 23.07

27.122 ( ) = −

 (228) 

 (1 ksi = 6.89 MPa) 

An augmented model, which accounts directly for cement content, is given in equation 229:(61) 

 

c Day w c c f ksi 28 / 0.000378 23.66

51,290 ( ) − + =

 (229) 

where, 

 c = cement content in pcy (1 lb/yd3 = 0.594 kg/m3

). 

Figure 62 compares these two models. At low w/c’s (w/c < 0.3), the compressive strength continues to 

increase according to the basic model. This relationship would be correct for fully compacted concrete, 

but at lower w/c’s, it is difficult to achieve full compaction.(13) The augmented model, used in COMET, 

provides a more reasonable prediction of compressive strength. 

0

20

40

60

80

100

120

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

w/c

f c (MPa)

Augmented Model

Basic Model

Figure 62. Compressive strength as a function of w/c and cement content. 

B.4.4 Relative Strength 

When investigating the effect of fly ash and age on the concrete’s compressive strength, the relative 

change in strength (frel) can be calculated within the limits of Abrams’ rule (equation 230). 
163 

w c

A

w c

A

A

A

rel B

B

A

A

f

f f /

/

1

1

1

1

= = ×

 (230) 

where, 

 concrete strength f is related to w/c and 

 concrete strength f1 is related to w/c1. 

Assuming AA = AA1, equation 231 follows: 

Ratio

B

B

f w c

A

w c

A

rel = = /

/ 1

1

 (231) 

B.4.4.1 Effect of Pozzolans 

Abrams’ rule is valid for blended cements. When a portion of the cement has been replaced by fly ash, 

the following approximation of BA has been derived in equation 232. 

5.5 6.3 6 / = × + p c BA (232) 

where, 

 c = mass of cement and 

p = mass of fly ash that has been added to the cement. 

To use this equation to predict the 28-day compressive strength of concrete, the w/cm of w/(c + p) 

applies. Also, it is only applicable for the range of p/c = 0 to 1. Although there is not a similar 

relationship for concretes containing silica fume, it is likely that Abrams’ rule is still valid. Its effect on 

BA has yet to be developed. 

B.4.4.2 Effect of Age 

It is also possible to relate the 28-day compressive strength to its early-age values at a specific time t

using Abrams’ rule. As given in Popovics:(61)

For Type I cement (equation 233): 

6 46 = +

t

BA

 (233) 

For Type III cement (equation 234): 
164 

6 27 = +

t

BA

 (234) 

This hyperbolic function approximates the strength gain of the concrete well within the limits of 3 days 

and 1 year. The values, however, are too low at 1 day. 

B.4.4.3 Effect of Aggregate Content 

To develop the relationship between compressive strength and aggregate content, the importance of 

aggregate gradation was recognized. According to Gilkey, concrete strength is influenced by: 1) the ratio 

of cement to mixing water, 2) the ratio of cement to aggregate, 3) grading, surface texture, shape, strength 

and stiffness of aggregate particles, and 4) maximum size of the aggregate.(61) For concretes with 

identical w/c’s, the compressive strength increases as the maximum particle size decreases. 

The following ratio (equation 235) was developed to account for the effect of aggregate: 

0.17

⎟

⎠

⎞ ⎜

⎝

⎛ = CA

FA RatioAggregate

 (235) 

where, 

 FA = fine aggregate content and 

 CA = coarse aggregate content. 

 

Equation 235 was calibrated using the data provided by Ganju.(99) 

B.4.5 Compressive Strength Prediction Model 

Combining the effects of w/c, pozzolan content, aggregate content, and age on compressive strength 

yields the relationship shown in equation 236: 

c Age Pozzolan Aggregate c f '= Ratio × Ratio × Ratio × f (236) 

where, 

 f′c = compressive strength that includes the effects of age, pozzolan content, and 

aggregate content, 

fc = compressive strength calculated using only the w/c, 

RatioAge = factor that incorporates the influence of time on the compressive strength, 

RatioPozzolan = factor that includes the effect of pozzolan content on compressive strength, 

and 

RatioAggregate = factor that accounts for aggregate content on compressive strength. 

This relationship is used in COMET to predict concrete compressive strength. 
165 

Limitations of this equation are: 

• It is only valid for normal weight concrete in the ranges for which it was calibrated. Notably, 

w/c ranges from 0.3 to 1.0. Compressive strength ranges from 0 to 82.7 MPa.(61)

• The only pozzolan for which it is calibrated is fly ash. 

• To account for the effect of pozzolan and age on compressive strength, it is assumed that AA

and AA1 values in Abrams’ formulation are the same. 

• It is assumed that all 10 conditions required to apply Abrams’ rule hold. 

B.5 MODELS USED IN THE HIPERPAV DOWEL-CONCRETE INTERACTION ANALYSIS 

MODULE 

Dowel bars are subjected to combined environmental loading and dynamic traffic loading at the joint 

during the pavement’s lifetime. The dowel bar module in HIPERPAV assesses how the dowel bars affect 

the early-age performance of JPCP. If the bearing stress is greater than the concrete’s early-age 

compressive strength, then it is probable that the dowel will loosen over the lifetime of the pavement at a 

faster rate than if the bearing stress is less than the concrete’s compressive strength. The model that 

predicts the early-age dowel bar bearing stress is summarized below. 

B.5.1 Dowel Bar Bearing Stress Model 

To calculate the dowel bar bearing stress, several inputs are needed in the model. These inputs are listed 

in table 39. 

Table 39. Input to the dowel bar bearing stress model. 

Input Category Parameter Units Variable 

Diameter m dD

Poisson ratio Unitless νD

Modulus MPa ED

Dowel bar 

Effective modulus of dowel support MPa/m KD

Joint Opening MPa w 

Modulus MPa Ec

Poisson ratio Unitless νc

CTE m/m/oC αc

Length m L 

Slab 

Thickness m h 

Linear temperature gradient oC/m ΔT Load and support Slab support reaction modulus MPa/m k 

For the system, the radius of relative stiffness is calculated in equation 237: 

( )

0.25

2

3

12 1 ⎥

⎦

⎤ ⎢

⎣

⎡

− = k

E h

c

c

ν

l

 (237) 
166 

as are the dowel moment of inertia, ID, in equation 238: 

4

64

1

D d D I = π

 (238) 

and the relative stiffness of the dowel-concrete system, β. Equations 237–239 can be found in Huang.(64)

 

4

4 D D

D D

E I

K d β =

 (239) 

A dowel at the joint is subjected to moments Mo, as shown in figure 63. 

Mo Mo

Figure 63. Schematic of dowel deformation and loading at the joint. 

To model the behavior of the dowel at the joint, some assumptions are made. Two cases are shown in 

figure 64. In the first case, the gray dowel depicts behavior at the joint, assuming that the concrete 

underneath it does not deform, or that there is no concrete compliance. In the second case, the concrete 

has deformed under the black dowel. 

yo

α

α’

Dowel without 

Concrete Compliance

Dowel with

Concrete Compliance

yo

α

α’

Dowel without 

Concrete Compliance

Dowel with

Concrete Compliance

Figure 64. Schematic of dowel deformation without concrete compliance and with concrete 

compliance at the joint. 

To relate the angles of the dowels as they leave the concrete to the deflection of the dowel at the slab face, 

yo, the relationship in equation 240 is used: 
167 

( ) dx

dyo tan α −α' =

 (240) 

where, 

 α = slope of the dowel without concrete compliance, 

 α′ = slope of the dowel with concrete compliance, and 

 yo = deflection of the dowel at the slab face. 

According to Timoshenko and Lessels, and as reported by Friberg, the deflection of the dowel at the slab 

face yo|x=0 when it is subjected to a moment is as shown in equation 241:(66,100)

 

( ) d d

o

x d d

x

o

x o E I

M

x x

E I

M e

y 2

0

0 2 2

cos sin

2 β β β β

β − ⎥ =

⎦

⎤ ⎢

⎣

⎡ − − =

=

−

=

 (241) 

From Westergaard, the slope of the dowel without concrete compliance can be calculated. Westergaard 

solved for the deflection of a curled pavement, z.

(101) Adjusted for the coordinate system presented here, it 

is shown in equation 242: 

z zo [ ] ( ) () tan tanh cosV coshV tan tanh sinV sinhV

sin 2 sinh 2

2cos cosh λ λ λ λ

λ λ

λ λ − + + + − = −

 (242) 

where, as defined in equations 243–246, 

8l

L λ =

 (243) 

( ) 2

z = 1+ ⋅ ⋅∇T ⋅l o ν c α c , (244) 

2l

coord x V =

 (245) 

2

L

xcoord

− =

 (246) 

Taking the differential of the deflection with respect to x yields the slope. With the small angle 

assumption, the slope of the dowel approximates the angle of the dowel, α, under deformation when it 

leaves the slab (equation 247): 
168 

[ ] [ ]

[ ][ ] ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⋅ ⋅ + ⋅

− + ⋅ − ⋅ + ⋅ + ⋅ − ⋅ ⋅ − = V V V VV V V V

zo tan tanh cos sinh sin cosh

tan tanh sin cosh cos sinh

sin 2 sinh 2

2cos cosh

2

1

λ λ

λ λ

λ λ

λ λ

α

l (247) 

To determine α′, the dowel is modeled as a cantilever beam. The angle of the deflected dowel shape, α′, 

at the center of the joint is given by equation 248, as derived by Timoshenko and Lessels.(66) 

D D

o

E I

M w

2

α'=

 (248) 

Mo, the moment causing the dowel to deflect at an angle of α′ now must be determined. Combining 

equation 248 with Friberg’s (equation 241) and the geometric relationship (equation 240), equation 249 

for the moment is derived as a function of α. 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

=

w

E I M D D

o

β

α

2

2

 (249) 

The resulting dowel bar bearing stress, from Huang, is shown in equation 250: 

b o K D f = y (250) 

The effect of varying nine of the model input are shown in figures 65 to 73 and is summarized in table 40. 

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30 35 40 45

Dowel Diameter (dD) (mm)

Bearing Stress (MPa)

Figure 65. Effect of varying the dowel diameter (dD) on the bearing stress. 
169 

0

2

4

6

8

10

12

0 100000 200000 300000 400000 500000 600000 700000 800000 900000

Effective Modulus of Dowel Support (KD) (MPa/m)

Bearing Stress (MPa)

Figure 66. Effect of varying the effective modulus of dowel support (KD) on the bearing stress. 

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30

Joint Opening (w) (mm)

Bearing Stress (MPa)

Figure 67. Effect of varying the joint opening on the bearing stress. 
170 

0

1

2

3

4

5

6

7

8

9

10

15000 20000 25000 30000 35000 40000 45000

Concrete Modulus (Ec) (MPa)

Bearing Stress (MPa)

Figure 68. Effect of varying the concrete modulus (Ec) on the bearing stress. 

0

1

2

3

4

5

6

7

8

9

10

6 7 8 9 10 11 12 13

Concrete Coefficient of Thermal Expansion (αc) (με/C)

Bearing Stress (MPa)

Figure 69. Effect of varying the concrete CTE (αc) on the bearing stress. 
171 

0

20

40

60

80

100

120

0123456789

Slab Length (L) (m)

Bearing Stress (MPa)

Figure 70. Effect of varying the slab length (L) on the bearing stress. 

0

20

40

60

80

100

120

150 200 250 300 350 400

Slab Thickness (h) (mm)

Bearing Stress (MPa)

Figure 71. Effect of varying the slab thickness (h) on the bearing stress. 
172 

0

20

40

60

80

100

120

0 50 100 150 200 250 300

Modulus of Subgrade Reaction (k) (MPa/m)

Bearing Stress (MPa)

Figure 72. Effect of varying the modulus of subgrade reaction (k) on the bearing stress. 

0

50

100

150

200

250

300

350

400

450

-1 -0.5 0 0.5 1

Linear Temperature Gradient (T) (oC/mm)

Bearing Stress (MPa)

Figure 73. Effect of varying the linear temperature gradient (T) on the bearing stress. 
173 

Table 40. Summary of the sensitivity analysis of the dowel model. 

Input Parameter Influence on 

Bearing 

Stress 

Influence on 

Bearing Stress 

According to 

Friberg(100)

Dowel diameter (dD) ↑ ↑ ↓

Effective modulus of dowel support (KD) ↑ ↑ – 

Joint opening (w) ↑ ↓ ↑

Concrete modulus (Ec)↑ ↑ – 

Concrete CTE (αc) ↑ ↑ – 

Slab length (L) ↑ ↓ – 

Slab thickness (h) ↑ ↑ – 

Modulus of subgrade reaction (k) ↑ ↓ – 

|Temperature gradient| (∇T)↑ ↑ – 

B.5.2 Dowel Bar Stress Due to Shear Loading 

When the joints in pavements are loaded in shear (Pslab in MPa/m) as illustrated in figure 74, the dowel 

bars resist this loading (Pdowel in MPa/m). The free edge deflection, yo (in meters), is restrained by twice 

the value of y1 (in meters) due to the dowels. 

Pslab

Pslab

Pdowel

yo

y1

Pslab

Pslab

Pdowel

yo

y1

Figure 74. Schematic representation of slabs loaded in shear. 

The resulting load on the dowel is shown in equation 251: 

( ) 2 1 P C y y dowel = o − (251) 
174 

where, 

 C = Huang’s spring constant (MPa).(64)

Derived from Hetenyi’s beam theory, the load on the slab is shown in equation 252:(102) 

 (252) 

where, 

 k = slab support reaction modulus (MPa/m), 

 λb = beam characteristic (m-1), and 

 l = radius of relative stiffness (m). 

Further proof of this derivation was provided by Skarlatos (equation 253):(71)

1 2 1

2

2 y k y

k Pslab l l ⎟ = ⎠

⎞ ⎜

⎝

⎛ =

 (253) 

Equilibrium (equation 254) is achieved when: 

Pdowel = Pslab (254) 

Solving for y1 in term of yo yields equation 255: 

k C

Cy y o

2 2 1+ = l (255) 

Since yo is known from Westergaard theory, Pdowel can be calculated using equation 256: 

P C(y y ) Dowel Spacing (m) dowel = o − 2 1 × (256) 

Then the deflection of the dowel at the joint face (δface in m) can be determined by equation 257: 

⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛ + = ×

EI

w

face Pdowel 3 4

2

β

β δ

 (257) 

where, 

 β, w, E, and I are previously defined. 

k k 1 

Pslab = 2 y1 = y1 = kl √2y1 since λb = 

2 λb λ b l √2 
175 

The dowel bearing stress (σb in MPa) can now be calculated in equation 258: 

( ) b face Kdowel σ bearing stress = δ ×

 (258) 

where, 

 Kdowel was previously defined in table 39. 

This bearing stress is plotted in the HIPERPAV dowel bar module and compared to the concrete’s 

compressive strength. 

B.5.3 Dowel Analysis Module in HIPERPAV II 

A screen capture of the dowel analysis module in HIPERPAV II is shown in figure 75. The calculated 

results are for the HIPERPAV II default input. 

Figure 75. HIPERPAV II screen capture showing typical output from the dowel bar module. 

177 

APPENDIX C FIELD INVESTIGATION 

Four field sites were investigated for validation of the HIPERPAV II system: 

• Two inservice JPCP sections were evaluated to validate the long-term performance models in 

the JPCP module. 

• Two newly constructed CRCP sections were instrumented to validate the CRCP early-age 

behavior module. 

It is believed that the number of field sites evaluated will provide the minimum level of information 

necessary to meet the objectives of this effort successfully. However, future data from field sites could be 

used for local customization. This section describes the steps performed for validation of both the JPCP 

and CRCP pavement sites investigated. 

C.1 JPCP SITES INVESTIGATED 

JPCP sites investigated include a section on U.S. Highway 50 in Illinois and a bypass section of a farm to 

market road near Ticuman, Mexico. The selection of both sites was heavily weighted on the fact that 

extensive early-age and performance information is available for both of these sections. 

C.1.1 JPCP Section on U.S. Highway 50, Illinois 

A field investigation and monitoring of a JPCP test section on U.S. Highway 50 near Carlyle, IL, was 

performed from August 7–10, 2001. Following is some background information on this section. 

C.1.1.1 Background Information 

The test sections were constructed and instrumented from April to August in 1986 on U.S. Highway 50 

just west of Carlyle, IL. Early-age monitoring was performed by researchers at the University of Illinois 

at Urbana-Champaign.(103) This data was used to develop mechanistic design procedures for the Illinois 

DOT. The following tables and figures provide a brief summary of the published data. Table 41 gives a 

brief description of the JPCP test sections. 

Table 41. JPCP test section descriptions.(103) 

Section 

Design 

Thickness 

(mm) 

Underdrains

Sealed 

Edge 

Joint 

Section 

Length (m) 

AA 241 Y N 304 

IA 216 N Y 311 

JA 216 N Y 305 

KA 216 Y Y 305 

LA 216 Y N 335 

MA 191 Y Y 335 

NA 191 Y N 305 
178 

Section AA borders a bridge abutment on the west and is located 4.8 km from the other sections, which 

run continuously between IA to NA from west to east. The JPCP sections in this study were constructed 

with 6.1-m dowelled transverse joints. A 102-mm cement aggregate mixture (CAM) was used as the 

subbase. The concrete mix design was kept constant throughout the test sections and is shown in table 

42. 

Table 42. Concrete mix design—88PCC0710.(104)

Constituent Description Quantity 

Cement Continental cement 341 kg/m2 

Coarse aggregate Falling springs quarry 022CAM07 1121 kg/m2 

Fine aggregate Keyesport sand and gravel #2 027FAM01 666 kg/m2 

Water – 148 kg/m2 

Air entrainment Darex – 

Water reducer Type A—WRDA® with Hycol – 

w/c – 0.43 

Mortar factor – 0.80 

Strength gain data was reported by Zollinger and Barenberg.(103) The reported centerpoint loading 

flexural strength at 28 days showed an average of 5.8 MPa, and the third point loading flexural strength at 

28 days showed an average of 4.9 MPa. The average 28-day modulus of elasticity for all sections is 

28,680 MPa. 

Table 43 contains traffic data for each test section between 1987 and 1999 provided by Illinois DOT. 

This table shows the accumulation of ESALs for all sections. In this analysis, the traffic is divided into 

vehicular categories and factors to calculate ESALs. 

Table 43. Accumulation of ESALs. 

Year 

Average 

Daily 

Traffic 

Heavy 

Commercial 

Vehicles 

Multiple 

Unit 

Vehicles 

Single 

Unit 

Vehicles

Passenger 

Vehicles 

MU 

Factor

SU 

Factor

PV 

Factor 

Distribution 

Factor 

ESALs

(106

) 

1987 3400 461 340 121 2939 567.21 135.78 0.15 0.5 0.10

1988 4175 475 350 125 3700 567.21 135.78 0.15 0.5 0.11

1989 4950 594 338 256 4356 567.21 135.78 0.15 0.5 0.11

1990 4875 713 325 388 4162 567.21 135.78 0.15 0.5 0.12

1991 4800 831 313 519 3969 567.21 135.78 0.15 0.5 0.12

1992 4750 950 300 650 3800 567.21 135.78 0.15 0.5 0.13

1993 4700 900 350 550 3800 567.21 135.78 0.15 0.5 0.14

1994 4800 850 400 450 3950 567.21 135.78 0.15 0.5 0.14

1995 4900 800 450 350 4100 567.21 135.78 0.15 0.5 0.15

1996 5000 750 500 250 4250 567.21 135.78 0.15 0.5 0.16

1997 5100 773 515 258 4327 567.21 135.78 0.15 0.5 0.16

1998 5253 796 530 265 4457 567.21 135.78 0.15 0.5 0.17

1999 5411 820 546 273 4591 567.21 135.78 0.15 0.5 0.17

 Total 1.80
179 

Table 44 compares the design ESALs versus the consumed ESALs as of 1999. All sections but section 

AA had surpassed the number of design ESALs by 1999. Sections MA and NA had nearly three times 

the number of design ESALs by 1999. 

Table 44. Design and consumed ESALs. 

Section Design 

ESALS 

1999 

Cumulative 

ESALs 

Percent 

Consumed

AA 2.60 1.80 69.1 

IA 1.50 1.80 119.8 

JA 1.50 1.80 119.8 

KA 1.50 1.80 119.8 

LA 1.50 1.80 119.8 

MA 0.64 1.80 280.8 

NA 0.64 1.80 280.8 

Table 45 gives friction and ride quality data for the test sections at different times between 1990 and 

1999, from Illinois DOT records. 

Table 45. Historical ride quality data. 

Year Age 

(years) IRI (m/km) 

1994 8 1.53 

1996 10 1.82 

1998 12 1.78 

Illinois DOT performed falling weight deflectometer (FWD) tests on the test sections in 1994 and 1998. 

Table 46 gives the results for D0, deflection under the load, and LTE. 

Table 46. Historical FWD data. 

Section Year D0 

(microns) 

Design 

Thickness 

LTE, 

Transverse 

(%) 

LTE, 

Shoulder 

(%) 

LTE, 

Cracks 

(%) 

1994 86.4 92.9 93.3 N/A AA 

1998 66.0 

241 mm 

83.8 76.4 N/A 

1994 121.9 85.1 70.8 N/A IA 

1998 106.7 

216 mm 

83.9 61.7 N/A 

1994 127.0 83.4 81.3 87.9 JA 

1998 109.2 216 mm 84.9 51.0 61.6 

1994 104.1 91.7 89.8 N/A LA 

1998 104.1 

216 mm 

85.4 68.1 N/A 

1994 139.7 89.8 75.3 88.0 NA 

1998 139.7 191 mm 82.8 64.0 81.0 

N/A = Not applicable (no cracks observed) 
180 

Before construction, the modulus of subgrade reaction was determined at several locations along the site 

and reported by Zollinger and Barenberg. An average static k-value of 130 psi was observed, although no 

test date was reported.(103) 

In addition, historical condition survey data for the seven test sections was obtained from Illinois DOT 

and is presented in tables 47 through 53. In summary, each section remains intact, with the only visible 

distresses being a very small amount of transverse cracking and construction joint deterioration in several 

sections and some patching in section IA. The sections are performing well, considering the level of 

ESALs and the age of the pavements. 

Table 47. Section AA—historical* and current condition survey. 

Year Distress Units Severity 1990 1992 1995 1997 2001 

Low 0 0 0 0 0

Corner break Number Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0 Longitudinal 

cracking Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 1

Medium 0 0 0 0 0

Random 

longitudinal 

cracking 

Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 17

Spalling Number Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0 Transverse 

cracking Number 

High 0 0 0 0 0

* Data provided by Illinois DOT 
181 

Table 48. Section IA—historical* and current condition survey. 

Year Distress Units Severity 1990 1992 1995 1997 2001 

Low 0 0 0 0 0

Corner break Number Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0 Longitudinal 

cracking Lane feet 

High 0 0 0 0 0

Low 96 96 96 96 0

Patching Lane feet Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0

Random 

longitudinal 

cracking 

Lane feet 

High 0 0 0 0 0

Low 1 1 1 1 2

Spalling Number Medium 0 0 0 0 0

High 0 0 0 0 0

Low 2 2 0 0 0

Medium 2 2 4 4 0 Transverse 

cracking Number 

High 0 0 0 0 2

* Data provided by Illinois DOT 
182 

Table 49. Section JA—historical* and current condition survey. 

Year Distress Units Severity 1990 1992 1995 1997 2001 

Low 0 0 0 0 0

Corner break Number Medium 0 0 0 0 1

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0 Longitudinal 

cracking Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 0

Patching Lane feet Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0

Random 

longitudinal 

cracking 

Lane feet 

High 0 0 0 0 0

Low 0 0 2 0 1

Spalling Number Medium 1 1 0 1 0

High 0 0 0 0 0

Low 0 0 3 2 0

Medium 4 6 3 6 1 Transverse 

cracking Number 

High 0 0 0 0 5

* Data provided by Illinois DOT 
183 

Table 50. Section KA—historical* and current condition survey. 

Year Distress Units Severity 1990 1992 1995 1997 2001 

Low 0 0 0 0 0

Corner break Number Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0 Longitudinal 

cracking Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 0

Patching Lane feet Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0

Random 

longitudinal 

cracking 

Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 5

Spalling Number Medium 0 0 0 0 2

High 0 0 0 0 0

Low 1 1 0 0 0

Medium 0 0 0 0 0 Transverse 

cracking Number 

High 0 0 0 0 0

* Data provided by Illinois DOT 
184 

Table 51. Section LA—historical* and current condition survey. 

Year Distress Units Severity 1990 1992 1995 1997 2001 

Low 0 0 0 0 0

Corner break Number Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0 Longitudinal 

cracking Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 0

Patching Lane feet Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0

Random 

longitudinal 

cracking 

Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 5

Spalling Number Medium 0 0 0 0 6

High 0 0 0 0 0

Low 7 7 0 0 0

Medium 0 0 0 0 0 Transverse 

cracking Number 

High 0 0 0 0 0

* Data provided by Illinois DOT 
185 

Table 52. Section MA—historical* and current condition survey. 

Year Distress Units Severity 1990 1992 1995 1997 2001 

Low 0 0 0 0 0

Corner break Number Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0 Longitudinal 

cracking Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 0

Patching Lane feet Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 0 0 0 0

Medium 0 0 0 0 0

Random 

longitudinal 

cracking 

Lane feet 

High 0 0 0 0 0

Low 0 0 0 0 5

Spalling Number Medium 0 0 0 0 0

High 0 0 0 0 0

Low 0 2 0 0 0

Medium 0 0 0 0 0 Transverse 

cracking Number 

High 0 0 0 0 0

* Data provided by Illinois DOT 
186 

Table 53. Section NA—historical* and current condition survey. 

Year Distress Units Severity 1990 1992 1995 1997 2001 

Low 0 0 0 0 0 

Corner break Number Medium 0 0 0 0 1 

High 0 0 0 0 0 

Low 0 0 0 0 1 

Medium 0 0 0 0 0 Longitudinal 

cracking Lane feet 

High 0 0 0 0 0 

Low 0 0 0 0 0 

Patching Lane feet Medium 0 0 0 0 0 

High 0 0 0 0 0 

Low 0 0 0 0 0 

Medium 0 0 0 0 0 

Random 

longitudinal 

cracking 

Lane feet 

High 0 0 0 0 0 

Low 0 0 0 0 17 

Spalling Number Medium 0 0 0 0 0 

High 0 0 0 0 0 

Low 3 6 5 5 0 

Medium 0 1 4 4 1 Transverse 

cracking Number 

High 3 3 2 3 7 

* Data provided by Illinois DOT 

C.1.1.2 Evaluation Activities 

The monitoring included the following activities: 

• Weather station installation to collect ambient temperature, relative humidity, and solar 

radiation. 

• Visual inspection of each JPCP section. 

• FWD measurements of slab deflection and load transfer. 

• Mastrad® demountable mechanical strain gage (DEMEC) caliper measurements of joint 

movement. 

• Face® Dipstick® profiling in longitudinal and diagonal directions. 

• Coring to determine depths and provide specimens for laboratory testing. 

The data collected from this experiment was used with early-age information available for this site to 

validate the long-term JPCP performance models in HIPERPAV II. 

A condition survey with photo and video documentation for all seven test sections was performed during 

the afternoon of August 7, 2001. The location and severity of each distress was documented. As in the 

historical condition survey data, few distresses were evident in the sections. The major distresses 

included a few slabs with transverse cracking and some low severity transverse joint spalling. The 
187 

pavement has performed well, considering all sections except section AA exceeded the number of design 

ESALs by 1999, according to the original design. 

Sections AA, IA, JA, KA, and LA were tested with FWD at midslab for backcalculation of the modulus 

of subgrade reaction (k) and at transverse and longitudinal shoulder joints for LTE. Each test consisted of 

a seating drop followed by drops at three increasing loads, typically near 9, 12, and 15 kips. The 

approach and leave sides of transverse joints were tested. Table 54 provides a summary of center slab 

deflection bowls that have been normalized to 9 kips and are compared to historical deflections in 1994 

and 1998. 

Table 54. Center slab deflections in microns, normalized to 4090 kg for Illinois JPCP evaluation. 

Section Statistic 0 mm 

(1994) 

0 mm 

(1998) 0 mm 304.8 mm 

609.6 

mm 

914.4 

mm 

1219.2 

mm 

1524 

mm 

1829 

mm 

Mean 86.4 66.0 67.8 62.2 54.1 46.7 39.4 33.3 28.2 AA 

St. Dev – – 5.6 4.8 3.6 2.8 2.0 1.5 1.0 

Mean 121.9 106.7 135.6 123.4 106.4 88.6 72.4 57.4 43.7 IA 

St. Dev – – 26.7 23.1 17.3 12.7 9.1 6.6 4.3 

Mean 127.0 109.2 131.6 124.0 110.5 93.0 78.0 62.2 47.2 JA 

St. Dev – – 4.3 4.3 5.1 5.1 5.1 4.6 3.8 

Mean N/A N/A 121.2 112.8 99.3 84.6 71.9 59.2 47.5 KA 

St. Dev – – 16.3 14.2 9.9 5.1 2.0 2.5 2.3 

Mean 104.1 104.1 128.0 121.9 106.7 92.7 75.9 61.5 48.8 LA 

St. Dev – – 16.0 13.7 9.7 6.6 3.0 2.0 1.0 

Table 55 contains load transfer data and statistics for transverse joints for approach slabs. 
188 

Table 55. Approach slab load transfer data for Illinois JPCP evaluation. 

Load Transfer Efficiency 

Section 

Avg. 

Load 

(N) 1994 (%) 1998 (%) Mean (%) St. Dev (%) Median (%) 15th Percentile (%)

39 77.3 1.41 77.2 76.1

AA 52 77.1 1.01 76.8 76.2

66 

92.9 83.8

77.1 1.08 77.0 76.3

40 80.4 1.17 80.3 79.4

IA 53 80.2 1.44 80.3 78.8

68 

85.1 83.9

80.0 1.38 80.3 78.7

39 81.2 1.32 81.6 80.0

JA 52 80.9 0.60 80.7 80.4

67 

83.4 84.9

80.6 0.74 80.7 79.9

39 81.6 1.06 81.4 80.9

KA 51 81.7 0.89 81.6 81.0

66 

N/A N/A

81.9 1.17 81.6 81.0

38 82.5 0.56 82.6 82.0

LA 50 83.2 0.99 83.5 82.3

65 

91.7 85.4

82.7 0.78 83.2 81.8

39 79.6 0.06

51 79.9 0.51

Cracks 

(Section 

IA) 66 

N/A N/A

80.1 0.20

Not enough data (two values) 

Table 56 includes load transfer data for transverse joints and cracks for leave slabs. Statistical data is also 

included in the table. The values for the leave slabs are greater than the approach slabs. 
189 

Table 56. Leave slab load transfer data for Illinois JPCP evaluation. 

Load Transfer Efficiency 

Section 

Avg. 

Load 

(N) 1994 (%) 1998 (%) Mean (%) St. Dev (%) Median (%) 15th Percentile (%)

39 89.5 2.72 91.1 87.3

AA 51 89.1 2.73 89.3 86.7

65 

92.9 83.8

88.9 2.98 89.9 86.3

40 87.4 1.55 87.6 86.4

IA 53 87.9 1.38 87.7 86.8

68 

85.1 83.9

87.4 1.28 87.5 86.5

39 87.4 1.86 88.4 85.5

JA 52 88.4 2.38 89.1 86.1

66 

83.4 84.9

87.7 2.03 88.0 85.8

39 92.2 2.08 92.7 90.5

KA 51 93.5 2.53 94.1 91.1

67 

N/A N/A

92.7 1.63 93.6 91.1

38 92.3 1.34 92.7 91.5

LA 50 93.4 0.79 93.4 92.6

64 

91.7 85.4

92.7 0.68 92.6 92.2

42 92.6 0.40 

56 93.3 0.99 

Cracks 

(Section 

IA) 72 

N/A N/A 

92.4 0.80 

Not enough data (two values) 

T-type thermocouples were installed at three different depths (13, 76, and 127 mm) at sections AA, IA, 

and KA to monitor the temperature profile of the pavement. An additional thermocouple was installed at 

section AA at 241 mm to monitor the temperature at the bottom of the pavement. Measurements were 

taken manually to provide corresponding pavement temperature data during FWD and DEMEC testing. 

Figure 76 gives the temperature profile for section AA. 
190 

0

50

100

150

200

250

300

25 30 35 40 45

Pavement Temperature (°C)

Depth (mm)

AM

Midday

PM

Figure 76. Pavement temperature profiles for Illinois JPCP evaluation. 

The gradient moves from slightly negative and increases throughout the day. The results for sections IA 

and KA mirrored the trends of section AA. 

A DEMEC caliper was used to measure the joint and crack movements by measuring the distance 

between metal studs epoxied to the pavement surface. Approximately five consecutive transverse joints 

were tested in each section. In addition, four longitudinal joints and all transverse cracks between the 

consecutive transverse joints were tested. Transverse cracks were included because they reduce the total 

movement at transverse joints by allowing expansion and contraction. Figure 77 shows the joint 

movement in section AA at different transverse joints. 

-0.1

0

0.1

0.2

0.3

0.4

0.5

28 30 32 34 36 38 40 42

Mean Pavement Temperature (°C)

Movement (mm)

AA 12

AA 13

AA 14

AA 15

AA Sh

Figure 77. Joint movement for section AA in Illinois JPCP evaluation. 
191 

The downward trend indicates joints closing under higher temperatures and opening under cooler 

temperatures. All other sections showed the same trend. After 36 oC, no further movement is observed, 

possibly because of joint closure after that temperature. Table 57 gives linear trendline data for all 

sections and includes transverse joints, transverse cracks, and longitudinal joints. High r2 values show 

that the joint and crack movements follow a linear trend. 

Table 57. Joint movement summary for Illinois JPCP evaluation. 

Type* Section AA Section IA Section JA Section KA Section LA Section MA Section NA 

mm/°

C 

r2 mm/°C r2 mm/°C r2 mm/°C r2 mm/°C r2 mm/°C r2 mm/°C r2 

T.J. −0.040 0.97 –0.026 0.99 –0.037 0.94 –0.034 0.98 –0.034 0.99 –0.080 1.00 –0.028 0.97 

T.J. –0.035 0.97 –0.054 1.00 –0.049 0.97 –0.024 1.00 –0.029 0.98 –0.041 0.97 –0.023 0.97 

T.J. –0.036 0.95 –0.035 0.99 –0.064 0.96 –0.047 1.00 –0.045 0.97 –0.053 0.96 –0.025 1.00 

T.J. –0.032 0.96 –0.026 0.99 –0.059 0.96 –0.020 1.00 –0.036 0.99 –0.030 0.96 –0.043 1.00 

Mean 

T.J. 

−0.036 – –0.035 – –0.052 – –0.031 – –0.036 – –0.051 – –0.030 – 

Crack – – –0.054 0.93 – – – – – – – – –0.080 0.86 

Crack – – –0.091 0.96 – – – – – – – – – – 

L.J. –0.020 0.90 –0.059 0.98 –0.057 0.96 –0.024 1.00 – – – – – – 

*T.J. = Transverse Joint, L.J. = Longitudinal Joint 

A Dipstick profiling device was used to establish longitudinal and diagonal surface profiles for pavement 

slabs and to compute IRI in each section. Profiles were measured during both the morning and afternoon 

to determine possible environmental effects of curling and warping on the pavement slabs. Figure 78 

shows a typical longitudinal profile for section AA after correcting for slope. A curling pattern at every 

6-m interval corresponding to the slab length for this section is evident from this figure. 

0

2

4

6

8

10

12

14

0 10 20 30 40 50

Distance (m)

Deviation from Grade (mm)

AA

Figure 78. Longitudinal profiles for section AA, 253-mm thickness. 
192 

Six 152-mm and six 102-mm cores were drilled. The following list describes the size and locations of the 

cores: 

• Section AA—five 102-mm cores. 

• Section IA—one 102-mm and one 152-mm cores. 

• Section JA—two 152-mm cores. 

• Section KA—three 152-mm cores. 

The 152-mm cores were tested for splitting tensile strength. The 102-mm cores were tested for Young’s 

Modulus of Elasticity (E) and CTE. Thickness measurements were also taken from the cores and are 

compared to the design thickness in table 58. 

Table 58. Summary of thickness measurements for Illinois JPCP evaluation. 

Section Design Thickness 

(mm) 

Mean Measured 

Thickness (mm) 

AA 241 253

IA 216 230

JA 216 220

KA 216 220

C.1.2 JPCP Section on Ticuman Bypass, Mexico 

In the past, the project team has closely followed the design, construction, and interim evaluations of a 

JCP section in Mexico. This section was part of a demonstration project to promote the use of PCC for 

highways in Mexico. In 1993, a cement producer in cooperation with the Mexican Secretariat of 

Communications and Transports conducted this demonstration JCP construction project. The project 

entailed rehabilitating an existing asphalt pavement structure with a JCP overlay. 

Pavement evaluation studies were initiated during and immediately after construction. Two years later, a 

performance evaluation was performed that included deflection testing, evaluation of the riding quality, 

and condition surveys. On the second evaluation, it was observed that the traffic patterns for that area of 

the country had changed drastically, subjecting the study section to an excessive increase in traffic 

loading. Some minor distresses were observed during that evaluation that later progressed as the traffic 

loads increased. 

 

Given that the Ticuman bypass possessed many of the characteristics desired for validation of the JCP 

long-term pavement performance models in HIPERPAV II, the project team decided to evaluate this 

section further after approval from FHWA. This section, describes the Ticuman bypass JCP section and 

summarizes the design, construction, and post-construction evaluations to date. 

C.1.2.1 Ticuman Bypass Preliminary Information 

The Ticuman bypass section is located on the Yautepec-Jojutla farm-to-market road in the State of 

Morelos. The section serves as a bypass to the town of Ticuman. Figure 79 shows the general location 

and layout of the road. The Ticuman bypass is oriented to the north and south and services a resort area, 
193 

an aggregate quarry, and local farming and ranching operations. The project length is approximately 8.5 

km that, for the most part, run along the edge of a ridge, down into a flood plain, and across a river. 

Pacific Ocean

Monterrey

Guadalajara

Mexico 

City

Puebla

Gulf of 

Mexico

Project 

Site

Ticuman

Pacific Ocean

Monterrey

Guadalajara

Mexico 

City

Puebla

Gulf of 

Mexico

Project 

Site

Ticuman

Figure 79. Ticuman bypass project location. 

The Ticuman bypass is a two-lane road with 3.35-m wide lanes. The pavement structure is composed of a 

nondoweled JCP overlaying an existing HMA pavement. The slab thickness averages 233 mm and has a 

joint spacing of 4.5 m. The existing structure is composed of an HMA layer with an average thickness 

ranging from 50 to 80 mm. From a site inspection before construction, it was observed that the HMA was 

severely cracked in some areas. Cores extracted before construction showed an average thickness of 250 

mm for the base layer. The base layer showed a plasticity index of 16.7 classified as GC under the 

unified classification system (UCS) or A–2–6 under the AASHTO classification system. The natural soil 

material showed a plasticity index of 17.6 with classification CL (UCS) or A–6 (AASHTO). 

The mix design used for this project had the following proportions: 

• Portland cement type I 280 kg/m3

• Coarse aggregate 1,006 kg/m3

• Fine aggregate 932 kg/m3

• Water 158 liters/cubed meter (l/m3

) 

• Air entrainer 115 millilters per cubed meter (ml/m3

) 

• Water reducer 1,333 ml/m3

Given that the existing HMA pavement was in very poor conditions, the traffic for this section was 

minimal. However, after construction of the JCP, the traffic patterns changed drastically, and significant 

traffic was generated. Table 59 summarizes the traffic conditions throughout the history of the road. 
194 

Table 59. Historical traffic data. 

Year Estimated 

Annual Average 

Daily Truck 

Traffic 

Estimated 

Cumulative 18-

kip ESAL (106

) 

1993 40 0 

1995 299 0.09 

2001 759 1.71 

Annual temperatures for Ticuman were reported to range from 5 oC to 38 oC. Historic weather records for 

the days during construction were obtained from the meteorological center in Mexico (Comision Federal 

de Electricidad). 

The JCP was constructed from September 23 to October 12, 1993, with slip form paving equipment. 

Construction proceeded as scheduled with minimal delays. 

Table 60 shows the concrete compressive strength and stiffness statistics for the specimens taken at the 

Ticuman bypass (laboratory specimens from samples taken in the field, and core specimens extracted 

directly from the slab) tested after 28 days. Figure 80 shows the mean concrete compressive and flexural 

strength gain curves for the Ticuman bypass. This information is based on mean values from test results. 

Table 60. Summary statistics for 28-day PCC compressive strength in Ticuman bypass. 

Statistic Laboratory 

(MPa) 

Cores 

(MPa) 

Modulus of 

Elasticity (MPa) 

Mean 30.3 29.1 23,622 

Standard deviation 4.7 5.8 3,300 

Minimum 17.4 18.4 16,250 

Maximum 37.7 35.8 27,294 

Count 22 11 11 

Coefficient of variation 15.50% 19.95% 13.97% 
195 

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

Time (days)

Strength (MPa)

Compressive

Flexural

Figure 80. Mean concrete compressive and flexural strength gain curves for the Ticuman bypass. 

Table 61 shows the statistics for the flexural strength and the splitting tensile test results at 28 days for the 

Ticuman bypass. 

Table 61. Summary statistic for flexural strength and splitting tensile test results for the Ticuman 

bypass. 

Statistic Flexural 

(kg/cm2

) 

Splitting 

(kg/cm2) 

Mean 48 30 

Standard deviation 6 4 

Count 22 15 

Coefficient of variation 13.20% 12.50% 

Table 62 shows the summary statistics of the slab thickness, as obtained from PCC cores. 

Table 62. Summary statistics of core thickness for the Ticuman bypass. 

Statistic Thickness (cm) 

Mean 233 

Standard deviation 22.9 

Minimum 185 

Maximum 270 

Count 28 

Coefficient of variation 10.17% 
196 

The minimum thickness, as specified in the pavement design for the Ticuman bypass, was 200 mm. In 

the case of this particular project, since the existing asphalt structure was not leveled up, the variability in 

slab thickness seems reasonable for a JCP overlay, considering the high level of roughness of the existing 

asphalt structure. 

C.1.2.2 Previous Evaluations 

During and after construction, an extensive evaluation of the concrete pavement was performed, including 

joint cracking surveys and Dynaflect® deflection data collection. A cracking survey was performed on 

October 12, 1993. The survey consisted of making an inventory by visual inspection of those joints that 

were cracked. From this evaluation, cracks were observed to occur on average at every third joint (every 

13.5 m). However, the spacing between cracked joints was reduced, as demonstrated in subsequent 

evaluations. During late December 1993 and early January 1994, pavement deflections were measured 

with Dynaflect equipment. These deflection measurements were taken at the midspan of the slab and at 

the joints to determine the pavement structural capacity and LTE between joints, respectively. In the case 

of the Ticuman bypass, load transfer between slabs is provided solely by aggregate interlock, since no 

load transfer devices were considered or installed during the pavement construction. The deflection 

measurements on which this analysis is based were taken during the winter, and although the temperature 

during measurement was not low, it was expected that during the summer this would be higher, and thus, 

joint openings would be smaller. 

During July 1995, Dynaflect deflections were taken at the slab center and edge. In addition, a traffic 

survey and PSRs were obtained. A distress survey also was conducted in July 1995. That survey 

concluded that 3.3 percent of the slabs in the project were suffering from some type of cracking or 

spalling distress. Concurrent with the deflection data collection, 24-hour traffic information was collected 

over a 6-day period from a portable weigh-in-motion (WIM) station on the Ticuman bypass, which 

provided directional volumes and axle weights. From this traffic data, an average daily traffic of between 

800 and 1200 vehicles was estimated. 

C.1.2.3 JPCP Ticuman Bypass Evaluation in 2001 

As part of this project, an extensive pavement evaluation was conducted for the Ticuman bypass during 

August 21 through 24, 2001. The pavement evaluation studies included testing deflection with Dynaflect 

equipment, determining PSI under morning and afternoon conditions, monitoring joint openings, 

conducting distress surveys, and extracting PCC cores for characterizing PCC properties. An initial data 

reduction of the above collected information is described in the following sections. 

To perform detailed condition surveys, five sections were selected along the project. The stations for 

those sections are: 

• Section 1—from km 0+000 to km 0+228. 

• Section 2—from km 0+686 to km 0+869. 

• Section 3—from km 1+655 to km 1+842. 

• Section 4—from km 4+400 to km 4+569. 

• Section 5—form km 8+076 to km 8+300. 
197 

Since limited traffic control was available for this project, the above sections were selected based on 

visibility conditions. A minimum representative sample of at least 40 slabs per section was evaluated 

(180 m), for a total of 1 km. 

 

Other distresses observed included localized separation of the longitudinal joint. This was reportedly due 

to the fact that tie bars were not installed on some pavement sections, as was determined soon after 

construction. Some tie bar retrofitting also was observed on the areas with no tie bars. Some spalling 

problems that appeared soon after construction were repaired with PCC patches. Although some crack 

sealing was performed in 1995, no more maintenance was observed thereafter. The majority of the cracks 

had not been sealed at the time of this survey. In some localized areas, lane-to-shoulder dropoff also was 

observed. In addition to the detailed condition survey, a video documentation of the entire road was 

performed at a relatively low speed to capture the distress condition throughout the project. The distress 

survey indicates that 63 percent of the distresses are located on the northbound direction, with a total of 

22.4 percent of slabs presenting some distress type, and 37 percent on the southbound direction, with 13.3 

percent distressed slabs. The distress percentages on both directions agree with the load conditions for 

this road, which indicate a greater percentage of heavy vehicles on the northbound direction. 

Figure 81 shows a compilation of the three distress surveys performed at different dates through the 

history of Ticuman bypass. This figure demonstrates that longitudinal cracking is the predominant 

distress type. In addition, a considerably large number of slabs have a mix of longitudinal, transverse, 

and/or corner cracking. These slabs were reported as shattered slabs. Researchers believe that the lack of 

preventive maintenance has contributed significantly to the distresses observed on this road. 

0

5

10

15

20

25

30

35

40

Sep-93 Sep-94 Sep-95 Sep-96 Sep-97 Sep-98 Sep-99 Sep-00 Sep-01

Date

Number of Distresses per Kilometer

Transverse cracks

Longitudinal cracks

Corner breaks

Shattered slabs

Figure 81. Number of distressed slabs per kilometer for the Ticuman bypass. 

In addition to the above distresses, a faulting survey was performed on both lanes. Faulting was 

considered positive when the approach slab was higher than the departure slab. Figure 82 shows a 

distribution plot of the faulting recorded for all the sections investigated. Most of the faulting observed in 

this figure is between 0 and 2.0 mm and ranges between −2.5 mm and +4.0 mm. From this evaluation, 

section 1 showed slightly higher faulting readings than the rest of the sections. This section also 

presented a greater occurrence of sealant damage and spalling problems. 
198 

DEMEC studs were epoxied at an average of five to six joints and cracks to measure joint movement due 

to changes in temperature as a consequence of the diurnal cycle. Joint movement monitoring was 

performed in the morning and afternoon conditions during the days of August 22, 23, and 24. Monitoring 

of PCC temperature was achieved by installing thermocouple sensors at different depths throughout the 

slab depth. Figure 83 shows a distribution and cumulative plot of the joint opening at the Ticuman 

bypass. The average joint opening observed at the joints was in the order of 0.31 mm/oC. This opening 

varied from 0.18 to 0.39 mm/oC. 

0

10

20

30

40

50

60

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

More

Faulting (mm)

Frequency

0

20

40

60

80

100

120

Cummulative (%)

Frequency

Cumulative %

Figure 82. Faulting distribution for the Ticuman bypass. 

0.0

1.0

2.0

3.0

4.0

5.0

-0.051-0.049-0.047-0.045-0.043-0.041-0.039-0.037-0.035-0.033-0.031-0.029-0.027-0.025-0.023-0.021-0.019-0.017-0.015-0.013-0.011-0.009-0.007-0.005

More

Joint Movement (mm/oC)

Number of Joints

0

10

20

30

40

50

60

70

80

90

100

Cumulative %

Frequency

Cumulative %

Figure 83. Measured joint opening during August 22 to 24. 

Deflection testing was performed on August 22 from 2 p.m. to 6 p.m. on both lanes and under two 

loading conditions: at midslab to measure structural capacity, and at the joints to measure LTE. From this 

analysis, an average LTE of 93.0 percent was measured for the southbound direction; 90.2 percent was 

measured for the northbound direction. A comparison of the LTE analysis performed with 1993 data 
199 

shows that the LTE in 2001 was much higher than the LTE observed in 1993 (70 percent in average). 

The higher LTE values measured in 2001 initially were believed to be a difference in temperature 

conditions for each testing period. However, the range of temperatures observed for 1993 was from 22 oC 

to 39 oC, and those observed during 2001 ranged from 29 oC to 32 oC. Although a wider range of 

temperatures was observed during the spring of 1993, a comparison of LTE versus temperature for that 

period did not show any significant trend in LTE. During winter of 1993, a deflection analysis indicated 

an average effective joint spacing of 7.9 m. On the other hand, the joint movement analysis for summer 

of 2001 showed that all joints are working joints; thus the average joint spacing corresponds to the design 

joint spacing of 4.6 m. Since longer slab lengths result in larger joint openings and therefore reduced 

LTE, it is believed that the higher LTE values measured during summer 2001 are a result of the effective 

joint spacing observed. 

Structural capacity for this road was performed in several occasions after construction of the JCP on the 

Ticuman bypass. The first evaluation was performed at the end of 1993. During that evaluation, 

extensive deflection testing was performed at midslab for most of the slabs. A second evaluation was 

performed 2 years later, in 1995. Finally, during the visit in 2001, Dynaflect deflections were taken again 

at midslab for this purpose. 

Tables 63 and 64 compare the deflections taken in 1993, 1995, and 2001. Deflections correspond to the 

sensor under the load (D1) and the farthest sensor from the load (D5), which is believed to represent more 

closely the soil support conditions. Higher deflections were observed in 2001 than in the previous dates. 

No deflection data was obtained for the northbound direction in 1993. 

Table 63. Deflection indicators for the southbound direction (microns). 

Evaluation Average D1 Average D5 Average D1–D5 

1993 8.6 4.8 3.6 

1995 9.1 5.1 4.1 

2001 12.2 6.4 5.6 

Table 64. Deflection indicators for the northbound direction (microns). 

Evaluation Average D1 Average D5 Average D1–D5 

1995 9.1 5.1 4.1 

2001 10.2 4.8 5.3 

From a backcalculation analysis, a significant reduction in stiffness was observed in the HMA subbase 

layer after 1995. It is believed that lack of maintenance, along with the increasing traffic loads in this 

highway, may have contributed to reduced structural capacity. 

To obtain a measure of the ride quality for the Ticuman bypass, Mays meter equipment was used for 

determination of PSI. A rather low riding quality was measured for this section, with no definitive 

difference between the southbound and northbound lanes. To detect any changes in the profile of the 

pavement slabs due to curling and warping, Mays meter measurements were performed in the morning 

(6:30 a.m.) and afternoon (1 p.m.) conditions. Figures 84 and 85 show the PSI measurements for the 

morning and afternoon conditions. For the southbound direction, the afternoon readings appear to be 

significantly higher than the morning readings. However, for the northbound direction, the opposite trend 

is observed on most of the readings. In these two figures, the PSI measurements taken on summer of 
200 

1995 are presented. The PSI measurements taken in 1995 on the southbound direction are slightly higher 

than the readings taken in the morning of summer 2001. However, they were very similar to those taken 

in the afternoon of 2001. The PSI results for the northbound direction did not show any definitive trend 

from morning to afternoon conditions. Furthermore, no difference in PSI readings was observed from 

summer of 1995 to summer 2001. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Station (km)

PSI

RL a.m. — 2001

RL p.m. — 2001

PSI right lane — 1995

Figure 84. Comparison of PSI ratings on the southbound direction (summer 2001 versus summer 

1995). 

 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Station (km)

PSI

LL a.m. — 2001

LL p.m. — 2001

PSI left lane — 1995

Figure 85. Comparison of PSI ratings on the northbound direction (summer 2001 versus summer 

1995). 

Twelve PCC cores were obtained for PCC strength, modulus of elasticity, and CTE testing. 

The following findings are presented from the site inspection visit on August 2001: 

• Extensive damage to the pavement structure was observed. 
201 

• The absence of maintenance to the drainage structures and a significant increase in the traffic 

loadings appear to be the primary factors contributing to the poor performance of this road. 

• Lack of crack sealing allows the water to infiltrate into the pavement, which further 

contributes to the distress formation. 

• A comparison of the LTE analysis performed with 1993 and 2001 data shows that the LTE 

measured in 2001 was much higher than that measured in 1993. The higher LTE values 

measured during summer 2001 are believed to be due to the fact that in 1993, not all joints 

had cracked, resulting in larger joint movements and therefore contributing to a reduction in 

LTE. In 2001, an evaluation of joint movement showed that every joint was cracked. 

• The deflection analysis appear to indicate that reduced structural capacity is occurring, 

possibly due to striping in the HMA layer. 

• Although the riding quality for this road is low, no significant reduction has been observed 

from previous evaluations. 

C.2 CRCP SITES INVESTIGATED 

C.2.1 CRCP Section at I–30 and I–35 Interchange in Fort Worth, TX 

Because of its extensive network of CRCP pavements, the State of Texas was selected for identification 

of one of the two CRCP sites used for validation of HIPERPAV II. During the summer of 2001, TxDOT 

was undertaking the improvement of the U.S. Interstate (I)–35/I–30 interchange in Fort Worth, TX. As 

part of the improvement, a private contractor was constructing CRCP pavement on the approach to a 

bridge structure on the main lanes and on several access ramps. It was deemed this site could provide an 

excellent opportunity for validation of the HIPERPAV II module. 

On July 16, 2001, a section of CRCP pavement was instrumented and monitored for 72 hours. This 

section was part of one of the access ramps on the I–35/I–30 interchange. Once at the site, all the 

preconstruction information was collected, including pavement design, mix design, and materials. The 

typical cross section at the construction site is shown in figure 86. The concrete was being placed in two 

stages. The right lane and monolithic curb were constructed first, and tie bars were installed to place the 

left lane and curb in a second stage. 
202 

(1 ft = 0.3048 m, 1 in = 25.4 mm) 

Figure 86. Typical cross section for the CRCP instrumented section. 

To characterize the properties for the concrete at the site, information was collected on the mix design, 

admixtures, and additives used, as well as the coarse and fine aggregate properties and geological type. 

The mix design for this project is shown in table 65. 

Table 65. Concrete mix design for CRCP on Jones-Stephenson access road, Texas. 

Mix Design Proportions 

Water 138 kg/m3

Cement type IP 309 kg/m3

Fine aggregate 678 kg/m3

Coarse aggregate, maximum aggregate size 

38.1 mm, crushed limestone 

1105 kg/m3

Retarder 1082 ml/m3

Air entrainer—(5%) 108 ml/m3

C.2.1.1 Instrumentation Procedures 

On July 12, 2001, the project team met with TxDOT and contractor representatives to identify the section 

to instrument. Due to repositioning of the paver, the next section to be placed was scheduled for Monday, 

July 16, 2001. During the days before placing the section to be monitored, the previously placed sections 

were surveyed to identify the typical crack spacing. In addition, a friction test was performed at the site 

(as described later in this section). From the previous sections placed, the average crack spacing 

measured was approximately 4.9 m. This survey helped determine the location for the crack inducers on 

the instrumented section. The crack inducers were spaced at approximately 4.9 m. Figure 87 shows the 

position of the crack inducers on the instrumented area. 
203 

Figure 87. Instrumented section delineated by crack inducers. 

RoctestTM embedment vibrating wire gages type EM–5 were installed on the instrumented area at three 

different depths at midslab, edge, and corner (150 mm from the crack). Type T thermocouples were also 

installed at seven different depths throughout the pavement depth. The thermocouple located at the PCC 

surface was installed just after the slip form paver passed by the instrumented area. In addition, resistance 

gages type CEA–06–125UN–120 were epoxied to the steel rebar at different distances from the expected 

crack along with embedment gages to monitor the steel and concrete strain. After adhering the gage, 

mechanical protection was applied to avoid damage of the gage during the construction operations. 

Figure 88 shows the strain gages in concrete and on the reinforcing steel at the corner location. 

Figure 88. Strain gages in PCC and on reinforcing steel. 
204 

On the paving day, the instruments were doublechecked for position, elevation, and tightness. References 

were marked outside of the slab to determine the exact location of the instruments after the slabs were 

paved. Every detail in the construction operations was recorded. Shortly before the paver passed by the 

instrumented slab, the gages and thermocouples were protected with fresh concrete and vibrated with 

manual equipment. Testers ensured that the concrete used to protect the sensors was from the same batch 

to be used in the rest of the instrumented area. Some records from the placement activities are: 

• Station at start of placement: 11+20.00. 

• Stations at instrumented section: 13+55. 

• Station at end of placement: 15+49 (the paver was repositioned and continued paving). 

• Placement time at instrumented section: 11:05 h. 

• Measured pavement thickness: 231 mm. 

• Tinning: 11:45 h. 

• Curing time: 12:30 h. 

• Sky conditions: sunny. 

• Mix temperature: 31.5 oC. 

• Subbase temperature during placement: 36.3 oC. 

• Transverse Soff-Cut® on instrumented section: 13:40 h. 

• Linear variable displacement transducers (LVDT) installed: 20:50 h. 

To measure CTE and free drying shrinkage in the field, two cylinder molds were instrumented with a 

vibrating wire strain gage and a thermocouple at the center of the specimen. 

To ensure development of crack formation, green sawing was performed on the adjacent cracks to the 

instrumented area with Soff-Cut equipment approximately 2.5 hours after placement. 

To measure the slab curling and warping, LVDTs were installed at the edge and at the corner of the test 

slab. These instruments were installed approximately 10 hours after placement and before the cracks had 

occurred. 

After the concrete had set, DEMEC buttons were glued on the location of the crack inducers and 0.51 m 

toward the center of the slab along the edge from each crack. On the second day, after the first cracks 

appeared, DEMEC buttons were also glued at 20 additional cracks to monitor the crack movement due to 

temperature fluctuations and drying shrinkage. 

A friction test also was performed to characterize the friction force developed at the concrete slab-subbase 

interface. The procedure consisted of casting a 0.9-m wide by 1.5-m long plain concrete slab, with the 

same thickness of the projected CRCP pavement, on top of the same subbase type. The slab was cast on 

July 13, 2001, and the friction test was performed 5 days later. For this test, a force was applied on one 

side of the slab with a hydraulic jack. A load cell was used to measure the applied load. Dial gages were 

installed at the opposite side to measure the slab movement. The friction force was determined from the 

applied load and the area under the slab. The history of friction force and slab movement during the 

pushoff procedure was recorded. The friction force at sliding also was identified. During the 

determination of the friction for this section, it was observed that the bond between concrete and asphalt 
205 

was so strong that shear forces developed in the asphalt. This originated a plane of failure in the asphalt 

along the border of the slab against which the load was applied, as illustrated in figure 89. Both the 

concrete slab and bonded asphalt slid together, originating the friction force underneath the asphalt 

subbase, between the asphalt layer and the lime-treated subgrade. 

Figure 89. Shear failure as a result of pushoff test. 

On the days following placement, pavement profiles were measured with Dipstick equipment to detect 

any changes in the profile of the CRCP slabs due to curling and warping. The pavement profiles were 

measured at several slab diagonals in between cracks at two different times during the day. The 

measurements were made early in the morning, when the pavement was at its coolest temperature at the 

surface, and in the afternoon, when the pavement surface had warmed up, to capture the maximum 

difference in shape of the CRCP slabs due to different thermal gradients. The climatic conditions at the 

site were monitored for the 72-hour period after placement. The air temperatures during the first days 

after construction ranged from 26.6 oC to 40.0 oC. 

C.2.1.2 Monitoring Program 

Dataloggers were used to constantly monitor the pavement. This equipment was programmed to retrieve 

concrete strains, concrete temperature, and vertical displacement every 10 minutes during the 72-hour 

period. Weather conditions were recorded every 15 minutes during the 72-hour period. 

Condition surveys were performed for the entire section placed on July 16, 2001, to observe the cracking 

pattern in terms of crack spacing and crack width. During the same period, crack movement and PCC 

strain were monitored with DEMEC calipers twice a day. 

During construction, the surface of the pavement was finished on two 76 by 76-mm squares 457 mm from 

the slab edge and separated 305 mm from each other, center to center. This was done to estimate the PCC 

set time with pulse velocity equipment. These areas were finished to leave a smooth surface. During 

monitoring of the test slab, the pulse velocity transducers were placed against both surfaces separated 305 

mm apart, center to center, to obtain the transit time of the ultrasonic pulses traveling in the concrete from 

one transducer to the other. Although the reinforcing steel affected the pulse velocity measurements 
206 

(resulting in an overestimation of the elastic modulus), the rate of change in pulse velocity with time 

provided a good indication of when set time occurred. Analysis of this information indicates that set time 

occurred at approximately 3 hours, which seems to correlate well with the high placement temperatures 

observed. 

C.2.1.3 Initial Observations 

During the condition surveys, it was observed that a crack formed at the location of both crack inducers, 

as planned. The average crack spacing for the rest of the placement on that day was very close to the 

crack spacing observed in previous days. On the second and third day, additional cracks were observed at 

some areas with previously large crack spacings. However, for the instrumented section, no intermediate 

cracks were observed during the monitoring period. Figure 90 shows the sensor locations with respect to 

the observed cracks as constructed. 

Crack Inducers

4.2 m

#5 rebar @ 229 mm center to center

0.50 m

127 mm

254 mm

152 mm

1

152 mm

Strain Gages in PCC

T

Thermocouples

Strain Gages on Steel 

2

0.32 m

0. 27 m

1219 mm

2.44 m

2.0 m

T

0.61 m

76.2 mm

76.2 mm

Crack Inducers

4.2 m

#5 rebar @ 229 mm center to center

0.50 m

127 mm

254 mm

152 mm

1

152 mm

Strain Gages in PCC

T

Thermocouples

Strain Gages on Steel 

2

0.32 m

0. 27 m

1219 mm

2.44 m

2.0 m

T

0.61 m

76.2 mm

76.2 mm

Figure 90. Position of strain gages and thermocouples as constructed. 

C.2.1.4 Laboratory Tests 

Concrete specimens were prepared at the site with the same batch of concrete delivered on the 

instrumented section. Personnel with the FHWA Mobile Concrete Laboratory helped prepare the 

concrete specimens. The specimens were cured in the field for the first 24 hours, then cured under 

laboratory conditions according to ASTM C 192. While at the site, sufficient materials to replicate the 

concrete mix in the laboratory were collected. The materials collected were used to perform adiabatic 

calorimetry, drying shrinkage, and set time tests. 

C.2.2 CRCP Section on I–29 near Sioux Falls, SD 

The second field section for the CRCP model validation was selected in the State of South Dakota. At the 

end of the summer of 2001, the South Dakota DOT was reconstructing I–29 south of Sioux Falls, SD, 

from approximately milepost 59 to milepost 70. In contrast to the CRCP instrumentation in Texas with 

air temperatures from 26.6 oC to 40.0 oC, the air temperatures in South Dakota ranged from 1 oC to 
207 

24.4 oC, providing a significant difference in terms of temperature and behavior under which the CRCP 

module will be evaluated and validated. 

South Dakota DOT representatives and a member of the South Dakota Chapter of the American Concrete 

Pavement Association (ACPA) helped locate a CRCP construction job in South Dakota. Beginning on 

September 25, 2001, a section of CRCP pavement was instrumented and monitored for 72 hours. Once at 

the site, all the preconstruction information was collected, including pavement design, mix design, and 

materials. The typical cross section at the construction site on I–29 is designed to accommodate a fourlane divided road. Each direction is 12.2-m wide, with a 1.8-m left shoulder, two 3.65-m lanes, and a 3-m 

right shoulder as indicated in figure 91 (this figure shows the section in the opposite direction to traffic). 

The central portion of the pavement was being constructed with CRCP pavement to conform a 3.65-m 

wide right lane with 0.6-m PCC widened shoulder and a 3.65-m wide left lane. The rest of the shoulders 

were being paved with HMA. A longitudinal joint was being cut between lanes. The CRCP pavement is 

279 mm thick on top of a 102-mm granular subbase. 

1 ft = 0.3048 m 

Figure 91. Typical cross section for I–29, South Dakota (from opposite direction to traffic). 

To characterize the properties for the concrete at the site, information was collected on the mix design, 

admixtures, and additives used, as well as the coarse and fine aggregate properties and geological type. 

The mix design for this project is shown in table 66. 

Table 66. Concrete mix design for reconstruction project on I–29, South Dakota. 

Mix Design (Saturated Surface Dry) kg/m3

Water 140 

Cement type I/II 303 

Fly ash class F 67 

Fine aggregate 724 

Coarse aggregate, maximum aggregate size 25.4 

mm, crushed ledge rock (Sioux quartzite) 

1043 

Water reducer—WRDA 82 774–1160 ml/m3, depending 

on weather conditions 

Air entrainer—Daravair® R 690 ml/m3 (6.5 percent air) 

C.2.2.1 Instrumentation Procedures 

The field crew arrived at the project the morning of September 24, 2001. After a briefing on the 

instrumentation procedures, the South Dakota DOT helped identify the section to instrument. The section 

that was placed on Friday, September 21, 2001, was surveyed to identify the average crack spacing. The 
208 

crack spacing observed varied from 4.3 m to 18.3 m, with an average spacing of 9.1 m. This survey 

helped determine the location for the crack inducers on the instrumented section. The crack inducers thus 

were spaced at approximately 9.1 m. 

Similar to the instrumentation of the CRCP section in Texas, embedment gages type EM–5 were installed 

at midslab, edge, and corner at three different depths. Thermocouples were also installed at seven 

different depths throughout the pavement. Micromeasurements CEA–06–125UN–120 gages were also 

installed on the steel rebars at different distances from the crack. In addition, similar procedures were 

used to monitor climatic conditions, CTE and free drying shrinkage in the field, slab curling and warping, 

and cracking behavior. 

To position the Roctest vibrating wire gages type EM–5, two wood dowels were driven into the subbase 

(granular subbase), separated approximately 102 mm for each set of gages, as indicated in figure 92. The 

gage then was fixed on the dowels at the proper height with plastic zip ties. Wood dowels were also used 

to install type T thermocouples at seven different depths throughout the pavement. The thermocouple 

located at the PCC surface was installed just after the slip form paver passed by the instrumented area. 

Figure 92. Strain gages in PCC and on reinforcing steel. 

The procedure to install the micromeasurements CEA–06–125UN–120 steel gages consisted of grinding 

the rebar corrugations to leave a smooth surface. After the corrugations were ground, a file was used to 

smooth any surface indentations. The surface was smoothed even more with sandpaper grade 60, then 

with sandpaper grade 400. The grinding was done so as not to reduce the diameter of the rebar. Before 

adhering the resistance gage to the surface, isopropyl alcohol was used to clean and degrease the treated 

surface of the rebar. The gages with preattached lead wires were taped to the rebar. A conditioning 

solution was brushed on the surface of the rebar and on the area of the gage to be bonded to the rebar. 

After 1 minute of drying, M-bond 200TM adhesive was used to adhere the resistance gage to the rebar. 

After M-bond 200 was applied, the gage was held down against the surface of the rebar for at least 1 

minute. After adhering the gage, researchers applied mechanical protection to avoid damage of the gage 

during the construction operations. 

After all the gages were installed, a small trench was dug into the subbase on the area of the paver track to 

lead all the sensor wires out of the pavement and to the dataloggers. 
209 

Some records from the placement activities are: 

• Stations at instrumented section: 536+65 to 536+95. 

• Placement time at instrumented section: 13:05 h. 

• End of placement approximately 15:00 h (due to paver breakdown). 

• Measured pavement thickness: 279 mm (average of several points). 

• Curing time: 14:15 h. 

• Sky conditions: mostly sunny. 

• Mix temperature: 21.2 oC. 

• Subbase temperature during placement (25.4 mm into subbase): 20.6 oC. 

• Saw cutting time (longitudinal joint): 9/25/01 (16:30–18:30 h). 

C.2.2.2 Initial Observations 

As discussed previously, the crack spacing initially estimated for this section was approximately 9.1 m. 

However, the cooling cycle after placement reached a low temperature of 1 oC, which was beyond the 

forecasted low temperature of 4.4 oC. This excessive temperature drop significantly reduced the crack 

spacing, and one intermediate crack occurred at the instrumented section on the first day. On the second 

day, two additional cracks were observed (see figure 93). However, the additional cracks in the 

instrumented section did not affect the main objective of the experiment, which was to determine the 

development of concrete and steel strains near the crack locations. In addition, the data collected for this 

site complemented the data collected for the Fort Worth, TX, section, where no intermediate cracks were 

observed. Figure 94 shows the sensor locations with respect to the observed cracks as constructed. 
210 

9.0 m

3.68 m

4.42 m

0.11 m

0.08 m 2.2 m 1.5 m 0.97 m 4.32 m

Sensors

Observed at 18 hrs

Observed at 18 hrs

Observed at 18 hrs

Observed at 34 hrs

Observed at 34 hrs

Crack Inducers

9.0 m

3.68 m

4.42 m

0.11 m

0.08 m 2.2 m 1.5 m 0.97 m 4.32 m

Sensors

Observed at 18 hrs

Observed at 18 hrs

Observed at 18 hrs

Observed at 34 hrs

Observed at 34 hrs

Crack Inducers

Figure 93. Cracking pattern on instrumented section. 

4.22 m

Crack Inducers

3.68 m

#6 rebar @ 127 mm center to center

#6 rebar @ 152 mm center to center

108 mm

356 mm

191 mm

127 mm

254 mm

102 mm

254 mm

T

0.93 m

165 mm

PCC Strain Gages

T

Thermocouples

Steel Strain Gages

4.22 m

Crack Inducers

3.68 m

#6 rebar @ 127 mm center to center

#6 rebar @ 152 mm center to center

108 mm

356 mm

191 mm

127 mm

254 mm

102 mm

254 mm

T

0.93 m

165 mm

PCC Strain Gages

T

Thermocouples

Steel Strain Gages

Figure 94. Location of the sensors with respect to the pavement edge and cracks as constructed. 
211 

C.2.2.3 Laboratory Tests 

Concrete specimens were prepared at the site. These specimens were prepared to characterize the 

concrete properties under laboratory and field conditions. Two sets of laboratory concrete specimens 

were prepared as described in table 67. The first was cured under field conditions according to ASTM C 

31, and the second set was cured under laboratory conditions according to ASTM C 192. The difference 

in curing procedures was done to verify the maturity properties for this specific concrete. 

Table 67. Laboratory testing plan of PCC concrete specimens. 

Test Field Curing 

Conditions 

Laboratory Curing 

Conditions 

Splitting tensile Three repetitions at 

1, 2, and 3 days 

Three repetitions at 1, 3, 

7, and 28 days 

Compression – Three repetitions at 3, 7, 

and 28 days 

Modulus of elasticity – Three repetitions at 7 

and 28 days 

CTE – Two repetitions at 28 

days 

Temperature 

monitoring 

One specimen One specimen 

C.2.2.4 Laboratory Results from Validation Field Sites 

This appendix presents the laboratory testing data for the HIPERPAV II sites in Illinois, Mexico, South 

Dakota, and Texas. Laboratory testing included compressive strength, splitting tensile strength, modulus 

of elasticity, CTE, drying shrinkage, and set time. The testing matrix is provided in table 68. 

Table 68. HIPERPAV II laboratory testing. 

Site Compressive 

Strength 

Splitting 

Tensile 

Strength 

Modulus 

of 

Elasticity 

Drying 

Shrinkage 

Set Time CTE 

Illinois X X X – – X 

Mexico X X X – – X 

South Dakota X X X X X X 

Texas X X X X X X 

The laboratory results are presented in the sections below, as are the concrete mix designs. 

C.3 MIX DESIGNS 

The concrete mix designs for the sites in Illinois, Mexico, South Dakota, and Texas are given in table 69. 
212 

Table 69. Concrete mix designs for the HIPERPAV II field sites. 

 Illinois Mexico South Dakota Texas 

Cement type I I II IP 

Cement content 341 kg/m3 280 kg/m3 303 kg/m3 309 kg/m3 

Cementitious materials 

content 

– – Fly ash class F 

67 kg/m3

 

– 

Water content 148 kg/m3 158 kg/m3 140 kg/m3 138 kg/m3 

Coarse aggregate 

content 

1121 kg/m3 1006 kg/m3 1043 kg/m3 1105 kg/m3 

Maximum aggregate 

size 

– 38.1 mm 25.4 mm 38.1 mm 

Aggregate type – – Sioux quartzite Limestone 

Fine aggregate content 666 kg/m3 932 kg/m3 724 kg/m3 678 kg/m3 

Water reducer Type A WRDA 

with Hycol 

1333 ml/m3 WRDA 82 

774–1160 ml/m3

 

HPS–R 

1082 ml/m3 

Air entrainer Darex® AEA 115 ml/m3 Daravair R 

690 ml/m3

AIR–INTX 

108 ml/m3

C.4 STRENGTH AND STIFFNESS FOR TEXAS SITE 

At the Fort Worth, TX, I–35 West/I–30 interchange, a 203-mm thick CRCP was constructed on July 16, 

2001. More details on the highway construction are given in section C.2.1. Several cylinders were 

molded to measure concrete material properties at 0.5, 1, 3, 7, and 14 days. The concrete specimens were 

cured in the field for the first 24 hours and then under laboratory conditions according to ASTM C 192. 

The compressive strength, splitting tensile strength, and modulus of elasticity as a function of time are 

shown in figures 95 to 97. All specimens were soaked until the time of testing. The individual data 

points are hollow, and the average is shown as a solid point. 

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16

Test Age (days)

Avgerage Compressive Strength (MPa) 

Figure 95. Time growth of Texas compressive strength. 
213 

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14 16

Test Age (days)

Average Splitting Tensile Strength (MPa)

Figure 96. Time growth of Texas splitting tensile strength. 

0.00

5000.00

10000.00

15000.00

20000.00

25000.00

30000.00

35000.00

0 2 4 6 8 10 12 14 16

Test Age (days)

Average Modulus of Elasticity (MPa)

ACI

ACI 318

Test Data

Figure 97. Time growth of Texas modulus of elasticity. 

Because the compressive strength was measured on 102-mm and 152-mm diameter cylinders, it had to be 

adjusted for the different cylinder sizes.(61) All the splitting tensile tests were completed on 152-mm 

cylinders. The compressive strength and the splitting tensile strengths continue to increase from 0.5 to 14 

days. Variability of the splitting tensile strength is high at early ages. 

The modulus of elasticity data does not increase with time. The modulus increases from 0.5 to 3 days, 

and then drops at 7 and 14 days. The FHWA Mobile Concrete Laboratory tested the early-age concrete 

(0.5 to 3 days), and Construction Materials Research Group at the University of Texas at Austin tested the 

7- and 14-day samples. Variability in testing and in data interpretation may have contributed to the 
214 

difference in modulus values. Using the ACI correlations between compressive strength and concrete 

modulus of elasticity shown in equations 259 and 260:(58) 

ACI 318 Code (1): 

4,700 ( ) 0.5 E = f c MPa (259) 

and 

ACI 318 Code (2): 

0.043 ( ) 0.5 5 ' 1. E w f MPa c c = ⋅ (wc = 2340 kg/m3

) (260) 

It is apparent that the expected modulus of elasticity value lies below the high values at early ages, and 

above the low values at 7 and 14 days. The raw laboratory data for the Texas site are given in tables 71 to 

74 in sections C.8 to C.10. 

C.5 STRENGTH AND STIFFNESS FOR SOUTH DAKOTA SITE 

The laboratory results for compressive strength, splitting tensile strength, and modulus of elasticity are 

presented here for the CRCP constructed in South Dakota on I–29. More details on the construction 

process and monitoring are provided in section C.2.2. It is apparent that the compressive strength, tensile 

strength, and modulus of elasticity increase with time in figures 98 to 100. Likewise, the modulus of 

elasticity for South Dakota is estimated from the compressive strength data using the ACI and ACI 318 

models in figure 100. The model predictions are lower than the measured data. 

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30

Test Age (days)

Average Compressive Strength (MPa)

Figure 98. Time growth of South Dakota compressive strength. 
215 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 5 10 15 20 25 30

Test Age (days)

Average Splitting Tensile Strength (MPa)

Field

Lab

Figure 99. Time growth of South Dakota splitting tensile strength. 

20,000

22,000

24,000

26,000

28,000

30,000

32,000

34,000

36,000

0 5 10 15 20 25 30

Test Age (days)

Average Modulus of Elasticity (MPa)

ACI (1)

ACI (2)

Test Data

Figure 100. Time growth of South Dakota modulus of elasticity. 

C.6 STRENGTH AND STIFFNESS FOR MEXICO SITE 

An extensive pavement evaluation was conducted on the JCP section of the Ticuman bypass on August 

21–24, 2001. This pavement was originally constructed from September 23 to October 12, 1993. The 

early-age laboratory data from 1993 are compared to the properties measured in 2001 in the figures below 

(figures 101 to 103). The concrete strength continued to increase over time, as expected, as does the 

splitting tensile strength and the modulus of elasticity. The modulus of elasticity is estimated using the 

ACI and ACI 318 models in figure 103. The predicted values are in the same range as the measured ones. 
216 

-

5

10

15

20

25

30

35

40

45

50

1 10 100 1000 10000

Test Age (days)

Average Compressive Strength (MPa)

Figure 101. Time growth of Mexico compressive strength. 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 10 100 1000 10000

Test Age (days)

Average Splitting Tensile Strength (MPa)

Figure 102. Time growth of Mexico splitting tensile strength. 
217 

-

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

1 10 100 1000 10000

Test Age (days)

Average Modulus of Elasticity (MPa)

ACI (1)

ACI (2)

Test Data

Figure 103. Time growth of Mexico modulus of elasticity. 

C.7 STRENGTH AND STIFFNESS FOR ILLINOIS SITE 

U.S. Highway 50, a JPCP near Carlyle, IL, was monitored from August 7 to 10, 2001. It was originally 

constructed from April to August of 1986. At that time, air content was 5.4 percent, slump was 51 mm, 

the 14-day flexural strength was 4.9 MPa, and the 28-day flexural strength was 492 MPa. Cores of the 

pavement were taken and tested in May 2002. The resulting concrete properties are listed in table 70. 

Table 70. Average concrete properties for the Illinois site (tested May 2002). 

Illinois Concrete Properties 

(MPa) 

CV (%) 

Compressive strength 40.7 3.9 

Splitting tensile strength 4.57 1.6 

Modulus of elasticity 27,441 2.2 

The flexural strength data, which is assumed to be measured under centerpoint loading, was also used to 

estimate the early-age compressive strength of this concrete using the following relationship shown in 

equation 261: 

1.5

2.3

0.864 ⎥

⎦

⎤ ⎢

⎣

⎡ ⋅ = Cnt Pt Flex Str CS

 (261) 

Its comparison to the compressive strength measured in May 2002 is shown in figure 104. After 14 days, 

the data shows a minimal increase in compressive strength, except for the 90-day calculated value. 
218 

0

10

20

30

40

50

60

1 10 100 1000 10000

Test Age (days)

Average Compressive Strength (MPa)

Estimate of compressive strength from flexural strength

Average of data points

Data points

Figure 104. Time growth of Illinois compressive strength. 

Likewise, the estimated compressive strength values are used to predict the modulus of elasticity (figure 

105). They correlate well to the measured modulus of elasticity, except for the 90-day value as 

mentioned previously. Modulus of elasticity is relatively stable after 14 days. 

-

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

1 10 100 1000 10000

Test Age (days)

Modulus of Elasticity (MPa)

ACI (1)

ACI (2)

Average of data points

Data points

Figure 105. Time growth of Illinois modulus of elasticity. 

C.8 DRYING SHRINKAGE FOR TEXAS AND SOUTH DAKOTA SITES 

The drying shrinkage of the concrete placed in Fort Worth, TX, and South Dakota was measured in the 

laboratory using ASTM C 157, with minor modifications. The specimens were 102-mm prisms that were 

286 mm long. The concrete mix quality control parameters are given in table 72. They were cured 24 

hours at 100 percent RH and 23 °C, then were stored at 50 percent RH at 23 °C for the remaining period 

of time. Readings were taken every day for the first 7 days, and then at 14, 28, and 112 days. The time 
219 

growth of drying shrinkage is shown in figure 106 for South Dakota and in figure 107 for Texas. The 

Baźant-Panula drying shrinkage model is fit to the laboratory data, as shown (described in section B.1.3). 

If the ultimate shrinkage is known, it can be input to the model, or the Baźant-Panula model can predict 

ultimate shrinkage. A more accurate prediction is made if the ultimate drying shrinkage is known. 

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25

t-to (days)

Drying Shrinkage (με)

South Dakota data

Ultimate shrinkage set

Ultimate shrinkage predicted

Figure 106. Drying shrinkage of South Dakota concrete. 

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25

t-to (days)

Drying Shrinkage (με)

Texas data

Ultimate shrinkage set

Ultimate shrinkage predicted

Figure 107. Drying shrinkage of Texas concrete. 

The drying shrinkage input parameters for the Baźant-Panula model are listed in table 71. The concrete 

mix proportions that were input to the model were taken from table 69. 
220 

Table 71. Drying shrinkage model input. 

Input South Dakota Texas 

28-day compressive strength (MPa) 37.3 33.4 

28-day modulus of elasticity (MPa) 33,784 27,580 

Set time (days) 0.28 0.20 

D (= 2 * volume/surface area) (mm) 46 46 

ks 1.28 1.28 

α1 0.85 1 

α2 1 1 

The 28-day compressive strength and modulus of elasticity values were estimated from the measured 

laboratory data. Set time was taken from the data in the following section. Finally, ks, the shape 

parameter, represents the shape of the laboratory produced drying shrinkage specimens. 

C.9 SETTING TIME FOR TEXAS AND SOUTH DAKOTA 

The set times for the concrete placed in Fort Worth, TX, and South Dakota were determined by following 

ASTM C 403. The quality control data for these mixes is given in table 72. 

Table 72. Quality control data for Texas and South Dakota concrete mixes. 

Concrete Property South Dakota Texas 

Slump 45 mm 70 mm 

Batching temperature 22.2° C 21.7° C 

Batching date 10/26/2001 10/26/2001 

Batching time 10:39 a.m. 11:27 a.m. 

Air content (%) 4 5.5 

Unit weight (kg/m3) 2340 2262 

The set time data for Fort Worth, TX was fit using a power function, with an r2 of 0.99 (figure 108). The 

corresponding initial and final setting times are listed in table 73. The ambient temperature for measuring 

the Texas mix set time was 37.8 °C. 

Using a regression analysis, the r2 for the South Dakota data is 0.97. This is less than the 0.98 required by 

the specification for the set time analysis, so the data was hand fit, as shown in figure 108. The initial and 

final setting times are listed in table 73. The ambient temperature for the set time measurements using the 

South Dakota concrete was 18.3 °C. 
221 

-

5

10

15

20

25

30

35

40

150 200 250 300 350 400 450

Elapsed Time (min)

Penetration Resistance (MPa)

South Dakota

Texas

Initial Set

Final Set

Figure 108. Setting times of concrete for Texas and South Dakota concretes. 

Table 73. Setting times of the Texas and South Dakota concrete mixes. 

Setting Time Texas South Dakota 

Initial setting (min) 242 304 

Final setting (min) 292 396 

The concrete and air temperatures for the fresh concrete mixes from South Dakota and Texas are shown 

in figures 109 and 110. 

15

17.5

20

22.5

25

0 5 10 15 20 25 30 35 40

Time (h)

Temperature (°C)

Concrete temperature

Ambient Temperature

South Dakota

Figure 109. Concrete and ambient air temperatures for the South Dakota concrete. 
222 

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40

Time (h)

Temperature (°C)

Concrete temperature

Ambient temperature

Texas

Figure 110. Concrete and ambient air temperatures for the Texas concrete. 

C.10 COEFFICIENT OF THERMAL EXPANSION 

CTE tests were also performed on concrete specimens for each field site on June 6, 2002. AASHTO test 

method TP–60–00 was followed. The average CTE values obtained for the PCC specimens tested are 

listed in table 74. 

Table 74. CTE values determined according to AASHTO TP–60–00. 

PCC Specimen ID CTE (×10-6 m/m/°C)

Fort Worth, TX 7.48 

Illinois 6.85 

Mexico 7.00 

South Dakota 10.91 
223 

APPENDIX D VALIDATION OF THE ENHANCED GUIDELINES 

Although the CRCP early-age behavior models and long-term JPCP models selected for use in this 

project have already undergone extensive validation efforts, modification to some of the models to reflect 

specific early-age conditions and to integrate well with the overall system warrant further validation. 

Validation focuses on determining the reliability of the model. Model reliability determines if the model 

is a good one or a poor one. If there is significant scatter in the data as compared to the prediction, then 

the model is possibly poor. Less scatter implies that the model is reliable. The reliability of the 

individual models in the long-term JPCP and early-age CRCP modules in HIPERPAV II was assessed 

under this concept. 

Two levels of validation were undertaken for both the long-term JPCP and early-age CRCP models 

incorporated into HIPERPAV II. The first level of validation was performed with the use of databases. 

The second level of validation consisted of selecting pavement sites and obtaining the necessary 

information for the validation analysis. 

The database validation efforts are discussed in section D.1, and the field validation work is discussed in 

more detail in section D.2. Additional validation also was performed for general early-age behavior 

enhanced models such as the finite-difference temperature prediction model and the improved drying 

shrinkage model. Also, initial attempts to incorporate an improved relaxation-creep model were 

performed. Validation of each of these early-age behavior models is presented in section D.3. 

D.1 DATABASE VALIDATION 

The primary databases used for this purpose were the database maintained by LTPP and the Texas CRCP 

database.(105,106) The wider geographical distribution and variety of pavement sections in the LTPP 

database were determinant factors for its use, while the extensive amount of early-age data for CRCP in 

the Texas rigid pavement database was a major factor for its selection. Other databases, such as the 

COPES and the RIPPER databases, were investigated; however, lack of early-age information and 

monitoring records made the validation efforts difficult.(107,108)

D.1.1 Validation of JPCP Structural Response Models with LTPP Data 

Information in the LTPP database was used exclusively for validation of the JPCP structural response 

models. Provided the LTE model has not been previously calibrated as a whole, pavement sections in the 

LTPP database were used for model calibration. Subsequently, validation of the JPCP long-term 

performance predictions was performed with information collected from existing field sites. Calibration 

of the LTE model is described in this section, and field validation of JPCP existing sites is discussed in 

section D.2.1. 

As previously presented in section B.2.3.1, a model for the prediction of stress and deflection transfer 

across JPCP joints due to traffic loads was incorporated in HIPERPAV II. Prediction of LTE for JPCP is 

a function of a number of factors including the presence of dowels, aggregate interlock, pavement 

geometry, PCC mechanical properties, slab support, and environmental conditions.( 69,70,73) The seasonal 

monitoring program (SMP) under the LTPP program includes monitoring of JPCP sections to observe the 

effects of temperature and moisture on the pavement structure and its response to loads.(109) Evaluation of 

LTE for SMP sections with enough information on the factors mentioned above was useful in better 
224 

understanding structural behavior of JPCP and provided the basis for calibrating the pavement response 

LTE model incorporated in HIPERPAV II. 

D.1.1.1 Evaluation of Joint Opening 

As part of the SMP study, joint movement is monitored along with PCC temperatures and deflections 

obtained with FWD equipment.(109) This information is believed to be useful in understanding the effect 

of joint opening on LTE. Lee and Stoffels reported several findings on analysis of joint movement 

information for the SMP sections.(110) The following observations from that study are of particular 

interest: 

• An increase in PCC temperature causes a reduction in joint opening. 

• Some joints appear to be locked, as joint opening does not appear to significantly change with 

a change in temperature. 

• For some pavement sections, joint opening decreases with an increase in PCC temperature up 

to a given temperature, where the joint opening seems to close, or extraneous material is 

present at the joint that does not permit further reduction in joint opening. 

• Some joints showed erratic large movements that appear to be associated with intermediate 

freezing joints. 

Although joint opening is not directly measured in the SMP study, it is believed that monitoring of the 

joint movement during hot weather may capture the temperature of joint closure, as was the case for some 

of the sections analyzed by Lee and Stoffels.(110)

To determine the temperature of closure, an important parameter in the LTE analysis, the procedure 

developed by Lee and Stoffels was followed for this study.(110) JPCP LTPP sections were investigated 

and the effective ratio of joint movement to change in PCC temperature (ER) determined. The effective 

ratio is understood as a reduction in joint opening, in millimeters, for a 100 °C increase in PCC 

temperature. For this analysis, the information was obtained from the LTPP DataPave 3.0. Table 75 

presents the ER statistics for each of the 12 sections investigated. From the analysis summarized here, 

although slight differences in the computed ER for a few sections were observed, similar findings were 

obtained to those presented by Lee and Stoffels. In addition to the JPCP sections previously investigated 

by Lee and Stoffels, SMP sections 39–0204 and 32–0204 were evaluated. 
225 

Table 75. Computed effective ratio of joint movement to change in 

temperature (ER) for SMP sections. 

Section 

ID 

Avg. ER 

(mm/100oC) 

Min. ER 

(mm/100oC) 

Max. ER 

(mm/100oC)

Locked 

Joints 

Closure 

Temp 

Observations 

04–0215 −5.82 −7.7 −3.9 1 of 8 32.3 – 

06–3042 – – – – – No correlation of PCC 

temperature to joint opening 

13–3019 −5.35 −8.7 −3.4 2 of 6 13.8 – 

18–3002 – – – – – No PCC temperature records in 

DataPave 3.0 for joint opening 

dates 

31–3018 −5.09 −6.8 −3.5 0 of 6 NR – 

32–0204 −11.72 −23.6 −3.8 3 of 6 NR Many joints appear locked 

37–0201 −2.84 −5.2 −1.8 2 of 6 NR – 

39–0204 −2.85 −6.6 −1.6 0 of 6 NR – 

49–3011 −5.25 −7.0 −3.3 0 of 8 30.5 – 

53–3813 – – – – – No correlation of PCC 

temperature to joint opening 

83–3802 −9.99 −28.9 −1.4 1 of 6 4.8–14.5 Most joints with small ER 

89–3015 −6.22 −12.1 −3.4 2 of 5 NR – 

ER = reduction in joint opening, in millimeters, for a 100 oC increase in PCC temperature. 

NR = temperature of closure not observed within range of temperatures monitored. 

The following are some comments on the findings obtained: 

• Sections 6–3042 and 53–3813 did not show a significant correlation of PCC temperature to 

joint opening. Although this could be attributed to joint freezing, a significant variability in 

joint movement readings (in some cases as high as 25 mm) indicates that the lack of 

correlation is probably due to measuring error. 

• Although ERs are reported for section 18–3002 in reference 110, no PCC temperature records 

were found in the LTPP database.(110,111)

• Section 32–0204 shows an erratic and large ER for three of the six joints analyzed. 

Furthermore, the remaining three joints appear to be locked, since the ERs for this section are 

positive (increase in joint movement for an increase in PCC temperature). Since this is an 

SPS–2 section, it could be identified from the LTPP records that a dowel bar inserter was 

used for this section. This possibly could have contributed to dowel misalignment and the 

subsequent joint freezing. 

• Section 83–3802 shows an erratic, large ER for at least two of the six joints investigated. For 

this section, the remaining joints show a small joint movement with only one of the six joints 

analyzed showing possible joint freezing. 

• Sections 04–0215, 13–3019, 49–3011, and 83–3802 showed some evidence of reaching the 

temperature of closure for some of the joints analyzed. For sections 31–3018, 32–0204, 37–
226 

0201, 39–0204, and 89–3015, the temperature of closure does not seem to be captured within 

the range of PCC temperatures monitored. 

D.1.1.2 Prediction of Joint Opening 

As part of this study, predictions with the HIPERPAV II joint opening model were made for the SMP 

sections evaluated. The HIPERPAV II joint opening model is documented elsewhere.(1,3)

For prediction of joint movement with the HIPERPAV II joint opening model, the following factors are 

required: 

• Pavement thickness: obtained from DataPave tables TST L05B or 

SPS2_LAYER_THICKNESS. 

• Slab length: obtained from INV_PCC_JOINT table. 

• Modulus of elasticity of PCC: obtained from TST_PC04 table or estimated from 

INV_PCC_STRENGTH table. 

• PCC CTE: obtained from TST_PC03 table, or estimated according to AASHTO 

recommendations from GEOL_CLASS_COARSE_AGGR field on 

SPS2_PCC_MIXTURE_DATA table or INV_PCC_MIXTURE table. 

• Shrinkage strain of PCC: assumed to be negligible for long-term analyses. 

• PCC set temperature: estimated to be temperature of closure obtained from ER analysis. 

• Change in PCC temperature: a 100 oC change according to the definition of the ER ratio was 

used. 

• Movement at maximum friction and maximum friction force: estimated according to subbase 

type LAYER_NO, LAYER_TYPE, DESCRIPTION, and MATL_CODE fields on TST L05B 

table. 

Figure 111 compares of the measured versus predicted joint movement for the investigated sections. In 

general, it can be observed that the HIPERPAV II joint opening model slightly overpredicted joint 

movement for most of the sections. 
227 

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

Measured ER (mm/100oC)

Predicted ER (mm/100oC)

Figure 111. Measured versus predicted joint opening. 

During this exercise, no attempt was made to predict the erratic and large joint movements measured for 

section 32–0204, since no CTE information for this section was found in DataPave 3.0. However, to 

match the measured average joint movement for section 83–3802, a 9.8-m joint spacing had to be 

assumed to account for the joint freezing effect observed for this section. The largest ER ratio for this 

section could be matched with a 28.4-m joint spacing. The last value would indicate that five joints were 

locked up, contributing to the large joint opening. 

D.1.1.3 LTE Analysis 

To perform the LTE analysis, information for the SMP sections in study was obtained from the following 

tables in DataPave 3.0: 

• MON_DEFL_DROP_DATA: contains peak deflections for each of the seven to nine FWD 

sensors used, date and time the test was performed, specific point location, and type of test 

(i.e., midslab, wheel path, LTE test on approach slab, LTE test on leave slab, etc.). FWD 

tests were conducted at three load levels, approximately 40 kN, 53.4 kN, and 71.2 kN, with 

four drops at each load level.(112) The second drop for the load level at approximately 40 kN 

was selected for use in this analysis. 

• MON_DELF_LOC_INFO: contains the FWD sensor configuration identification number for 

a specific testing date. Although the LTPP Manual for Falling Weight Deflectometer 

Measurements indicates that the sensor configuration for the LTPP tests was kept constant, 

the records in the DataPave 3.0 software indicate that the sensor configuration varied.(112) For 

the LTE testing, the distance from the load for sensors 1, 2, and 3 changed from 0 mm, 305 

mm, and −305 mm to 0 mm, 203 mm, and 305 mm, respectively. For the first case, the 

deflection on the unloaded slab was recorded by the third sensor. In the later case, the 

deflection on the unloaded slab was recorded by sensor 9 at −305 mm from the load. To 

compute the LTE properly, this configuration information had to be known. Along with this 

information, the MON_DEFL_DEV_SENSORS table was used to obtain the sensor location 

for a particular configuration. 
228 

• MON_DEFL_TEMP_DEPTHS and MON_DEFL_TEMP_VALUES tables were used to 

obtain PCC temperatures manually measured at the time of FWD testing.(112)

• SMP_MRCTMP_AUTO_HOUR and SMP_MRCTMP_DEPTHS tables were used to obtain 

PCC hourly temperatures automatically obtained with thermistor sensors embedded in the 

concrete.(109,111)

In most cases, manual readings and automatic temperature readings differed for less than 3 °C. In cases 

when both manual PCC temperature measurements and automatic thermistor measurements were 

available, the PCC temperature reported by the thermistors was used. It was assumed that automatic 

monitoring would give less room to measurement error than manual readings. 

A number of points were discarded for this analysis based on the following criteria: 

• Only records with PCC temperature information available within 1 hour of the FWD testing 

were used in the current LTE analysis. This procedure minimizes the likelihood that PCC 

temperatures differ no more than 2 °C or 3 °C from the time the FWD testing was performed. 

• Records with a lack of information on sensor configuration were discarded. 

• A semiautomatic procedure with the use of regression techniques was used to identify 

illogical deflection basins. These records were filtered out of the LTE analysis. 

Table 76 shows the total number of points used after the above filtering process was performed. 

Table 76. Data points used for LTE analysis. 

Section 

ID 

Points in 

Database 

Points Used for 

LTE Analysis 

Points Used for 

LTE Analysis 

(%) 

Points with 

Computed LTE > 

100% 

Points with 

Computed LTE > 

100% (%) 

04–0215 754 604 80.1 3 0.5 

06–3042 660 597 90.5 14 2.3 

13–3019 793 611 77.0 3 0.5 

18–3002 383 329 85.9 0 0.0 

31–3018 719 650 90.4 1 0.2 

32–0204 405 404 99.8 6 1.5 

37–0201 774 718 92.8 10 1.4 

39–0204 422 381 90.3 12 3.1 

49–3011 1038 971 93.5 3 0.3 

53–3813 635 470 74.0 10 2.1 

83–3802 868 845 97.4 35 4.1 

89–3015 737 679 92.1 16 2.4 

The LTE across joints was evaluated based on the deflection ratio using the procedure documented by 

Teller and Sutherland (equation 262):(113) 

100 2 ⋅ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⋅ =

u l

u

W W

W LTE

 (262) 
229 

where, 

 LTE = load transfer efficiency, percent, 

 Wu = deflection on the unloaded slab, and 

 Wl = deflection on the adjacent loaded slab. 

Figure 112 shows a typical plot of PCC temperature versus joint LTE for a doweled section. It is 

observed that for high PCC temperatures the joint LTE remains high, typically above 80 percent. 

However, there is a threshold temperature below which LTE is significantly reduced, most likely due to 

the loss of aggregate interlock as the joint opens. 

0

10

20

30

40

50

60

70

80

90

100

110

120

-5 0 5 10 15 20 25 30 35 40 45

Temperature (oC)

LTE (%)

Trendline

Threshold 

Temperature

Figure 112. Typical plot of PCC temperature versus joint LTE, section 37–0201. 

Table 77 shows some computed LTE statistics for the sections analyzed and some design and 

construction characteristics. In this table, the JPCP sections are sorted as a function of the average 

computed LTE, from lowest to highest. From this sorting procedure, the following observations are 

made: 

• As expected, the sections with dowels show higher LTE than do the sections with no dowels. 

A lower average LTE is observed for sections with high threshold temperatures (temperature 

after which LTE > 80 percent). This LTE threshold temperature is believed to be related to 

the temperature of joint closure. 

• In table 77, the temperature of joint closure computed during the joint opening analysis also 

is shown. Although this value could be computed only for a few sections, it appears to 

correlate to the computed average LTE. 

• Other parameters examined include construction date, joint spacing, slab thickness, climate, 

and subbase type. None of these parameters seem to have as strong of an effect on LTE as is 

the case for the presence of dowels or the effect of PCC temperature (or joint opening). 
Table 77. LTE statistics for SMP sections evaluated and some design and construction characteristics. 

Section 

ID 

Min. 

LTE 

(%) 

Max. 

LTE 

(%) 

Avg. 

LTE 

(%) 

CV 

(%) 

T 

after 

which 

LTE > 

80% 

T min. T 

max. 

Closure 

Temperature

Construction 

Date 

Joint 

Spacing 

(m) 

D 

(mm) Climate Dowels Base 

31–3018 18.6 100.0 58.6 33.0 30 −3.3 32.6 Not within 

range May 1985 4.7 302 WF No Soil cement 

49–3011 9.2 106.4 63.1 38.5 25 −4.2 41.6 30.5 May 1986 4.6 259 DF No CAM 06–3042 14.6 102.5 75.5 26.5 25 2.9 36.7 – Jun 1979 4.7 224 DNF No CAM 83–3802 30.0 104.7 77.3 26.9 22 −16.0 31.6 4.8–14.5 Sep 1985 4.6 249 WF No Subgrade 53–3813 

39.9 105.2 88.2 14.7 20 1.9 44.1 – Aug 1966 4.6 203 WNF No 

Coarse soil agg. mixture 

37–0201 46.8 105.5 85.9 15.0 26 0.2 39.7 Not within 

range 

Nov 1993 4.6 229 WNF Yes Crushed stone 

04–0215 45.2 104.7 86.3 12.8 36 12.3 48.4 32.3 Sep 1993 4.6 287 DNF Yes Crushed gravel 18–3002 63.1 99.1 90.5 7.6 17 −1.7 36.9 – Aug 1976 4.7 241 WF Yes Crushed stone 13–3019 53.9 101.9 91.3 9.4 17 −0.5 43.0 13.8 Dec 1981 6.1 231 WNF Yes Crushed stone 32–0204 82.7 102.5 93.8 3.3 all −0.9 34.4 Not within 

range 

Jul 1995 4.6 300 DF Yes crushed gravel 

89–3015 62.3 111.9 95.2 3.4 6 −17.0 32.7 Not within 

range Sep 1984 6.0 208 WF Yes Crushed stone 

39–0204 80.0 105.5 95.6 3.6 all 0.1 30.8 Not within 

range Aug 1995 4.6 282 WF Yes Crushed stone 

CAM – Cement-aggregate mixture, CV – Coefficient of variation, D – Thickness, DF – Dry freeze, DNF – Dry-no freeze, T – Temperature (oC), WF – Wet freeze, WNF – Wet-no freeze *Random joint spacing 

230
231 

D.1.1.3.1 LTE Variability

For a number of sections, a large variability was found, as can be seen from the LTE CV in table 77. A 

large variability of LTE for JPCP sections in the LTPP database has been reported previously.(114) A more 

detailed analysis of section 49–3011 with the highest CV was performed to try to determine the reason for 

the large variability. Figure 113 shows a plot of PCC temperature versus LTE for that section. It is 

evident that several factors affect the variability of this section. 

0

10

20

30

40

50

60

70

80

90

100

110

120

-5.000 0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000 40.000 45.000

Temperature (oC)

LTE (%)

Trendline

Threshold 

Temperature

Figure 113. Computed LTE versus PCC temperature for section 49–3011. 

The most remarkable factor from figure 113 is the effect of PCC temperature. As discussed before, above 

a certain threshold temperature (in this case, 25 °C), the LTE for this section remains above 80 percent. 

This is believed to be associated with the slabs expanding and causing a reduction in joint opening. 

Below that PCC temperature, the aggregate interlock is lost as the joint opens, and the LTE decreases 

significantly. It is also interesting to note that below freezing (PCC temperature < 0 °C), LTE is slightly 

higher than at PCC temperatures immediately above freezing. It is possible that the freezing effect 

provides higher soil support, therefore maintaining high LTE values. It is also hypothesized that ice in 

the joint can lead to a bridging effect. However, in figure 113, it is not quite clear why, for the range of 

temperatures above freezing and below 25 °C, a high variability occurs. Other factors that are believed to 

have an effect on LTE are pavement age, type of LTE test (load on approach slab or load on leave slab), 

variability in joint opening (figure 113 includes LTE tests for all joints monitored in that section), season 

of the year, and joint spacing (this section has random spacing). 

D.1.1.3.2 Effect of Different Parameters on LTE

To further investigate the possible impact of the above factors, the LTE measurements for section 49–

3011 were individually analyzed for each joint as a function of type of LTE test, and date LTE tests were 

performed. Figure 114 shows the average LTE computed for each joint. For each joint, the computed 

LTE was grouped into two categories: tests performed before 1996, and tests performed in 1996 and 

thereafter. The Joint ID in figure 114 includes the type of LTE test (load positioned on approach slab—
232 

LTPP designation J4, or load positioned on leave slab—LTPP designation J5), distance from the start of 

the section to the joint in meters, and testing date group. An evident decrease in LTE is noted for the tests 

performed after 1996 as compared to the tests performed in previous years. It is also interesting to note 

that the approach slab tests show a lower average LTE than the leave slab tests for most of the joints, 

except for the joint located 8.95 m from the start of the section, where the trend is reversed. 

0

10

20

30

40

50

60

70

80

J4,-9.4 before 96

J4,-9.4 after 96

J5,-9.1 before 96

J5,-9.1 after 96

J4,1.2 before 96

J4,1.2 after 96

J5,1.5 before 96

J5,1.5 after 96

J4,5.2 before 96

J4,5.2 after 96

J5,5.5 before 96

J5,5.5 after 96

J4,8.8 before 96

J4,8.8 after 96

J5,9.1 before 96

J5,9.1 after 96

J4,14 before 96

J4,14 after 96

J5,14.3 before 96

J5,14.3 after 96

J4,19.5 before 96

J4,19.5 after 96

J5,19.8 before 96

J5,19.8 after 96

Joint ID and Date of Testing

Average LTE (%)

J4 – LTE on approach slab 

J5 – LTE on leave slab 

X.XX distance from start of section to joint location in meters 

B–96 – LTE tests before 1996 

A–96 – LTE tests after 1996 

Figure 114. Average LTE above freezing and below 25 oC, section 49–3011. 

A statistical analysis for the average LTE is presented in table 78. The percent decrease in LTE for tests 

performed before 1996 and tests performed after 1996 is included along with a paired t-test to determine 

whether or not the means belong to the same population. It is observed that for most of the joints, except 

for joints −9.25 and 19.65 for the leave slab test, the null hypothesis that the mean LTE for tests 

performed before and tests performed after 1996 is the same is rejected at the 5 percent confidence 

interval. Therefore, quantitative evidence is obtained suggesting that age is a significant factor in joint 

LTE. The average decrease in LTE for tests after 1996 for all joints analyzed is 15.3 percent. The dates 

considered in the analysis range from November 1993 to September 1997. 

Table 78 also shows the difference in LTE for approach slab tests and leave slab tests. For most of the 

joints, higher LTE values are observed for the leave slab test than for the approach slab test. On average, 

the leave slab tests show 9.8 percent higher LTE values. 

A large variability in LTE also was noted between individual joints that also contribute to the overall LTE 

variability for that section. A typical example of the variability between joints is presented in figure 115. 

In general, lower values of LTE are noted for the joint located at −9.25 m from the start of the section 

than for the joint located at 8.95 m (for LTE tests below 25 oC). In addition, the variability for the joint at 

8.95 m is notoriously higher than that for the joint at −9.25 m, as implied by the lower coefficient of 

determination (r2) for that joint, determined with a linear regression analysis. 
233 

Table 78. Summary statistics for effect of pavement age on LTE. 

Type of 

LTE 

Test 

Joint 

Location 

(m) 

Date Average 

LTE (%)

Standard 

Deviation

Coefficient 

of Variation

Change in 

Average 

LTE 

t-test for 

Means 

Difference in 

LTE (J5–J4) 

before 96 0.471 0.173 36.6% J4 −9.25 after 96 0.370 0.100 27.1% −10.1% 2.0% – 

before 96 0.614 0.242 39.5% 14.3% J5 −9.25 after 96 0.565 0.292 51.7% −4.8% 10.1% 19.5% 

before 96 0.548 0.140 25.4% J4 1.35 after 96 0.380 0.119 31.4% −16.8% 0.0% – 

before 96 0.644 0.159 24.7% 9.6% J5 1.35 after 96 0.436 0.183 42.0% −20.9% 0.0% 5.5% 

before 96 0.709 0.174 24.5% J4 5.35 after 96 0.442 0.119 26.9% −26.6% 0.0% – 

before 96 0.766 0.175 22.8% 5.7% J5 5.35 after 96 0.533 0.189 35.5% −23.3% 0.0% 9.0% 

before 96 0.695 0.177 25.5% J4 8.95 after 96 0.524 0.139 26.6% −17.1% 0.2% – 

before 96 0.640 0.220 34.4% −5.4% J5 8.95 after 96 0.547 0.232 42.5% −9.3% 1.5% 2.3% 

before 96 0.594 0.222 37.3% J4 14.15 after 96 0.365 0.143 39.2% −23.0% 0.0% – 

before 96 0.700 0.251 35.9% 10.6% J5 14.15 after 96 0.534 0.280 52.5% −16.6% 1.1% 16.9% 

before 96 0.546 0.156 28.6% J4 19.65 after 96 0.443 0.187 42.1% −10.2% 3.7% – 

before 96 0.667 0.217 32.6% 12.1% J5 19.65 after 96 0.620 0.221 35.7% −4.8% 38.0% 17.6% 

 −15.3% 9.8% 
234 

R2 = 0.5555

R2 = 0.1698

0

20

40

60

80

100

120

-10 -5 0 5 10 15 20 25 30 35 40 45

Temperature (oC)

Measured LTE (%)

Joint -9.25

Joint 8.95

Linear (Joint -9.25)

Linear (Joint 8.95)

Figure 115. Variability of LTE for individual joints, section 49–3011. 

In addition, as noted in table 77, section 49–3011 has a random joint spacing. Since the point location 

corresponds to the distance from the start of the section, and since most of these joints are consecutive to 

each other, individual joint spacings could be determined. Figure 116 shows the results of evaluating the 

effect of joint spacing on LTE for that section. Although a slight decrease in LTE is observed for larger 

joint spacings, a rather low r2 is obtained. It must be noted that a similar variability between joints also 

was noted for sections with constant joint spacing. It is believed that the pavement age at which the crack 

formed at the joint may also play an important role on joint opening, and therefore on LTE. From 

previous experience, it has been noted that after construction, the joints that crack first tend to have larger 

joint openings than joints that crack later. 
235 

R2 = 0.37

R2

 = 0.03

R2

 = 0.57

R2

 = 0.19

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5

Joint Spacing (m)

LTE (%)

Approach test, before 1996 Aproach test, after 1996

Leave test, before 1996 Leave test, after 1996

Linear (approach test, after 1996) Linear (leave test, after 1996)

Linear (approach test, before 1996) Linear (leave test, before 1996)

Figure 116. Effect of joint spacing on LTE, section 49–3011. 

Figures 117 through 126 present the LTE computed for the remaining nondoweled and doweled sections 

in the SMP study, respectively. Individual analyses for each section showed similar trends in LTE, with 

testing date and type of LTE test, to those observed for section 49–3011. However, sections 04–0215 and 

83–3802 showed reversed trends of LTE versus testing date. For these two sections, a higher LTE was 

observed for LTE tests after 1996. Although the increase in load transfer could be attributed to an 

improvement of the load transfer, records in DataPave 3.0 show no load transfer restoration for these 

sections nor any other rehabilitation activity of this sort. 

D.1.1.3.3 LTE as a Function of Joint Opening 

The temperature at joint closure and ER can be used to determine the joint openings at different 

temperatures for the sections in study. 

Figure 127 shows a plot of LTE versus joint opening for an individual joint in section 49–3011. For this 

section, the temperature of closure could be clearly identified from the joint opening analysis. In figure 

127, testing dates are split in LTE tests before and after 1996. A linear fit is used to differentiate between 

testing dates. This figure corroborates some of the findings previously presented. 
236 

31-3018

0%

20%

40%

60%

80%

100%

120%

-10 0 10 20 30 40

Temperature (oC)

LTE (%)

31-3018

0%

20%

40%

60%

80%

100%

120%

-10 0 10 20 30 40

Temperature (oC)

LTE (%)

Figure 117. Computed LTE versus PCC temperature for nondoweled section 31–3018. 

06-3042

0%

20%

40%

60%

80%

100%

120%

-5 5 15 25 35 45

Temperature (oC)

LTE (%)

06-3042

0%

20%

40%

60%

80%

100%

120%

-5 5 15 25 35 45

Temperature (oC)

LTE (%)

Figure 118. Computed LTE versus PCC temperature for nondoweled section 06–3042. 
237 

83-3802

0%

20%

40%

60%

80%

100%

120%

-20 -10 0 10 20 30

Temperature (oC)

LTE (%)

83-3802

0%

20%

40%

60%

80%

100%

120%

-20 -10 0 10 20 30

Temperature (oC)

LTE (%)

Figure 119. Computed LTE versus PCC temperature for nondoweled section 83–3802. 

53-3813

0%

20%

40%

60%

80%

100%

120%

-5 5 15 25 35 45

Temperature (oC)

LTE (%)

53-3813

0%

20%

40%

60%

80%

100%

120%

-5 5 15 25 35 45

Temperature (oC)

LTE (%)

Figure 120. Computed LTE versus PCC temperature for nondoweled section 53–3813. 
238 

04-0215

0%

20%

40%

60%

80%

100%

120%

0 10 20 30 40 50

Temperature (oC)

LTE (%)

04-0215

0%

20%

40%

60%

80%

100%

120%

0 10 20 30 40 50

Temperature (oC)

LTE (%)

Figure 121. LTE versus PCC temperature for doweled section 04–0215. 

18-3002

0%

20%

40%

60%

80%

100%

120%

-10 0 10 20 30 40

Temperature (oC)

LTE (%)

18-3002

0%

20%

40%

60%

80%

100%

120%

-10 0 10 20 30 40

Temperature (oC)

LTE (%)

Figure 122. LTE versus PCC temperature for doweled section 18–3002. 
239 

13-3019

0%

20%

40%

60%

80%

100%

120%

-5 5 15 25 35 45

Temperature (oC)

LTE (%)

13-3019

0%

20%

40%

60%

80%

100%

120%

-5 5 15 25 35 45

Temperature (oC)

LTE (%)

Figure 123. LTE versus PCC temperature for doweled section 13–3019. 

32-204

0%

20%

40%

60%

80%

100%

120%

-10 0 10 20 30 40

Temperature (oC)

LTE (%)

32-204

0%

20%

40%

60%

80%

100%

120%

-10 0 10 20 30 40

Temperature (oC)

LTE (%)

Figure 124. LTE versus PCC temperature for doweled section 32–0204. 
240 

89-3015

0%

20%

40%

60%

80%

100%

120%

-15 -5 5 15 25 35

Temperature (oC)

LTE (%)

89-3015

0%

20%

40%

60%

80%

100%

120%

-15 -5 5 15 25 35

Temperature (oC)

LTE (%)

Figure 125. LTE versus PCC temperature for doweled section 89–3015. 

39-0204

0%

20%

40%

60%

80%

100%

120%

-10 0 10 20 30 40

Temperature (oC)

LTE (%)

39-0204

0%

20%

40%

60%

80%

100%

120%

-10 0 10 20 30 40

Temperature (oC)

LTE (%)

Figure 126. LTE versus PCC temperature for doweled section 39–0204. 
241 

0

10

20

30

40

50

60

70

80

90

100

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Joint Opening (mm)

LTE (%)

LTE before 1996

LTE after 1996

Linear (LTE before 1996)

Linear (LTE after 1996)

Figure 127. LTE versus joint opening for section 49–3011, joint at 5.5 m from start of section. 

D.1.1.3.4 Summary of Findings

A number of analyses were performed to understand the effect of various parameters on joint LTE. An 

analysis was performed with LTPP data from SMP sections to determine the effect of temperature on 

joint movement and to identify the temperature of closure necessary in determining the joint opening. In 

addition, the computed LTE from the SMP sections was evaluated, and a number of factors were found to 

have a significant effect on LTE. These factors include: 

• Doweled sections showed a higher LTE than nondoweled sections. 

• The PCC temperature has a large effect on joint opening. Because the aggregate interlock is 

reduced for large joint openings, a decrease in temperature causes a reduction in LTE. 

• High LTE values were observed for PCC temperatures above the temperature of closure at 

which the joint is tight. 

• At freezing temperatures, higher values of LTE were observed from deflection testing. 

• The type of LTE test (load on approach or leave slab) showed to be a significant factor in the 

computed LTE values. Higher LTE values were observed for the leave slab tests. 

• Variability between joints also was a significant factor contributing to the overall variability 

of LTE. This variability is believed to be due to random joint spacing and time of crack 

formation at the joint after construction, among other factors. 

It is believed that the procedures used in this investigation are effective in better understanding the effects 

of various factors on LTE. 
242 

D.1.1.4 Calibration of the LTE Model with JPCP Nondoweled Sections 

For calibration of the LTE model, LTE was predicted as a function of joint opening and compared to the 

computed LTE from FWD tests. The temperature at closure and ER were used to determine the joint 

openings at different temperatures for the sections in study. 

For sections where the temperature at joint closure could not be identified, this temperature was estimated 

based on a subjective assessment of the effect on LTE with change in temperature. It was noted that in 

most sections with information on temperature at joint closure, the LTE remained above 90 percent for 

joint openings smaller than 0.5 mm. Assuming this same behavior would hold true for the remaining 

sections with no joint closure information, the temperature at closure was backcalculated in such a way as 

to observe that drop below 90 percent on LTE at a joint opening of approximately 0.5 mm. 

Figure 128 shows a plot of predicted versus computed LTE at a representative joint on section 31–3018. 

The LTE tests presented for this section date from 1995 to 2000. Because LTE prediction changes with 

load applications, the LTE tests were separated into two different periods: LTE tests on 1996 and before, 

and LTE tests after 1996. It can be observed in figure 128 that at the same joint opening, tests performed 

before 1996 show higher LTE values than those performed after 1996. However, a significant variability 

is noted, which makes it slightly difficult to determine a clear difference between testing dates. 

The predicted LTE values are also shown in figure 128 at different load applications. LTE was predicted 

for the following loads: 0, 250,000, 500,000, and 12,400,000 ESALs. The last load level was obtained 

from traffic records in the LTPP database as the estimated cumulative ESALs at the end of 1996 for 

section 31–3018. Looking at figure 128 however, the predicted LTE at 250,000 ESALs seems to better 

match the computed LTE from tests at the end of 1996. After 500,000 ESALs, the predicted LTE seems 

to have very little variation with cumulative traffic. 

0

10

20

30

40

50

60

70

80

90

100

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted LTE, ESALs = 0

Predicted LTE, ESALs = 250,000

Predicted LTE, ESALs = 500,000

Predicted LTE, ESALs = 12,400,000

Figure 128. Predicted versus computed LTE for section 31–3018, joint 5.5 m from start of section. 

It was mentioned in section B.2.3.1.12 that the laboratory testing data used to develop the aggregate 

wearout model is based on slabs of small dimensions to which 9-kip loads were applied. The 9-kip loads 
243 

subjected the slabs to higher deflections than normally observed in the field. It is possible that the 

250,000 ESALs entered in the model represent the 12,400,000 ESALs actually applied to that section. 

That is, the model would need an ESALs multiplication factor of 0.02 to predict LTE properly. 

The above exercise was repeated for all the sections in study to determine the number of load applications 

and ESALs correction factor that better matched the computed LTE in each case. Figures 129 through 

132 present the LTE predictions at different levels of cumulative ESAL applications. A representative 

joint is shown with LTE tests for two different loading periods: before 1996 and after 1996. 

0

10

20

30

40

50

60

70

80

90

100

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted LTE, ESALs = 0

Predicted LTE, ESALs = 280,000

Predicted LTE, ESALs = 500,000

Predicted LTE, ESALs = 8,088,000

Figure 129. Predicted versus computed LTE for section 49–3011, joint 5.5 m from start of section. 

0

20

40

60

80

100

120

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted, ESALs = 0

Predicted, ESALs = 150,000

Predicted, ESALs = 500,000

Predicted, ESALs = 29,066,000

Figure 130. Predicted versus computed LTE for section 06–3042, joint 148.1 m from start of 

section. 
244 

0

10

20

30

40

50

60

70

80

90

100

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted, ESALs = 0

Predicted, ESALs = 200,000

Predicted, ESALs = 300,000

Predicted, ESALs = 500,000

Predicted, ESALs = 1,975,000

Figure 131. Predicted versus computed LTE for section 83–3802, joint 149.7 m from start of 

section. 

0

10

20

30

40

50

60

70

80

90

100

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted, ESALs = 0

Predicted, ESALs = 100,000

Predicted, ESALs = 3,790,000

Figure 132. Predicted versus computed LTE for section 53–3813, joint 0.0 m from start of section. 

Note from the above plots that, except for section 83–3802, the LTE test showed lower values for the 

period after 1996. Again, this seems to corroborate the effect of traffic loads on LTE. Although not 

indicated in the LTPP database maintenance records for section 83–3802, it is believed that some possible 

rehabilitation of this section could have been performed that resulted in the increased LTE after 1996. 
245 

As performed for section 31–3018, the number of ESALs that fit the LTE for 1996 was estimated with the 

LTE model in a rather subjective fashion. Table 79 presents the cumulative ESALs for every section on 

the analysis year along with the ESALs used in the model to fit the results from LTE tests. The last 

column presents the ESALs multiplication factor necessary to convert from the actual ESALs to the 

ESALs number required by the model to produce a good fit of the computed LTE. The average 

multiplication factor for all the sections analyzed was 0.048. However, a large variation of this factor was 

found among sections. 

It is believed that although the LTE model is capable of producing the same trends in LTE as observed in 

the field, an accurate prediction will be possible only after a major investigation of the many factors that 

could affect these predictions such as aggregate type, aggregate shape, slab support conditions, and slab 

thickness is performed. 

Table 79. Cumulative ESALs measured on design lane versus ESALs required to fit LTE model 

predictions. 

Section Year Cumulative 

ESALs 

ESAL fit ESALs Multiplication Factor 

31–3018 1996 12,409,440 250,000 0.020 

49–3011 1996 8,088,833 280,000 0.035 

06–3042 1996 29,065,803 180,000 0.006 

83–3802 1995 1,973,712 300,000 0.152 

53–3813 1996 3,792,431 100,000 0.026 

Figure 133 shows the results of a sensitivity analysis of the LTE model for nondoweled joints. It is 

observed that, according to this model, the most predominant factors affecting LTE are joint opening, 

cumulative load applications, and slab thickness. No major effect from PCC stiffness, wheel load, 

pressure, nor k-value were observed on LTE. As previously mentioned, factors that are not included in 

the model but that are believed to somehow affect the development of load transfer at joints include the 

aggregate type and shape, as well as slab curling and warping. 

It was found during the verification process that, although the LTE model predictions follow the general 

trends of LTE as computed from FWD tests, further investigation of a number of factors are necessary to 

be able to predict LTE with more accuracy. 
246 

0

10

20

30

40

50

60

70

80

90

100

Parameter

LTE (%)

High 

Low

Mid

High 8.6 93.4 96.5 93.6 93.3 93.6 44.8

Low 97.6 93.5 83.3 93.2 93.5 93.2 93.4

Mid 93.4 93.4 93.4 93.4 93.4 93.4 71.8

JO Epcc h W p k-value ESALs

5 mm

0.5 mm

178 mm

330 mm 0

270,000

0.7 MPa

0.5 MPa

13.6 MPa/m

40.7 MPa/m

22 kN

40 kN

34,470

20,680

0

10

20

30

40

50

60

70

80

90

100

Parameter

LTE (%)

High 

Low

Mid

High 8.6 93.4 96.5 93.6 93.3 93.6 44.8

Low 97.6 93.5 83.3 93.2 93.5 93.2 93.4

Mid 93.4 93.4 93.4 93.4 93.4 93.4 71.8

JO Epcc h W p k-value ESALs

5 mm

0.5 mm

178 mm

330 mm 0

270,000

0.7 MPa

0.5 MPa

13.6 MPa/m

40.7 MPa/m

22 kN

40 kN

34,470

20,680

Figure 133. Sensitivity analysis of LTE model for nondoweled pavements. 

D.1.1.5 Calibration of JPCP Doweled Sections 

In this section, an attempt to calibrate the LTE model for SMP doweled sections is performed. Similar to 

the nondoweled sections, LTE is predicted as a function of joint opening. The temperature at closure, and 

ER was used to determine the joint openings at different temperatures for the sections in study. 

For sections where the temperature at joint closure could not be identified, this temperature was estimated 

based on a subjective assessment of the effect on LTE with change in temperature as described in the 

calibration of nondoweled sections. 

For doweled sections, in addition to the PCC and support properties, the dowel characteristics are inputs 

to the LTE model. Among these characteristics, dowel looseness is one of the factors that has a 

significant effect on load transfer, as can be seen in the sensitivity analysis results presented in figure 134. 
247 

40

45

50

55

60

65

70

75

80

85

90

95

100

Parameter

LTE (%)

High 

Low

Mid

High 70.1 43.3 70.0 65.4 59.0 59.0 76.0 69.8 57.2 65.9

Low 69.0 95.9 69.0 71.7 73.1 79.0 49.8 69.4 82.3 69.6

Mid 69.6 69.6 69.6 69.6 69.6 69.6 69.6 69.6 69.6 66.6

Dowel 

Diameter Looseness Dowel Support

Joint 

Opening Epcc Thickness Load Weight Load 

Pressure k-value ESALs

5.1 mm

0.51 mm

330 mm

178 mm

25.4 mm

38.1 mm

0.102 mm

0.000254 mm

20,682 MPa 53 kN

13.6 MPa/m

81.4 MPa/m

270,000

0

34,470 MPa

22 kN

6,894 MPa

17,235 MPa 0.7 MPa

0.5 MPa

40

45

50

55

60

65

70

75

80

85

90

95

100

Parameter

LTE (%)

High 

Low

Mid

High 70.1 43.3 70.0 65.4 59.0 59.0 76.0 69.8 57.2 65.9

Low 69.0 95.9 69.0 71.7 73.1 79.0 49.8 69.4 82.3 69.6

Mid 69.6 69.6 69.6 69.6 69.6 69.6 69.6 69.6 69.6 66.6

Dowel 

Diameter Looseness Dowel Support

Joint 

Opening Epcc

40

45

50

55

60

65

70

75

80

85

90

95

100

Parameter

LTE (%)

High 

Low

Mid

High 70.1 43.3 70.0 65.4 59.0 59.0 76.0 69.8 57.2 65.9

Low 69.0 95.9 69.0 71.7 73.1 79.0 49.8 69.4 82.3 69.6

Mid 69.6 69.6 69.6 69.6 69.6 69.6 69.6 69.6 69.6 66.6

Dowel 

Diameter Looseness Dowel Support

Joint 

Opening Epcc Thickness Load Weight Load 

Pressure k-value ESALs

5.1 mm

0.51 mm

330 mm

178 mm

25.4 mm

38.1 mm

0.102 mm

0.000254 mm

20,682 MPa 53 kN

13.6 MPa/m

81.4 MPa/m

270,000

0

34,470 MPa

22 kN

6,894 MPa

17,235 MPa 0.7 MPa

0.5 MPa

Figure 134. LTE model sensitivity for doweled sections. 

Teller and Cashell explored the effect of dowel looseness under repeated loading.(115) They reported an 

increase in dowel looseness as a function of the load cycles. They also found some correlations of dowel 

diameter to dowel looseness. In this study, the correlations presented in equations 263 and 264 were 

made with the data reported by Teller and Cashell. 

0 6.4

20.32

1

0.0032 0.0016

⎟

⎠

⎞ ⎜

⎝

⎛ +

= +

φ

DL

 (263) 

where, 

 DL0 = dowel looseness after construction and 

 φ = dowel diameter (mm). 

( )

0.185

0 DL DL 0.00019 ESALS N = + (264) 

where, 

 DLN = dowel looseness after N cumulative loading and 

 ESALS = cumulative 8.2-ton single axle load applications. 

Figure 135 shows a plot of predicted versus computed LTE at a representative joint on section 37–0201. 

The computed LTE presented for this section dates from 1994 to 2001. Because LTE has been observed 

to decrease with load applications, LTE tests were separated into two different periods: LTE tests in 1996 
248 

and before, and LTE tests after 1996. Although it can be observed that measurements after 1996 show 

lower LTE values, some variability is noted, which makes it difficult to determine differences between 

measurement dates clearly. 

0

10

20

30

40

50

60

70

80

90

100

-0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted LTE, ESALs = 0, loose = 0.05 mm

Predicted LTE, ESALs factor = 0.048, loose = 0.11 mm

Predicted LTE, looseness = 0.05 mm, no AGG

Predicted LTE, Looseness = 0.11 mm, no AGG

Figure 135. Predicted versus computed LTE for section 37–0201, joint 145.1 m 

from start of section. 

The predicted LTE values at different load applications are also shown in figure 136. LTE was predicted 

for no loads and for 1593,467 ESALs (load level at the end of 1996 obtained from LTPP traffic records) 

adjusted by the multiplication factor of 0.048 previously determined for nondoweled sections. From 

equations 263 and 264, the predicted dowel looseness for those two load levels is 0.0018 and 0.0044, 

respectively. Figure 136 also includes the predicted LTE, assuming no aggregate interlock for the above 

looseness levels. For the looseness level with no traffic (0.0018), an LTE between 74 percent and 77 

percent is obtained for the actual range of joint movement. For the looseness level at the end of 1996, the 

LTE varies between 40 percent and 45 percent. Given that the LTE for aggregate interlock is higher than 

the LTE for dowel support, it is difficult to verify the goodness of fit for the dowel looseness model in 

this LTPP section. 

The above exercise was repeated for all the other sections in study to verify the accuracy of the ESALs 

multiplication factor for LTE determination and to verify the accuracy of the dowel looseness prediction 

model. Figures 137 through 140 present the LTE predictions at different levels of cumulative ESAL 

applications. For each section, a representative joint is shown with LTE measurements for two different 

loading periods: before 1996 and after 1996. 
249 

0

10

20

30

40

50

60

70

80

90

100

-1.000 -0.500 0.000 0.500 1.000 1.500 2.000

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted LTE, ESALs = 0, loose = 0.05 mm

Predicted LTE, ESALs factor = 0.074, loose = 0.13 mm

Predicted LTE, ESALs factor = 0.048, loose = 0.12 mm

Predicted LTE, Looseness = 0.12 mm, no AGG

Predicted LTE, Looseness = 0.05 mm, no AGG

Figure 136. Predicted versus computed LTE for section 04–0215, joint 144.5 m 

from start of section. 

0

10

20

30

40

50

60

70

80

90

100

-1.500 -1.000 -0.500 0.000 0.500 1.000 1.500 2.000

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted LTE, ESALs = 0, loose = 0.048 mm

Predicted LTE, ESALs factor = 0.122 mm

Figure 137. Predicted versus computed LTE for section 13–3019, joint 21.3 m from start of section. 
250 

0

10

20

30

40

50

60

70

80

90

100

0.000 0.500 1.000 1.500 2.000 2.500

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and after)

Computed LTE (after 1996)

Predicted LTE, ESALs = 0, loose = 0.042 mm

Predicted LTE, ESALs factor = 0.048, loose = 0.099 mm

Predicted LTE, looseness = 0.043 mm, no AGG

Predicted LTE, looseness = 0.061 mm, no AGG

Predicted LTE, ESALs factor = 0.048, looseness = 0.000 mm

Figure 138. Predicted versus computed LTE for section 32–0204, joint 8.5 m from start of section. 

0

10

20

30

40

50

60

70

80

90

100

0.000 0.500 1.000 1.500 2.000 2.500

Joint Opening (mm)

LTE (%)

Computed LTE (1996 and before)

Computed LTE (after 1996)

Predicted LTE, ESALs = 0, loose = 0.042 mm

Predicted LTE, ESALs factor = 0.048, looseness = 0.095

mm

Predicted LTE, ESALs factor = 0.048, looseness = 0.000

mm

Figure 139. Predicted versus computed LTE for section 89–3015, joint 36.3 m from start of section. 
251 

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120

Joint Opening (mm)

LTE (%)

Computed LTE (1998 and before)

Computed LTE (after 1998)

Predicted LTE, ESALs factor = 0.048, loose = 0.122 mm

Predicted LTE, ESALs = 0, loose = 0.041 mm

Predicted LTE, looseness = 0.041 mm

Predicted LTE, ESALs factor = 0.048, loose = 0.000 mm

Figure 140. Predicted versus computed LTE for section 39–0204, joint 0.0 m from start of section. 

Table 80 shows the cumulative ESALs for every section and the ESALs multiplication factor required to 

fit the computed LTE. 

Table 80. Cumulative ESALs measured on design lane and ESALs multiplication factor required 

to fit LTE model predictions. 

Section Year Cumulative ESALs ESALs Multiplication Factor 

37–0201 1996 1,593,467 0.048 

04–0215 1996 3,395,341 0.074 

13–3019 1996 1,553,000 0.090 

32–0204 1996 559,708 0.048* 

89–3015 1996 4,195,817 0.048* 

39–0204 1998 1,967,539 0.048* 

* Possibly biased due to no dowel looseness. 

From a comparative analysis of the LTE predictions for the above pavement sections, the following 

findings are observed: 

• ESALs factor for sections 04–0215 and 13–3019 seem to be higher than the average ESALs 

factor obtained for nondoweled sections. However, the ESALs factor for these sections fall 

within the variability range observed for the nondoweled sections. 

• It appears that for sections 37–0201, 04–0215, and 13–3019, LTE is being provided mainly 

by aggregate interlock. For sections 32–0204, 89–3015, and 39–0204, LTE appears to be 

provided mainly by dowel support. It appears that to obtain an adequate prediction of LTE 

for the last three sections, dowel looseness must be very small or not present. 
252 

• None of the sections appear to show dowel looseness as high as that predicted by the dowel 

looseness observed by Teller and Cashell. Furthermore, it is likely that dowel looseness may 

be also a function of other variables not investigated by Teller and Cashell. 

From this analysis, it was possible to verify the trend in LTE as a function of joint opening and load 

applications for a number of doweled LTPP SMP sections. The average ESALs multiplication factor 

previously found for nondoweled sections seems to work reasonably for the doweled pavement sections 

evaluated here. 

For the sections evaluated, it was rather difficult to determine the level of dowel looseness, because for 

half of the sections, LTE appears to be provided by aggregate interlock with some dowel looseness, while 

the remaining sections appear to have very little or no dowel looseness. Therefore, further work is 

required to verify the dowel looseness models presented. It is recommended that factors such as 

aggregate characteristics, dowel coatings, and compressive stresses at the dowel location due to curling 

stresses in the early ages be investigated. 

D.1.2 Validation of CRCP Early-Age Behavior Models 

Validation of the CRCP early-age behavior models had two objectives: validation of cracking behavior 

during the early age and validation of cracking behavior in the long term. Although, as its name implies, 

the CRCP module in HIPERAV should predict cracking behavior at early ages, long-term performance 

can be better estimated based on the cracking characteristics after the lowest temperature (typically after 1 

year). Therefore, validation was also performed on existing CRCP sections with crack spacing 

information. Validation of cracking characteristics for existing CRCP sections is described in the 

following section. Validation of early-age cracking behavior was performed with information collected 

on construction field sites and is described in section D.2.2. 

The CRCP–8 model included in HIPERPAV II has been validated extensively in the past.(106,116,117) 

However, during its incorporation into the HIPERPAV II system, new enhancements were made. These 

enhancements consisted of using the capabilities for pavement temperature prediction and development of 

mechanical properties in the HIPERPAV II system. The above enhancements warranted an additional 

validation of this module. 

Provided the mechanistic nature of the CRCP–8 model, extensive information on the input parameters for 

a few sections was desired as opposed to limited information on several sections. For this reason, 16 

sections on State Highway (SH)–6 in Houston, TX, that have been monitored continuously since 

construction were selected for this effort. Other CRCP sections also were investigated, such as the GPS–

5 sections of the LTPP database; however, only limited early-age information was available for validation 

of the CRCP–8 model.(118,119) 

D.1.2.1 Description of CRCP Sections in Houston, TX 

Reference 106 provides a detailed description of the section characteristics, construction, instrumentation, 

and testing procedures. A brief summary is presented below. 

The test sections in study are located on SH–6 on two different segments, one placed during summer 

1989 and other placed during winter 1990. For each segment, two different aggregate types were used 

with four different reinforcement designs for eight different design sections per construction season. 

Table 81 shows the factorial of designs used for both the summer and winter sections. 
253 

Table 81. Factorial design for CRCP test sections constructed in SH–6. 

Section ID A B C D E F G H 

Coarse Aggregate SRG SRG SRG SRG LS LS LS LS 

Bar Size #6 #6 #6 #7 #7 #6 #6 #6 

Steel (%) 0.63 0.53 0.42 0.53 0.63 0.52 0.61 0.68 

SRG – Siliceous river gravel 

LS – Limestone 

D.1.2.2 Instrumentation 

To measure temperatures in the concrete, thermocouples were installed 25 mm from the surface, in the 

middle, and 25 mm from the bottom of the slab. In addition, DEMEC points were used to measure the 

magnitude of thermal changes in the concrete. 

D.1.2.3 Condition Surveys 

Condition surveys were performed during the month following construction to monitor crack spacing and 

crack width. In addition, long-term cracking characteristics have been monitored at different times 

throughout the pavement life.(106,116,117)

D.1.2.4 Laboratory Testing 

A number of cylinders were cast at the job to measure concrete splitting tensile strength, compressive 

strength, elastic modulus, drying shrinkage, and CTE under field and laboratory conditions at different 

ages. 

D.1.2.5 CRCP–8 Input Parameters 

Validation of the CRCP HIPERPAV II module required collecting information on all the input 

parameters considered. This information and assumptions made are presented below. 

D.1.2.5.1 Design Inputs

The CRCP design thickness for all sections was 279 mm. Since no construction information on thickness 

was reported, the design thickness was used in the analysis. A single layer of steel was used, with bar 

size and steel percentage as shown in table 81. 

Slab support was provided by a 152-mm cement-treated base and 25-mm asphalt-stabilized base as a 

bond breaker. No restraint tests were reported. Typical restraint conditions for asphalt-stabilized bases 

were assumed for this exercise. A restraint stress of 41.4 kPa and movement at sliding of 0.63 mm were 

selected based on previous experiences by the authors. 

D.1.2.5.2 Materials and Mix Design

As previously mentioned, the type of coarse aggregate used was SRG and limestone. The mix design 

information is reported by Suh et al. and is presented in table 82 below.(106)
254 

Table 82. Mix design for SH–6 test sections. 

Project SH–6 Summer SH–6 Winter 

Coarse aggregate type SRG LS SRG LS 

Coarse aggregate—kg/m3 1,204 1,127 1,236 1,127 

Water—kg/m3 139 134 125 133 

Cement—kg/m3 230 251 203 230 

Fly Ash—kg/m3 63 68 95 63 

Fine Aggregate—kg/m3 658 722 640 746 

Entrained air (%) 5 5 5 5 

D.1.2.5.3 Concrete Properties

Test results on concrete properties were reported by Suh et al. and are summarized in tables 83 and 84 for 

summer and winter placements, respectively.(106) 

Table 83. Test results (SH–6—summer).(106)

Property Agg. Type Value (Lab/Field) 

28-day splitting tensile (MPa) SRG 3.9/4.1 

LS 3.6/3.4 

28-day modulus of elasticity (MPa) SRG 32884/37228 

LS 36125/38124 

28-day compressive strength (MPa) SRG 44.8/43.1 

LS 42.1/50.8 

28-day shrinkage (με) SRG 204.8/208.5 

LS 196.3/170.8 

CTE (με/oC) SRG 8.6/9.9 

LS 5.2/5.6 

Table 84. Test results (SH–6—winter).(106)

Property Agg. Type Value (Lab/Field) 

28-day splitting SRG 4/3.8 

tensile (MPa) LS 3.7/3.8 

28-day modulus of SRG 37779/37848 

elasticity (MPa) LS 34746/37159 

28-day compressive SRG 40.5/38.2 

strength (MPa) LS 47.4/46.5 

28-day shrinkage (με) SRG 90/115* 

LS 165/165 

CTE (με/oC) SRG –/11.9 

LS –/6.8 

* 30-day result 
255 

D.1.2.5.4 Construction

During construction, the placement temperature (temperature of the mix) was monitored, as was the time 

of day when construction began. This information is reported in tables 85 and 86, respectively. 

Table 85. Mix temperature for test sections in SH–6 (oC).(106)

Section Summer Winter 

Section A 30 21 

Section B 30 20 

Section C 30 19 

Section D 31 18 

Section E 29 21 

Section F 29 14 

Section G 30 14 

Section H 30 15 

* Values in bold were reported, all other values were estimated. 

Table 86. Time of placement for test sections in SH–6.(106)

Section Summer Winter 

Section length (m) 70 70 

Section A 6/16/1989 8:30 1/10/1990 13:00 

Section B 6/16/1989 10:30 1/10/1990 15:00 

Section C 6/16/1989 12:20 1/11/1990 10:00 

Section D 6/16/1989 14:00 1/11/1990 12:30 

Section E 6/19/1989 9:40 1/11/1990 16:00 

Section F 6/19/1989 11:30 1/12/1990 10:00 

Section G 6/19/1989 13:00 1/12/1990 11:20 

Section H 6/19/1989 14:20 1/12/1990 14:00 

* Values in bold were reported, all other values were estimated. 

Curing method was not reported, and white curing compound was assumed; however, inconsistencies in 

the prediction of temperatures for sections G and H during winter placement lead to indications that 

polyethylene sheeting or cotton mats could have been used during the first few hours. This was based on 

the low temperatures observed during those days. 

D.1.2.6 Environment 

Historical air temperature, windspeed, relative humidity, and cloud cover data was retrieved from the 

National Oceanic and Atmospheric Administration (NOAA) database for the construction dates for every 

section. This information was obtained from the Houston Intercontinental Airport, the closest weather 

source to the site. 
256 

D.1.2.7 Measured Cracking Characteristics 

Crack spacing and crack width information has been monitored continuously for the sections on SH–6. 

During construction, condition surveys were performed during the first 30 days. In addition, condition 

surveys have been performed at 180, 500, 1000, 2500, 2800, and 4700 days for the summer sections and 

at 300, 800, 2300, 2600, and 4700 days for the winter sections (data provided by CTR of the University of 

Texas at Austin). Average crack spacings for the above survey dates are presented in figures 141 and 

142. A typical trend of reduced crack spacing with age can be observed; however, for most sections, 

higher average crack spacings were reported for the surveying date at 4700 days than for previous dates. 

Since no rehabilitation has been reported for those sections, it is believed that the higher average crack 

spacings at 4700 days possibly may be due to omitted cracks during crack spacings measurement (this 

may be possible if the measurements were taken during a hot summer day when concrete expansion 

closes the cracks, making some of them imperceptible to the human eye). During hot days, hairline 

cracks are difficult to identify, which may result in cracks not included in the condition survey. For this 

reason, the crack spacing at 2500 days for the summer sections and 2600 days for the winter sections was 

selected for validation of the long-term crack spacings. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1 10 100 1,000 10,000

Pavement Age (days)

Crack Spacing (m)

Section A

Section B

Section C

Section D

Section E

Section F

Section G

Section H

Figure 141. Crack spacing history for summer sections, SH–6. 
257 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1 10 100 1,000 10,000

Pavement Age (days)

Crack Spacing (m)

Section A

Section B

Section C

Section D

Section E

Section F

Section G

Section H

Figure 142. Crack spacing history for winter sections, SH–6. 

D.1.2.8 Long-Term Crack Spacing Validation Results 

With the above information, each section was analyzed with the CRCP HIPERPAV II module to compare 

the measured crack spacings to the predicted values. Figure 143 shows the comparison results using the 

above input parameters as reported. Although a general slight overprediction of crack spacing is 

observed, a reasonably good r2 with respect to the 45o line was obtained (r2 = 0.82). 

0

1

2

3

4

5

012345

Observed Average Crack Spacing (m)

Predicted Average Crack Spacing (m)

R2

45o = 0.71

Figure 143. Preliminary long-term crack spacing prediction. 
258 

Given the reasonable fit obtained and because this validation effort was intended to determine if the 

differences in prediction are within reasonable limits rather than to calibrate the model, no model 

adjustments were performed. 

D.1.2.9 Early-Age Crack Spacing Validation Results 

Crack spacing during the early age was also compared to the predicted crack spacings with the CRCP 

HIPERPAV II module. Figure 144 shows the prediction results at 3 days from construction. 

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Observed Average Crack Spacing (m)

Predicted Average Crack Spacing (m)

R 2

45o = 0.36

Figure 144. Crack spacing prediction at 3 days from construction. 

For the early age, a generally poor prediction of crack spacings was observed. Similar results had been 

observed in previous validation efforts with this data set. Suh et al. had found good predictions for the 

first few months after construction; however, significant deviations were observed for the first 5 to 10 

days.(106) This poor prediction may be attributed to a number of reasons: 

• Monte Carlo Simulation: The stochastic nature of the crack spacing prediction model 

requires of a minimum number of data points to generate accurate predictions. Because the 

sections were relatively short (70 m long) and the crack spacings relatively large, it is 

possible that the data points generated were not sufficient to predict with accuracy. 

• Inability to accurately predict early-age temperatures due to lack of curing information. It has 

been mentioned that no curing information was provided. In some cases, during winter, it is 

possible that curing with polyethylene sheeting or blankets might have been used due to the 

low temperatures. Information on this type of curing would be necessary for an accurate 

prediction. 

Validation of the CRCP model during early ages is discussed further in section D.2.2. 
259 

D.1.2.10 Validation Results for Long-Term Crack Widths 

Measurements of crack width 2 years after placement for the SH–6 test sections, were reported by Otero 

et al.(116) The HIPEPRAV CRCP module was used to predict crack widths at the temperature observed in 

the concrete during the crack width measurements. A comparison of the long-term crack width 

predictions against the measured values is presented in figure 145. Although a fair trend in crack width 

prediction is observed, all crack widths were largely overpredicted. This overprediction in crack widths 

had been observed in previous validation efforts.(116) Although Otero et al. proposed a new model for 

crack width prediction, the use of this model in this study did not show reasonable results. As has been 

previously reported, the overprediction may be because the CRCP–8 model does not account for the time 

when the crack forms, but rather depends on the predicted crack spacing, PCC thermal properties, and 

total shrinkage. As figure 146 illustrates, the drying shrinkage after crack formation depends on the 

concrete age when the crack occurs. It is believed that the residual drying shrinkage after the crack forms 

has a large effect on crack width. 

R 2

 = 0.44

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Observed Average Crack Width (mm)

Predicted Average Crack Width (mm)

R 2

45o = 0.11

Figure 145. Measured versus predicted crack widths, SH–6. 
260 

Z1

Z2

Z3

d1 d2

Shrinkage

Pavement Age

d1=Age at time of crack

Z1=Shrinkage at d1

d2=Age at time of measurement

Z2=Residual shrinkage

Z3=Total shrinkage Z1

Z2

Z3

d1 d2

Shrinkage

Pavement Age

d1=Age at time of crack

Z1=Shrinkage at d1

d2=Age at time of measurement

Z2=Residual shrinkage

Z3=Total shrinkage

Figure 146. Conceptual representation of residual drying shrinkage effect (adapted from 

Otero et al.).(116)

The CRCP–8 crack width algorithm could be modified to account for the time of crack formation and 

residual drying shrinkage. However, such modification is out of the scope for this study, since additional 

data would be required for calibration and validation. 

D.1.2.11 Validation Results for Early-Age Crack Widths 

Only scattered information on crack widths during the early age was reported, and no attempt was made 

to perform validation with these data. It is believed that crack width information collected from the field 

sites evaluated in this study will shed some light on the accuracy of early-age crack width predictions. 

D.1.2.12 Summary and Conclusions 

During the database validation of the CRCP models in HIPERPAV II, good predictions of long-term 

crack spacing were observed. However, poor early-age crack spacing predictions were obtained. The 

inaccuracy in the early-age predictions is believed to be due to the nature of the stochastic algorithm used 

to predict crack spacings combined with the small length of the experimental sections (approximately 60 

m) and the typically large crack spacings observed at early ages (from 2 to 8 m). Another possible reason 

contributing to the overprediction is the lack of information on curing procedures used. In the long term, 

the crack spacings were much smaller compared to the length of the experimental sections, with much 

better predictions achieved. 

D.2 FIELD VALIDATION 

Four field sites were investigated for validation of the HIPERPAV II system: 

• Two inservice JPCP sections were evaluated to validate the long-term performance models in 

the JPCP module. 

• Two newly constructed CRCP sections were instrumented to validate the CRCP early-age 

behavior module. 
261 

It is believed that the number of field sites evaluated will provide the minimum level of information 

necessary to meet the objectives of this effort successfully. However, additional data from field sites in 

the future could be used for local customization. The objective of this section is to describe the steps 

performed for validation of both, the JPCP and CRCP pavement sites investigated. The detailed data 

collection procedures and data reduction is presented in appendix C. 

D.2.1 Validation of Long-Term Performance Models with Inservice JPCP Sites 

The information collected from the pavement sections in Illinois and Ticuman, Mexico were used for 

validation of the long-term performance prediction models in HIPERPAV II. In this effort, the reliability 

of prediction for these two sites was evaluated. Several factors were considered in the validation of the 

long-term JPCP HIPERPAV II module for each field site. This validation included a comparison of 

measured and predicted mechanical properties, LTE, and long-term distresses. Validation of each factor 

is discussed in the following paragraphs. 

D.2.1.1 Validation Results for JPCP Section on U.S. Highway 50, Illinois 

As previously mentioned in section C.1.1, the Illinois site consisted of several pavement sections with 

different designs. Design features that were varied included the slab thickness, presence of longitudinal 

underdrain, and presence of sealant on longitudinal joint. Therefore, each of the sections evaluated was 

analyzed separately. In addition, to account for the effect of time of day of construction on performance, 

analyses for placement times at 2 a.m., 8 a.m., 2 p.m., and 8 p.m. were evaluated. 

Information on pavement design, materials, and construction procedures was extracted from historical 

records for this site. Climatic information was extracted from NOAA records for the date of construction 

of every section for input into HIPERPAV II. 

D.2.1.1.1 Mechanical Properties

Information on concrete flexural strength is available from records at 14, 28, and 90 days.(103) In addition, 

the flexural strength almost 16 years after construction was estimated based on the splitting tensile 

strength obtained from cores extracted during the field visit in 2001. Figure 147 shows the flexural 

strength for these ages along with the early-age and long-term strength predicted with HIPERPAV II. 
262 

0

1

2

3

4

5

6

7

0.0001 0.001 0.01 0.1 1 10 100

Years

Flexural Strength, MPa

Measured

Predicted early age

Predicted long term

Figure 147. Comparison of measured and predicted strength, Illinois site. 

In general, although the 90-day strength is slightly underpredicted, a reasonably good prediction of the 

measured long-term strength is obtained. 

A similar analysis was performed for prediction of the elastic modulus. Figure 148 shows the measured 

modulus of elasticity at 28 days and the one obtained from concrete cores extracted from the field visit in 

2001. While the predicted elastic modulus shows an increasing trend, the elastic modulus obtained from 

field cores in 2001 shows a slight decrease from the 28-day value. A significant difference in predicted 

versus measured elastic modulus is thus observed after 16 years. Although no further investigation was 

performed to determine the cause of the unexpected decrease in measured modulus of elasticity, possible 

reasons for this trend include variability in testing and in data interpretation, since the tests at 28 days and 

those in the long term were performed by different laboratories. 
263 

-

5,000

10,000

15,000

20,000

25,000

30,000

35,000

0.0001 0.001 0.01 0.1 1 10 100

Years

Elastic Modulus, MPa

Measured

Predicted early age

Predicted long term

Figure 148. Comparison of measured and predicted modulus of elasticity, Illinois site. 

D.2.1.1.2 LTE

LTE has been measured on this site at 8, 12, and 15 years of age. Figure 149 shows the measured and 

predicted LTE for the sections with 216-mm thickness. The predicted LTE is shown as continuous lines 

for four times of day: 2 a.m., 8 a.m., 2 p.m., and 8 p.m. The fluctuating trend observed is due to seasonal 

effects. Higher LTE values are observed for the summer months when the joints are tight due to the 

higher temperatures on those months. Both the approach and leave slab LTE is shown for the tests 

performed at 15 years. In general, a slight overprediction of LTE is observed for all testing ages. 
264 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 2 4 6 8 10 12 14 16 18

Years

Load Transfer Efficiency (%)

LTE at 2 a.m.

LTE at 8 a.m.

LTE at 2 p.m.

LTE at 8 p.m.

Average Measured LTE

for 216-mm Thickness

Figure 149. Comparison of measured versus predicted LTE. 

D.2.1.1.3 Early-Age Analysis

Figures 150 to 152 show typical early-age results for these sections in terms of strength and stress 

development for the first 72 hours after construction. In these figures, the results for the placement time 

at 2 p.m. are shown for sections AA, IA, and NA. It is particularly interesting to observe the excessive 

stresses for section NA. As previously mentioned in section C.1.1, a cement-aggregate mixture base was 

used under the slab, which is believed to have induced high restraint conditions. In addition, higher air 

temperatures for that day were observed from historical weather records. These analysis results suggest 

that the transverse cracking observed from condition surveys on these sections possibly originated in the 

early age rather than from fatigue cracking. 
265 

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60 70 80

PCC Age (h)

Strength or Stress (MPa)

PCC strength

Critical stress

Figure 150. Early-age analysis for section AA, for placement at 2 p.m. 

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60 70 80

PCC Age (h)

Strength or Stress (MPa)

PCC strength

Critical stress

Figure 151. Early-age analysis for section IA, for placement at 2 p.m. 
266 

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60 70 80

PCC Age (h)

Strength or Stress (MPa)

PCC strength

Critical stress

Figure 152. Early-age analysis for section NA for placement at 2 p.m. 

D.2.1.1.4 Long-Term Distresses

In addition to the early-age analysis, materials characterization, and structural response evaluation above, 

a comparison of measured versus predicted long-term distresses was made to assess the accuracy of 

prediction of the HIPERPAV II long-term module. Individual runs were performed at 10 percent, 50 

percent, and 90 percent reliability levels. 

Figure 153 shows the predicted faulting for sections MA and NA with 191 mm of thickness. These 

predictions closely follow the observations made during the field visit in 2001, where no apparent faulting 

was reported. 
267 

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14 16 18

Years

Faulting (mm)

At 90% reliability

Observed faulting

Figure 153. Predicted faulting for sections MA and NA (191-mm thick). 

Figures 154 to 156 show a comparison of measured and predicted midpanel cracking in the transverse 

direction for the sections evaluated. As previously mentioned in the early-age analysis for this site, it is 

believed that the amount of transverse cracking present is due to early-age factors rather than to fatigue 

cracking. The predicted fatigue cracking observed for these sections is minimal compared to the 

transverse cracking observed from surveys. 

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0 2 4 6 8 10 12 14 16 18

Years

Transverse Cracking (%)

At 90% reliability

Section MA

Section NA

Figure 154. Comparison of measured and predicted transverse cracking (sections NA and MA). 
268 

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0 2 4 6 8 10 12 14 16 18

Years

Transverse Cracking (%)

At 90% reliability

Section IA

Section JA

Section KA

Section LA

Figure 155. Comparison of measured and predicted transverse cracking for sections 

(IA, JA, KA, LA). 

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18

Years

Transverse Cracking (%)

Transverse Cracking (90% built-in

curling), Thickness = 241 mm

Section AA

Figure 156. Transverse cracking for section AA, thickness = 241 mm. 

Figure 157 shows a comparison of transverse cracking for sections MA and NA with 191-mm thickness. 

Only one low severity longitudinal crack was observed for section NA. Similar to the transverse cracking 

present in some of these sections, the longitudinal cracking observed is believed to be due to thermal 

effects and restraint conditions. No longitudinal cracking was either predicted or observed in the fields 

for all other sections. 
269 

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0 2 4 6 8 10 12 14 16 18

Years

Cracking (%)

At 90% reliability

Section MA

Section NA

Figure 157. Comparison of measured and predicted longitudinal cracking (sections MA and NA) 

No longitudinal cracking was observed for sections AA, IA, JA, KA, and LA. The model predictions for 

these sections showed no longitudinal cracking, either. 

Figure 158 shows the IRI predicted for section NA. The average IRI for all sections for 1994, 1996, 

1998, and 2001 also is shown in this figure. Because no data was available for the IRI after construction, 

an estimated IRI of 1.42 m/km was assumed for this analysis. From this figure, a high scatter in the 

measured IRI is observed. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 2 4 6 8 10 12 14 16 18

Years

IRI (m/km)

At 90% reliability At 50% reliability

At 10% reliability Measured IRI

Figure 158. Comparison of measured and predicted IRI (section NA).
270 

D.2.1.2 Validation Results for JPCP Section on Ticuman Bypass, Mexico 

Similar to the Illinois site, a comparison of the measured and predicted mechanical properties, structural 

response, and long-term performance distresses was made for the Ticuman bypass. 

D.2.1.2.1 Mechanical Properties

Figure 159 shows a comparison of the measured and predicted third-point flexural PCC strength for the 

Ticuman bypass. Flexural strength tests were performed at 1, 3, 7, 14, and 28 days of age. The long-term 

flexural strength value at 8 years of age was estimated from compressive and indirect tensile strength tests 

results obtained from cores extracted in the 2001 field evaluation. In general, a rather good prediction of 

the PCC strength was achieved. 

0

1

2

3

4

5

6

0.0001 0.001 0.01 0.1 1 10

Years (log scale)

Flexural Strength, MPa

Measured

Predicted long term

Predicted early age

Figure 159. Comparison of measured versus predicted flexural strength, Ticuman, Mexico. 

Figure 160 shows a comparison of the measured versus predicted modulus of elasticity. The measured 

values correspond to 28 days and 8 years of age. A significant underprediction of the elastic modulus at 8 

years of age is observed. While the predicted modulus of elasticity shows an increase of 12 percent from 

28 days to 8 years, the measured value shows an increase of 55 percent. This finding is opposite to the 

one observed for the Illinois site, where the elastic modulus was overpredicted. 
271 

-

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

0.0001 0.001 0.01 0.1 1 10

Years (log scale)

Elastic Modulus, MPa

Measured

Predicted early age

Predicted long term

Figure 160. Comparison of measured versus predicted modulus of elasticity, Ticuman, Mexico. 

D.2.1.2.2 LTE

LTE tests results are available for two instances: during the first few months after construction, and at 8 

years of age. These results are compared to the model predictions in figure 161. As previously 

mentioned in section C.1.2.2, the low LTE test results observed in 1993 are attributed to the fact that 

some of the joints had not cracked, leading to wider joint widths and poor load transfer. In comparison, 

the LTE tests results at 8 years of age show a high LTE. Compared to the LTE predicted with 

HIPERPAV II, the LTE predicted is higher than the measured in 1993 and slightly lower than the one 

measured in 2001. 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0123456789

Years

Load Transfer Efficiency (%)

LTE at 2 a.m.

LTE at 8 a.m.

LTE at 2 p.m.

LTE at 8 p.m.

Measured LTE

(average)

Figure 161. Comparison of measured versus predicted LTE, Ticuman, Mexico. 
272 

D.2.1.2.3 Long-Term Distresses

A total of 54 factorial runs were considered for analysis of the distresses at the Ticuman bypass. This 

factorial was to account for the variability on thickness observed at this site and the different times of 

placement. In addition, the factorial was expanded to account for different levels of reliability in the 

long-term analyses. 

For the early-age scenarios, three different thicknesses were considered: 203, 229, and 254 mm. Each one 

of these scenarios was evaluated for placement times at 8 a.m., 2 p.m., and 6 p.m. For the long-term 

scenarios, three levels of reliability were considered: 10 percent, 50 percent, and 90 percent. Each 

strategy was analyzed under two conditions: curling stresses computed from thermal gradient at time of 

loading only, and curling stresses computed for the thermal gradient at time of loading plus built-in 

curling present at PCC set time. 

Figure 162 shows the effect of built-in curling for longitudinal cracking on placement times at 10 a.m. 

and 6 p.m. For the 10 a.m. placement, the gradient at time of loading with no gradient built-in at set 

produces higher cracking than the condition with built-in curling. In contrast, the placement at 6 p.m. 

shows the opposite trend, with the condition with built-in curling showing higher longitudinal cracking. 

Further investigation into this effect shows that the slabs placed at 10 a.m. set with a positive built-in 

curling, while the slabs placed at 6 p.m. set with a negative built-in curling. In addition, the most critical 

loading condition in the long-term for both cases is found to be at 2 p.m., when the slab is being subjected 

to a positive thermal gradient. For the 10 a.m. placement, the positive thermal gradient built-in at set 

counteracts the positive thermal gradient during loading and thus reduces the total tensile stresses at the 

slab bottom for that condition. The opposite occurs for the placement at 6 p.m., where the negative builtin gradient adds to the positive thermal gradient at the time of loading, effectively increasing the stresses 

for this condition. Because the relaxation occurring on the curling shape of the slab with time, it is 

believed that the actual stress state at time of loading lies somewhere between these two conditions. 

0

2

4

6

8

10

12

14

0123456789

Years

Longitudinal Cracking (%)

10 a.m., no gradient built-in

6 p.m., built-in gradient

10 a.m., built-in gradient

6 p.m., no gradient built-in

Figure 162. Analysis for 229-mm slab at different construction times and built-in gradient 

conditions, Ticuman bypass. 
273 

Faulting was measured for the Ticuman bypass on the field visit in 2001. Figure 163 shows a comparison 

of measured and predicted faulting for this site. The average measured faulting of 1.0 mm is lower than 

the faulting predicted at 50 percent reliability and above the faulting predicted at 10 percent reliability. 

0

0.5

1

1.5

2

2.5

3

0123456789

Years

Joint Faulting (mm)

Predicted at 90% reliability

Predicted at 50% reliability

Predicted at 10% reliability

Measured faulting

Figure 163. Comparison of measured versus predicted joint faulting, Ticuman, Mexico. 

Figures 164 and 165 show the observed and predicted cracking in both, the transverse and longitudinal 

directions respectively. The amount of both, transverse and longitudinal cracking observed for this site is 

between the cracking predicted at 50 percent and 90 percent reliability. 

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0123456789

Years

Transverse Cracking (%)

Predicted at 90% Reliability

Predicted at 50% Reliability

Predicted at 10% Reliability

Measured

Figure 164. Comparison of measured versus predicted transverse cracking, Ticuman, Mexico. 
274 

As previously mentioned in section C.1.2.3, the significant amount of cracking is attributed to the lack of 

maintenance and the excessive traffic loading on this road. 

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0123456789

Years

Longitudinal Cracking (%)

Predicted at 90% Reliability

Predicted at 50% Reliability

Predicted at 10% Reliability

Measured

Figure 165. Comparison of measured versus predicted longitudinal cracking, Ticuman, Mexico. 

Figure 166 show a comparison in terms of measured and predicted serviceability index. PSI 

measurements with Mays meter have been performed in 1993 just after construction, in 1995, and in 

2001. The PSI in 2001 (after 8 years) is just above the PSI predicted at 90 percent reliability. However, 

this condition was also observed in 1995 (2 years after construction). While the predicted PSI shows a 

gradual decrease with time, the PSI measurements show a significant drop for the first few years, and then 

this condition is maintained. 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0123456789

Years

Serviceability (PSI)

Predicted at 90% reliability

Predicted at 50% reliability

Predicted at 10% reliability

Measured PSI

Figure 166. Comparison of measured versus predicted present serviceability index, Ticuman, 

Mexico. 
275 

In summary, it can be concluded that reasonable predictions were obtained in terms of long-term 

performance for both field sites. Although limited, this validation was done with extensive and quality 

data on pavement design, materials, climatic, and construction inputs. It is recommended that continued 

validation of the models be made as more sites are available with enough information on materials 

characterization and construction. 

D.2.2 Validation of Early-Age Behavior Models with Newly Constructed CRCP Sites 

D.2.2.1 Validation Results for CRCP Section in Fort Worth, TX 

This section presents the data reduction and analysis of the information collected for the CRCP 

instrumentation in Fort Worth, TX. Measured responses in terms of steel stresses, crack widths, and 

crack spacings for this site and those predicted with HIPERPAV II also are presented. 

D.2.2.1.1 Slab/Subbase Restraint

As documented in appendix C, a slab pushoff test was performed to determine the restraint conditions at 

the slab/subbase interface. Figure 167 shows a plot of the measured restraint values. The restraint curve 

observed was fitted with a nonlinear restraint power function with ultimate displacement of 3.8 mm, 

critical restraint stress of 58.6 kPa, and power coefficient of 3.5. The resulting fit is also shown in figure 

167. 

0

10

20

30

40

50

60

70

012345678

Displacement (mm)

Restraint Stress (kPa)

Nonlinear fit

Measured

Figure 167. Restraint at the slab/subbase interface. 

D.2.2.1.2 PCC Set Time

PCC set time is an important parameter, because the development of many concrete properties depends on 

it. It is anticipated that set time from laboratory testing and set time in the field will differ, since the 

aggregate matrix and environmental conditions are different. For determining PCC set time in the field, 
276 

information from three sources was considered: laboratory testing, pulse velocity testing, and analysis of 

PCC strains from an unconfined specimen. 

PCC set time tests were performed under laboratory conditions with materials collected from the Fort 

Worth, TX, CRCP site. The procedure and results from these tests are presented in section C.9. Under 

laboratory conditions, initial and final set times of 4.0 hours and 4.9 hours were obtained, respectively. 

Although attempts were made to maintain the temperature of the sample under the same environmental 

conditions than those observed in the field, slight differences were noted. Therefore, the equivalent time 

at set was obtained to determine the set time at 20 oC and determine the set time in the field corresponding 

to that equivalent time. Using the Arrhenius relationship for equivalent time, initial and final set times at 

20 oC would occur at 8.8 hours and 11.3 hours, respectively. For the temperatures observed in the field, 

initial and final set for those equivalent ages correspond to 3.5 hours and 4.4 hours real time, respectively. 

To corroborate the lab results, the pulse velocity readings were analyzed. For CRCP, pulse velocity time 

is affected by the presence of steel in the concrete. However, the rate of change of wave travel time still 

depends on stiffening of the concrete and can be related to set time. In figure 168, a significant decrease 

in wave travel can be observed between 2.5 and 5.0 hours, which indicates a significant stiffening of the 

concrete and initial set time occurrence. The estimated set times are indicated in this figure to be within 

the transition zone between the plastic and hardened state of concrete. 

0

50

100

150

200

250

300

350

1 10 100

Age (h)

PV Time (μsec)

Set time

Figure 168. Determination of set time with pulse velocity equipment. 

Analysis of the PCC strains in an unconfined concrete specimen also can be used to estimate PCC set 

time. Figure 169 shows a plot of observed PCC strain versus PCC temperature for an unconfined field 

concrete specimen instrumented with an embedded strain gage. When the strain gage is initially 

embedded in the concrete cylinder, relative strain readings do not follow a definitive trend with change in 

temperature, as the concrete is still plastic. As time progresses and the concrete stiffens, the strains tend 

to follow the temperature changes in the concrete. The transition, as observed in figure 169, occurs 

between 2.1 and 4.5 hours, corresponding to the set times from laboratory testing. After this time, the 

strains in the specimen follow a trend with temperature, fluctuating between contraction and expansion 

cycles. 
277 

-50.00

0.00

50.00

100.00

150.00

200.00

30 35 40 45 50 55

Temperature (oC)

PCC Strain (μs)

Final set time

2.1 h

Figure 169. PCC strains during PCC set time as a function of temperature changes. 

It most be noted that during construction, joint sawing of the instrumented slab was performed shortly 

after the slab was strong enough to withstand the Soff-Cut equipment. This occurred at 3.25 hours of age, 

which is before the measured final set time of 4.4 hours as determined from laboratory testing. According 

to the pulse velocity readings and the observations of joint sawing in the field, it is evident that initial set 

time for the instrumented slab occurred approximately at 3.0 hours after placement. 

D.2.2.1.3 PCC CTE

The CTE was determined with two different procedures: laboratory testing according to AASHTO TP–

60–00 and PCC strain analysis of a field unconfined concrete cylinder as a function of temperature. From 

laboratory testing, a CTE of 7.48 × 106

 m/m/oC was reported. From the analysis of strains versus 

temperature, a CTE of 6.6 × 106

 m/m/oC is determined (see figure 170). A slight difference is observed 

between testing procedures. It is believed that the difference in relative humidity conditions at which the 

CTE for each procedure was determined may have contributed to the difference in CTE. 
278 

y = 6.5703x - 307.87

R 2

 = 0.9892

-120.00

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

30 35 40 45 50 55

Temperature (oC)

PCC Strain (μs)

Figure 170. Determination of PCC CTE with the use of PCC strains on an 

unconfined concrete cylinder. 

D.2.2.1.4 Validation Procedures

Validation of the CRCP HIPERPAV II module required collection of information on all the input 

parameters. With the above information, the CRCP monitored section was analyzed with the CRCP 

HIPERPAV II module to compare the measured and predicted cracking characteristics. 

D.2.2.1.4.1 Analysis of Steel Strains 

Steel strains were evaluated at different distances from the crack, as observed in figure 171. 
279 

-1.50E-04

5.00E-05

2.50E-04

4.50E-04

6.50E-04

8.50E-04

1.05E-03

1.25E-03

Age (h)

Steel Measured Strain

0

10

20

30

40

50

60

70

80

90

100

PCC Temperature (oC)

Strain at the crack 

Strain 127 mm from crack

Strain 254 mm from crack

Strain at 508 mm from crack

Strain at midslab

Temperature

Figure 171. Steel strains at various distances from the crack location. 

Note from this figure that steel strain increases at lower temperatures and also as a function of time. This 

last trend possibly is due to the increase in PCC drying shrinkage. Figure 172 shows a plot of steel strains 

along the slab length for the strain peaks observed at 21.0, 44.8, and 68.5 hours. The strain plotted is the 

average strain of the two strain gages installed at each distance. 

Jones-Stephenson

I-30/I35 Interchange, Fort Worth, TX

Slab Thickness = 231 mm

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Distance from Crack (m)

Steel Strain 

Strain at 21.0 h

Strain at 44.8 h

Strain at 68.5 h

Bond Development 

Length

Figure 172. Steel strain along the slab length at different ages. 
280 

From figure 172, the bond development length can be identified; this is the slab segment from the crack 

location for which the steel strain is variable. In this case, a bond development length of approximately 

279 mm is observed for these ages. 

D.2.2.1.4.2 Analysis of Concrete Strains 

Concrete strains were analyzed to determine their influence on the stress development in the steel. Figure 

173 shows the strains observed in the concrete at different distances from the crack. The time of crack 

formation can be clearly identified by the sharp increase in strains on the gages at 127 mm from the crack. 

The crack is observed to occur close to 12 hours after construction, which also coincides with the 

significant development in steel strain at the crack seen in figure 171. 

-60

-40

-20

0

20

40

60

0 10 20 30 40 50 60 70 80

Age (hrs)

PCC Strains (microstrains)

0.0

10.0

20.0

30.0

40.0

50.0

60.0

127 mm from crack (Bar A)

PCC Temperature (oC)

127 mm from crack (Bar B)

254 mm from crack

508 mm from crack

1219 mm from crack

PCC Temperature

Time of crack formation

Figure 173. Concrete strains at middepth along slab length. 

Comparing the individual ages of 21.0, 44.8, and 68.5 hours with steel strains, the average concrete 

strains for those ages are 4.4 × 10-6 m/m, −26.7 × 10-6 m/m, and −40.6 × 10-6 m/m. A negative trend in 

PCC strain is observed, which can be attributed to the decreasing temperature in the concrete and to 

drying shrinkage. The drying shrinkage observed on an unrestrained PCC cylinder in the field after 

subtracting temperature effects is presented in figure 174. 
281 

-60

-40

-20

0

20

40

60

0 10 20 30 40 50 60 70 80

Age (h)

Shrinkage Strain (m/mx10-6) Figure 174. Drying shrinkage observed in the field on an unrestrained PCC cylinder. 

Figure 175 shows the steel strains in the concrete and in the steel at 68.5 hours after construction. The 

strains in the concrete appear almost constant along the slab at approximately 40 microstrains. The 

strains in the steel also appear within the same order of magnitude along most of the slab, except near the 

crack, where they increase significantly. 

-200

0

200

400

600

800

1000

1200

1400

0 0.5 1 1.5 2 2.5 3

Distance from crack (m)

Strains (microstrains)

Concrete strains

Steel strains

Linear (Concrete strains) (concrete strains)

Figure 175. Strains in concrete and steel at 68.5 hours after construction. 

Assuming a strain level in the steel similar to the one observed in the concrete at midslab and integrating 

the strains along the slab length, the displacement of concrete and steel is plotted in figure 176. 
282 

-0.120

-0.100

-0.080

-0.060

-0.040

-0.020

0.000

0.020

0.040

0 0.5 1 1.5 2 2.5 3

Distance from midslab (m)

Displacement (mm)

Movement concrete

Movement steel

Figure 176. Displacements in steel and concrete along slab length at 68.5 hours. 

D.2.2.1.4.3 Evaluation of Stress and Bond Development Length 

The bond development length predicted with HIPERPAV II for this site for the first 3 days of age varied 

from 0.56 to 0.79 m. The bond development length predicted is significantly higher than the measured 

one of approximately 279 mm. 

From the strains measured, the steel stress is computed and is shown in figure 177 for the age of 68.5 

hours. The steel stress at the crack is 246.8 MPa. The steel stress computed by HIPERAV for that age is 

392.3 MPa at the crack location. The predicted stress is also shown in this figure. It is believed that the 

difference in predicted and measured bond development length and steel stress is related to the limitations 

in the bond-slip relationships assumed in the CRCP–8 model. These limitations have been previously 

identified by Palmer et al.(120)
283 

-100

-50

0

50

100

150

200

250

300

350

400

450

0 0.2 0.4 0.6 0.8 1

Distance from Crack (m)

Stress (MPa)

Predicted steel stress

Stress from measured strains

Figure 177. Steel stress along the slab at 68.5 hours. 

D.2.2.1.4.4 Analysis of Crack Widths 

Crack width data was evaluated as a function of pavement age and also as a function of pavement depth. 

Table 87 shows the crack widths observed during the first 3 days after construction for the top, middle, 

and bottom of the slab. 

Table 87. Comparison of average crack width predicted and measured values. 

Age Measured Top Measured Middle Measured Bottom Predicted Middle 

Day 1 0.005 0.003 0.002 0.027

Day 2 0.009 0.004 – 0.042

Day 3 0.010 0.005 – 0.050

A large discrepancy in measured and predicted crack width is observed. The predicted crack width is 

overpredicted by a factor of 5 compared to the average crack width at the top, and by a factor of 10 

compared to the crack width measured at middepth. 

Crack width tends to increase as a function of time. In addition, larger crack widths are observed at the 

top of the slab compared to middepth and bottom; this is attributed to increased drying shrinkage at the 

slab surface. Crack width measurements were obtained at the slab edge. The crack width at the steel 

location was not measured. It is believed that, due to the steel restraint, the crack width near the steel is 

smaller than those reported here and therefore increasing the overprediction. 

The limitations in crack width prediction have been discussed in section D.1.2.10. The differences in 

steel stress and bond development length found in this analysis also are believed to contribute to the 

overprediction of crack widths. 
284 

D.2.2.1.4.5 Crack Spacing Validation Results 

Table 88 shows a comparison of measured versus predicted crack spacings for the first 3 days after 

construction. Although the measured crack spacings show a slight decreasing trend, the predicted crack 

spacing is constant for the early ages and is reduced to an average crack spacing of 1.55 m after 1 year. 

However, the average crack spacing predicted of 3.32 m matches very closely the measured average crack 

spacing of 3.59 m at 3 days of age. The predicted crack spacing at 1 year for this site is 1.55 m. 

Table 88. Comparison of predicted and measured average crack spacings. 

Age Measured (m) Predicted (m) 

Day 1 4.36 3.32 

Day 2 3.99 3.32 

Day 3 3.60 3.32 

After construction traffic – 2.71 

1 year – 1.55 

The crack spacing distributions are presented in figure 178. Although a reasonably good fit for the crack 

spacings observed after 3 days is achieved, it is believed that the bond slip relationships in the CRCP–8 

program must be further investigated to predict steel stresses and crack widths accurately. 

.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

0 2 4 6 8 10 12 14

Crack Spacing (m)

Cumulative Frequency

Measured

Predicted

Figure 178. Measured versus predicted crack spacing at 3 days of age, Fort Worth, TX 
285 

D.2.2.2 Validation Results for CRCP Section on I–29, South Dakota 

This section presents the data reduction and analysis of the information collected for the CRCP 

instrumentation in South Dakota. Measured responses in terms of steel stresses, crack widths, and crack 

spacings for this site and those predicted with HIPERPAV II also are presented. 

D.2.2.2.1 Slab/Subbase Restraint

Although no pushoff test was performed for this site, the subbase restraint conditions were observed to be 

typical of an unbonded aggregate base. Default values for this subbase type were selected. 

D.2.2.2.2 PCC Set Time

For determination of PCC set time in the field, information from two sources was considered: laboratory 

testing and analysis of PCC strains from an unconfined specimen. 

PCC set time tests were performed under laboratory conditions with materials collected from the South 

Dakota CRCP site. The procedure and results from these tests are presented in appendix C. Under 

laboratory conditions, initial and final set times of 5.1 hours and 6.6 hours were obtained, respectively. 

However, given the inability to relate laboratory set time to the time set occurred in the field for the South 

Dakota site, set time was identified with the analysis of PCC strains from an unconfined specimen. With 

this procedure, a set time of approximately 6 hours was measured. 

The equivalent time at set was obtained to determine the set time at 20 oC and determine the set time in 

the field corresponding to that equivalent time. Using the Arrhenius relationship for equivalent time, 

initial and final set times at 20 oC would occur at 4.9 hours and 6.4 hours, respectively. For the 

temperatures observed in the field, set times for those equivalent ages correspond to approximately 4.0 

hours and 5.0 hours in real time, respectively. 

Analysis of the PCC strains in an unconfined concrete specimen used can also be to estimate PCC set 

time. Figure 179 shows a plot of observed PCC strain versus PCC temperature for an unconfined field 

concrete specimen instrumented with an embedded strain gage. When the strain gage is initially 

embedded in the concrete cylinder, relative strain readings do not follow a definitive trend with change in 

temperature, as the concrete is still plastic. As time progresses and the concrete stiffens, the strains tend 

to follow the temperature changes in the concrete. The transition, as observed in figure 179, occurs 

between 2.8 hours and 6.5 hours. The initial and final set times from laboratory tests fall within this 

range. After this time, the strains in the specimen follow a trend with temperature, fluctuating between 

contraction and expansion cycles. 
286 

-300

-250

-200

-150

-100

-50

0

50

10 15 20 25 30 35

Temperaure (oC)

Strains (microstrains)

2.8 h

6.5 h

Transition

zone

Figure 179. PCC strains during PCC set time as a function of temperature changes. 

According to the above analysis, the initial and final set times of 4.0 hours and 5.0 hours, respectively, 

were used for analysis. 

D.2.2.2.3 PCC CTE

The CTE was determined with two different procedures: laboratory testing according to AASHTO TP–

60–00 and PCC strain analysis of a field unconfined concrete cylinder as a function of temperature. From 

laboratory testing, a CTE of 10.9 × 106

 m/m/oC was reported. From the analysis of strains versus 

temperature, a CTE of 11.6 × 106

 m/m/oC is determined (see figure 180). A slight difference is observed 

between testing procedures. It is believed that the difference in relative humidity conditions at which the 

CTE for each procedure was determined may have contributed to the difference observed. 
287 

y = 11.61x - 347.01

R 2 = 0.93

-200

-150

-100

-50

0

50

0 5 10 15 20 25 30 35

Temperature (oC)

Strains (microstrains)

Figure 180. Determination of PCC CTE with the use of PCC strains on an 

unconfined concrete cylinder. 

D.2.2.2.4 Validation Procedures

Validation of the CRCP HIPERPAV II module required collecting information on all the input 

parameters. With the above information, the CRCP monitored section was analyzed with the CRCP 

HIPERPAV II module to compare the measured and predicted cracking characteristics. 

D.2.2.2.4.1 Analysis of Steel Strains 

Steel strains were evaluated at different distances from the crack as observed in figure 181. Gages were 

installed on two different bars and are identified as either “A” or “B” in the figure. The crack occurred 

108 mm from the expected location, thus shifting the location of the gages by that amount. In addition, a 

second crack was noticed later 356 mm from midslab, leaving the gages at that location at that distance 

from the new crack. Crack occurrences can be identified clearly by the sharp change in strain at 

approximately 19, 34, and 40 hours from placement. 

Similar to the Fort Worth, TX, site, the strain gages closer to the crack recorded higher strains than those 

far from the crack. However, the gages at 356 mm from the second crack did not show a significant 

increase in strain after crack occurrence, as would be expected. However, it most be noted that, for the 

Fort Worth, TX site, the bond development length was smaller than 356 mm. Therefore, it is possible 

that the bond development length for the second crack could have been less than 356 mm. 
288 

-2.50E-04

-5.00E-05

1.50E-04

3.50E-04

5.50E-04

7.50E-04

9.50E-04

1.15E-03

Age (h)

Measured Steel Strains

0

5

10

15

20

25

30

35

Temperature (oC)

108 mm from crack (A)

108 mm from crack (B)

235 mm from crack (B)

362 mm from crack (B)

616 mm from crack (A)

356 mm from 2nd crack (A)

356 mm from 2nd crack (B)

Temperature

Crack 

occurrences 

Figure 181. Steel strains at various distances from the crack location. 

Figure 182 shows a plot of steel strains along the slab length for the strain peaks observed at 20.3, 43.2, 

and 67.2 hours. The strain plotted is the average strain of the two strain gages installed at each distance. 

-200

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Distance from Crack (m)

Steel Strain (microstrains)

Steel strain at 20.3 h

Steel strain at 43.2 h

Steel strain at 67.2 h

Figure 182. Steel strain along the slab length at different ages. 

From figure 182, the bond development length can be identified; this is the slab segment from the crack 

location for which the steel strain is variable. In this case, a bond development length of approximately 

0.5 to 0.6 m is observed for these ages. Extrapolating the steel strains to estimate the strain at the crack 

yields 550 microstrains at 20.3 hours and 1200 to 1500 microstrains for the other two ages. 
289 

D.2.2.2.4.2 Analysis of Concrete Strains 

Concrete strains were analyzed to determine their influence on the stress development in the steel. Figure 

183 shows the strains observed in the concrete at different distances from the crack. The time of crack 

formation can be identified clearly by the sharp increase in strains on the gages at 235 mm from the crack. 

The cracks are observed to occur close to 19, 34, and 40 hours after construction, which also coincide 

with the significant development in steel strain seen in figure 181. 

-75

-50

-25

0

25

50

75

Age (h)

PCC Strains (microstrains)

0

5

10

15

20

25

30

35

Temperature (oC)

235 mm from crack

375 mm from crack

616 mm from crack

Temperature

Crack Occurrences

Figure 183. Concrete strains at middepth along slab length. 

In the above figure, the concrete strains at 20.3, 43.2, and 67.2 hours are compared with the steel strains; 

the average concrete strains for those ages are 0.2 × 10-6, −34.7 × 10-6, and −44.3 × 10-6. Similar to the 

Fort Worth, TX, site, a negative trend in PCC strain is observed. The drying shrinkage observed on an 

unrestrained PCC cylinder in the field after subtracting temperature effects is presented in figure 184. 
290 

-150

-125

-100

-75

-50

-25

0

25

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0

Age (h)

Drying Shrinkage Strains (m/m/oC)

Figure 184. Drying shrinkage observed in the field on an unrestrained PCC cylinder. 

Figure 185 shows the steel strains in the concrete and in the steel at 67.2 hours after construction. The 

strains in the concrete appear almost constant along the slab at approximately 40 microstrains. The 

strains in the steel also appear within the same order of magnitude along most of the slab, except near the 

crack, where they increase significantly. 

-200

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.5 1 1.5 2

Distance from midslab (m)

Microstrains

PCC strains at 43.2 h

Steel strains at 43.2 h

Figure 185. Strains in concrete and steel at 67.2 hours after construction. 
291 

D.2.2.2.4.3 Evaluation of Stress and Bond Development Length 

A comparison of measured and predicted bond development lengths for this site is presented in figure 

186. The bond development length predicted with HIPERPAV II for this site for the first 3 days of age 

varied from 0.48 to 0.66 m. A rather good prediction is observed on the bond development length for this 

site. 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72

Age (h)

Bond Development Length (m)

Measured

Predicted

Figure 186. Comparison of measured and predicted bond development length. 

From the strains measured, the steel stress is computed and is shown in figure 187 for the age of 67.2 

hours. 

(50)

-

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Distance from Crack (m)

Steel Stress (MPa)

Measured

Predicted

Figure 187. Steel stress along the slab at 67.2 hours. 
292 

In general, a rather good prediction of stresses at the steel were observed for this site. 

D.2.2.2.4.4 Analysis of Crack Widths 

Crack width data was evaluated as a function of pavement age and also as a function of pavement depth. 

Table 89 shows the crack widths observed during the first 3 days after construction for the top, middle, 

and bottom of the slab. 

Table 89. Comparison of average crack width predicted and measured values. 

Age Measured Top Measured Middle Predicted Middle 

Day 1 – 0.002 0.018 

Day 2 – 0.008 0.025 

Day 3 0.010 0.008 0.029 

A large discrepancy in measured and predicted crack width is observed. The predicted crack width is 

overpredicted by a factor of three compared to the average crack width measured at middepth. 

Similar trends to the Fort Worth, TX site in terms of increasing crack widths with time also are observed 

for this site. Crack width measurements were obtained at the slab edge. The crack width at the steel 

location was not measured. It is believed that due to the steel restraint, the crack width near the steel is 

smaller than those reported here, therefore increasing the overprediction. 

D.2.2.2.4.5 Crack Spacing Validation Results 

Table 90 shows a comparison of measured versus predicted crack spacings for the first 3 days after 

construction. Although the measured crack spacings show a slight decreasing trend, the predicted crack 

spacing is constant for the early ages and is reduced to an average crack spacing of 1.25 m after 1 year. 

However, the average crack spacing predicted of 3.47 m matches very closely the measured average crack 

spacing of 3.08 m at 3 days of age. The predicted crack spacing at 1 year for this site is 1.25 m. 

Table 90. Comparison of predicted and measured average crack spacings. 

Age Measured (m) Predicted (m)

Day 1 5.33 3.47

Day 2 3.32 3.47

Day 3 3.08 3.47

1 year – 1.25

The crack spacing distributions are presented in figure 188. Although a reasonably good fit for the crack 

spacings observed after 3 days is achieved, the predictions for earlier ages do not follow the 

measurements in the field. Inaccuracy to match earlier ages also was reported on the validation for the 

Fort Worth, TX, site. 
293 

0

10

20

30

40

50

60

70

80

90

100

012345678

Crack Spacing (m)

Cumulative Frequency (%)

Predicted

Measured

Figure 188. Measured versus predicted crack spacing at 3 days of age, Sioux Falls, SD. 

D.3 VALIDATION OF GENERAL EARLY-AGE BEHAVIOR MODELS 

Improvements to the concrete pavement temperature prediction, drying shrinkage, and creep-relaxation 

models were investigated in this study. Results of the validation efforts for this models are presented 

below. 

D.3.1 Finite-Difference Temperature Prediction Model 

Over the course of its development, HIPERPAV has employed two different temperature prediction 

models. Originally, the temperature prediction model was a transient two-dimensional FEM. However, 

this procedure had proven to require excessive solution times. The model has since been replaced by a 

one-dimensional finite-difference approach, which allows quicker execution without a compromise in 

accuracy. However, the accuracy of the finite-difference model needed to be verified by comparison with 

field data. Verification of the temperature predictions with the improved model is presented in appendix 

E. 

D.3.2 Drying Shrinkage Prediction Model 

D.3.2.1 Drying Shrinkage Calibration for JPCP Early-Age Predictions 

Using the field data collected from the five early-age HIPERPAV I field sites, the calibration factor (Deff) 

for the Baźant-Panula shrinkage model could be determined.(121) The vibrating wire strain gages placed at 

midslab 25 mm from the pavement surface and 152 mm from the edge, in the transverse direction, were 

used for the calibration. The restraint strains induced by the subbase would be small at this location, 

allowing the drying shrinkage strains to be modeled. Calibration results are presented below. 
294 

All of the slabs in field were cured with white curing compound (α2 = 1.1), and the cement types varied 

between Type I and Type II (α1 = 1 and 0.85). The coarse aggregate used at the sites had a relatively low 

CTE. In Minnesota, limestone and gravel were mixed. In Nebraska and Texas, limestone was used. In 

North Carolina, slate was used. In Arizona, a gravel basalt was used. The Baźant-Panula shrinkage 

model was developed for similar aggregate types to those found in the HIPERPAV I sites, so relatively 

good fits resulted. Fly ash content was not included in the mix components input to the model, since it 

does not greatly influence concrete shrinkage.(37)

The Deff values determined for each site are listed in table 91. Deff for Nebraska is 0.6; this is the highest 

value. The Nebraska mix was not typical; more sand/fine aggregate was used than coarse aggregate. 

Averaging all of the sites yields an average Deff of 0.45 with a standard deviation of 0.09. A Deff of 0.50 

has also been reported by Persson, and it is used to account for specimen shape in HIPERPAV II drying 

shrinkage calculations.(36)

Table 91. Calibration of Deff for the HIPERPAV I field sites. 

Site Location Deff Without Fly Ash 

Arizona 0.35 

Minnesota 0.40 

Nebraska 0.60 

North Carolina 0.45 

Texas 0.46 

The fit of the Baźant-Panula shrinkage model to these five field sites is shown in the following plots 

(figures 189-193). 

-100

-80

-60

-40

-20

0

20

0 10 20 30 40 50 60 70

Time (h)

Strain (με)

Data

Bazant-Panula

North Carolina Slab 4 

Figure 189. Drying shrinkage results for North Carolina site. 
295 

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

0 20 40 60 80 100 120

Time (h)

Strain (με)

Data

Bazant-Panula

Texas Slab 1

Figure 190. Drying shrinkage results for Texas site. 

-120

-100

-80

-60

-40

-20

0

20

0 10 20 30 40 50 60 70 80

Time (h)

Strain (με)

Data

Bazant-Panula

Arizona Slab 5

Figure 191. Drying shrinkage results for Arizona site. 
296 

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 10 20 30 40 50 60 70

Time (h)

Strain (με)

Data

Bazant-Panula

Nebraska Slab 1

Figure 192. Drying shrinkage results for Nebraska site. 

-50

-40

-30

-20

-10

0

10

0.00 20.00 40.00 60.00 80.00 100.00 120.00

Time (h)

Strains (με)

Data

Bazant-Panula Minnesota Slab 1

Figure 193. Drying shrinkage results for Minnesota site. 

D.3.2.2 Drying Shrinkage Calibration for CRCP 28-Day Predictions 

To calibrate the size factor Deff for CRCP, 28-day drying shrinkage predictions from the Baźant-Panula 

model were matched to the experimentally measured drying shrinkage values taken in concrete placed on 
297 

SH–6 in winter and summer.(106) Limestone was the coarse aggregate. At 28 days, the drying shrinkage 

was 171 με in the summer and 165 με in the winter. These values were matched using an Deff of 0.2. A 

comparison of drying shrinkage predictions at different ages are shown in figures 194 and 195 as a 

function of Deff. The drying shrinkage measured for the Houston, TX, sections is presented in these 

figures with its corresponding calibration factor. 

0

50

100

150

200

250

300

350

400

0 0.1 0.2 0.3 0.4 0.5 0.6

D eff

Drying Shrinkage (με)

Data summer

T = 23° C

3 days

28 days

1 year

Figure 194. Calibration of drying shrinkage factor for Houston, TX, sections 

constructed in summer. 

0

50

100

150

200

250

300

0 0.1 0.2 0.3 0.4 0.5 0.6

D eff

Drying Shrinkage (με)

Data winter

3 days

28 days

1 year

T = 23° C

Figure 195. Calibration of drying shrinkage factor for Houston, TX, sections constructed in winter. 
298 

D.3.3 Relaxation-Creep Model 

Attempts to validate the creep model based on the extended Triple Power Law presented in appendix B 

were made. However, preliminary sensitivity analyses showed that, in some instances, tensile stresses 

were being overpredicted significantly as compared to results from the previous validation efforts of the 

current prediction models in HIPERPAV II. Possible reasons for inaccuracy are: 

• In this model, it is assumed that creep in compression is equivalent to creep in tension. Due 

to the cyclic stress state in the pavement between tension and compression, if this assumption 

does not hold true, it is possible that compressive stresses may be underpredicted while 

tensile stresses are overpredicted, or vice versa. 

• In implementing creep compliance formulation, there are two possible approaches as outlined 

in appendix B: 1) with numerical integration; and 2) with the use of a Maxwell chain model 

for conversion of creep compliance into relaxation values. In this effort, both methods were 

explored. However, the required user intervention in the second method made it 

inappropriate for this effort. The first method was investigated further; however, the large 

matrix array required to store the stress history limited the minimum time step that could be 

implemented to 1 hour. It is believed that the large time step possibly contributed to the 

cause of the observed overpredictions of tensile stresses. 

Further work is required to validate this method properly. It is believed that, after calibrated and 

validated, it will prove helpful in properly determining creep and relaxation effects for stress prediction, 

built-in curling prediction, and possibly determining the curled slab shape. 
299

APPENDIX E FINITE-DIFFERENCE TEMPERATURE MODEL VALIDATION 

The HIPERPAV II temperature model predicts the temperature development of concrete at early ages. 

The temperature development in the concrete structure is determined by the balance between heat 

generation in the concrete and heat exchange with the environment. This model includes the heat of 

hydration of the cementitious materials and the heat transfer mechanisms of thermal conduction, 

convection (including evaporative cooling), solar radiation, and irradiation. In section B.1.2, all the 

models and material properties necessary to predict the temperature distribution in the pavement structure 

were presented. 

Over the course of its development, HIPERPAV has employed two different temperature prediction 

models. Originally, the temperature prediction model was a transient two-dimensional FEM. However, 

this procedure required excessive solution times. The model has since been replaced by a onedimensional finite-difference approach, which allows quicker execution without a compromise in 

accuracy. However, the accuracy of the finite-difference model needs to be verified by comparison with 

field data. 

The model was calibrated by comparing the predicted versus measured field temperatures. To validate the 

temperature model, the concrete temperatures measured in the field were compared to the concrete 

temperatures predicted with the temperature model. Early-age temperature data was collected from PCC 

paving applications located across the United States. Eighteen slabs were instrumented; nine of these 

were selected for calibration and nine for validation of the model. Table 92 provides a brief summary of 

the different sites, and it also indicates which slabs will be used for the model calibration and validation. 

Table 92. Different construction sites and their use for calibration and validation. 

Pavement Construction Site Description Calibration Validation 

Eden Prairie, MN, U.S. Highway 212 October 1998, 305-mm JPC Slab 1 and 4 Slab 2 and 3 

Tucson, AZ, I–10 Frontage December 1998, 254-mm JCP Slab 1, 3, and 6 Slab 4 and 5 

Lufkin, TX, U.S. Highway 69 April 1999, 305-mm JCP Slab 2 and 3 Slab 1 and 4 

Surry County, NC, I–77 May 1999, 279-mm JPC Slab 2 and 3 Slab 1 and 4 

Fort Worth, TX, I–30/I–35 July 2001, 203-mm CRPC – Slab 1 

E.1 FIELD INSTRUMENTATION SITES 

Two separate mechanisms are considered to predict changes in pavement temperature: environmental 

effects and the PCC heat of hydration. Environmental conditions, including air temperature, solar 

radiation, windspeed, and relative humidity, were monitored by using a portable weather station. The 

heat of hydration over time of the cementitious materials was determined by adiabatic calorimeter testing. 

Concrete temperatures during the first 72 hours after concrete placement were measured with 

thermocouples installed at various depths: at 25 mm from the top, middepth, and 25 mm from the bottom 

of each slab. At some sites, concrete temperatures were recorded by free vibrating strain gauges located 

at the three depths described above. 

Many parameters influence the development of concrete temperatures. During the field instrumentation, 

these parameters were measured or recorded in the field or obtained through laboratory tests, and these 

parameters are summarized in table 93. In addition to this information, the results of the cement heat of 

hydration tests and the properties used to model the boundary conditions and heat transfer for all the 

concrete mixes is listed in table 94. 
300

Based on the data collected for these paving projects, the ranges of values covered during this calibration 

and validation effort are as follows: 

• Pavement thickness: 200 to 305 mm. 

• Subbase type: unbound granular, AC, and crushed concrete base. 

• Cement type: I, IP, II, and I/II. 

• Admixtures: 7 percent to 21 percent cement replacement with Class C fly ash and, 18 percent 

to 23 percent cement replacement with Class F fly ash. 

• W/cm: 0.36 to 0.44 and w/c: 0.45 to 0.56. 

• The air temperature during the instrumentation varied as follows: Minnesota 0.5 to 22 oC, 

Arizona -1.1 to 23 oC, Texas (Lufkin) 8 to 30 oC, North Carolina 8 to 28 oC, and Texas (Fort 

Worth) 25 to 37 oC. In general, the paving conditions for Minnesota and Arizona were colder 

than for the rest of the States. 

• Curing method: White liquid curing compound was used at most of the sites. However, due 

to cold weather conditions in Arizona, polyethylene sheets were used to retain concrete 

temperatures during the first and second days after placement. 

E.2 MODEL CALIBRATION 

The temperature model was calibrated by comparing the predicted versus measured concrete temperatures 

during the first 72 hours after placement. It was determined that some parameters had to be adjusted to 

calibrate the finite-difference model. After all the concrete temperatures from all the sites were evaluated 

against the predicted values, it is recommended that the following modifications be made to the 

temperature model: 

• Solar absorptivity constant: The solar absorptivity of PCC is a function of the surface color, 

with typical values ranging from 0.5 to 0.6. An ideal white body would have a value of 0.0, 

and an ideal black body would have a value of 1.0. A solar absorptivity constant of 0.50 was 

found most appropriate for concrete pavements cured with white curing compound. 

• Heat transfer by convection/conduction: The model outlined in section B.1.2.3 provides an 

accurate means to model the heat loss on the pavement surface. During the construction of 

the Arizona pavement, plastic sheets were used. Using the thickness of the plastic sheet and 

its thermal conductivity underestimated the amount of heat being retained by the pavement. 

However, when sheets are used, they are not in total contact with the slab, and the air void 

between the concrete and sheets act as additional insulation. An average air void thickness of 

5 mm in addition to the plastic sheet provided an accurate account of the surface insulation 

for all the slabs where sheets were used. It is recommended that an additional air void 

thickness of 5 mm be used for all future cases where plastic sheets are used. 

• Heat transfer due to evaporative cooling: When evaporation of the water from a surface 

occurs, the energy associated with the phase change is the latent heat of vaporization, which 

causes evaporative cooling. A preliminary model to account for heat transfer due to 

evaporative cooling was developed.(122) The use of the model depends on the interaction 

between curing, bleeding, and environmental conditions. These effects were noticeable only 

for some of the slabs in North Carolina. This is an area where further research is required to 

model the interaction between moisture movement, bleeding, concrete materials, curing 

compound effectiveness, and evaporation. 
301

• Solar radiation: The amount of heat gain due to solar radiation varies with longitude, 

latitude, altitude, time of day, day of year, and the prevailing atmospheric conditions. Next to 

the heat of hydration, the flux due to solar radiation is the most important heat source to the 

pavement system and should be modeled. In HIPERPAV II, the environmental data for any 

location in the United States is generated based on averaged 30-year historical data obtained 

from a weighted average of nearby weather stations. It is recommended that the hourly 

values from this database be used for the temperature prediction. The maximum solar flux 

may be determined as the 99th percentile of the 30-year average hourly global horizontal 

radiation. 

• Cloud cover: During day times, cloud cover affects the intensity of the direct and diffuse 

solar radiation that reaches the pavement surface. During night times, the cloud cover also 

determines the amount of reradiation from surfaces, and affects the magnitude of the 

irradiation. To achieve accurate temperature predictions, the amount of cloud cover should 

be defined as accurately as possible by the user. 

• AE: The AE determines the temperature sensitivity of the concrete’s hydration process 

relative to that at the reference temperature. The AE model described in section B.1.1 is 

recommended for use. 

• Ultimate degree of hydration: Complete hydration of all the cementitious materials is 

seldom attained in actual concrete structures. This depends on the amount of space available 

for the hydration products, and also on the need for sufficient free mix water, which ensures 

continued hydration.(123,124) The model described in section B.1.1 is recommended to 

determine the ultimate degree of hydration for saturated concrete. 
Table 93. Summary of variables collected during instrumentation of some HIPERPAV field sites.(121) 

Variable Description Arizona** Minnesota** North Carolina** Lufkin, Texas** Fort Worth, Texas*** 

Transverse joint spacing (m) 4.57 4.57 Variable from 4.88 to 6.71 m 4.57 None Pavement thickness (mm) 254 305 279 305 200 

General Subbase type HMA base Granular HMA leveling course HMA base HMA base 

Cement type II I/II I/II I/II IP Aggregate type River gravel 19 mm - Natural gravel 19 mm + Crushed limestone Phyllite Crushed limestone Crushed limestone Cement content (kg/m3) 285 267 250 247 248 Cementitious materials (kg/m3) Fly ash Class F Fly ash Class C Fly ash Class F Fly ash Class F Fly ash Class C Cementitious materials content (kg/m3) 61 71 75 67 61 Cementitious materials replacement 18% 21% 23% 21% 20% Water content (kg/m3) 128 122 141 113 136 Coarse aggregate content (kg/m3) 1102 (19 mm +) 544 (19 mm -) 559 1149 1143 1,217 Fine aggregate content (kg/m3) 802 776 836 588 670 Chemical admixtures: Water reducer-air entrainer Water reducer-air entrainer Water reducer-air entrainer Water reducer-air entrainer Water reducer-air entrainer Water reducer (ml/m3) 889.6 1,315 1,060 595.7 1083 Air entrainer (ml/m3) 0-1482 (as needed) 213 106 139.2 108.3 w/c 0.45 0.46 0.56 0.46 0.55 

Concrete Mixture Proportions 

w/cm 0.37 0.36 0.43 0.36 0.44 Slab number 1 3 4 5 6 1 2 3 4 1 2 3 4 1 2 3 4 1 Curing method Curing compound and plastic sheet Curing compound Curing compound Curing compound Curing compound Construction date 12/3 8 Dec 1998 11 Dec 1998 7 Oct 1998 14 Oct 1998 19 May 1999 22 May 1999 31 March 6 April 1999 7 July 2001Time of day of construction (hh:mm) 9:20 10:25 15:00 9:50 13:35 9:05 13:08 9:05 10:25 12:00 14:05 10:20 12:30 8:35 9:30 8:10 11:30 10:40 Saw cutting time after placement (hh:mm) 16:40 23:10 21:30 26:25 26:35 20:00 17:30 18:00 17:30 7:00 6:55 8:40 9:30 14:15 12:50 12:30 9:50 - Initial concrete mix temperature (oC) 17.2 13.3 17.2 12.8 16.7 13.9 15.0 10.0 11.1 27.8 28.9 27.2 27.2 20.6 20.0 22.2 26.7 32.2Initial subbase temperature (oC) 15.6 11.7 15.6 8.9 11.7 15.5 14.4 11.1 11.7 30.6 28.9 25.6 26.1 18.3 18.3 18.3 22.8 36.1 Measured pavement thickness (mm) 248 260 254 267 273 308 305 308 302 276 274 284 281 305 305 305 305 205 

Construction 

Measured slab length (m) 4.6 4.7 4.6 4.6 4.6 4.5 4.5 4.5 4.6 6.4 6.8 5.2 5.2 4.5 4.5 4.3 4.5 - Air temperature range (oC) -1.1-23 0.5-22 8-28 8-30 25-37 Air temperature at placement (oC) 7.8 5.6 12.8 7.8 13.9 8.9 11.1 3.9 5.6 16.1 22.2 12.2 22.2 13.9 15.6 9.4 8.3 30.5 Relative humidity (%) 15-99 29-100 28-99 30-100 30-67 Windspeed (kph) 0-52.29 0-25.7 0-24 0-27 0-9 

Environment 

Overcast conditions at placement * S S S S S S PC PC PC S S C OC OC OC S S Sunny and hot 

Notes: * S – Sunny, PC – Partly Cloudy, C – Cloudy, OC – Overcast ** - Collected under HIPERPAV I validation *** - Collected under HIPERPAV II validation 

302
303 

Table 94. Summary of hydration parameters for all the field sites. 

Parameter a

Arizona 

Minnesota 

North 

Carolina 

Fort Worth, 

TX 

Lufkin, TX 

Hydration parameters, λ1 1.0 1.0 1.0 1.0 1.0 

Hydration parameters, t1 (h) 11.21 9.32 16.93 16.47 9.57 

Hydration parameters, k1 2.029 1.694 1.188 0.783 1.909

Total heat of hydration, Hu (J/g) 388 438 390 415 416 

AE, E (J/mol) 27,910 40,004 35,350 39,260 37,995 

Ultimate degree of hydration 0.75 0.70 1.00 1.00 0.65 

a

 Hydration parameters were determined by adiabatic calorimeter tests 

The measured temperatures and the predicted temperatures for all the calibration sites are presented in 

figures 196 to 231 in section E.5. The goodness of the temperature prediction was calculated in terms of 

the coefficient of determination (r2 value). The calculation of the r2 value was also performed to the 45o 

line (measured versus predicted temperature). Two r2 values were computed for each instrumented 

section: 

• An average r2 value obtained after comparing the temperatures at 25 mm from the top, 

middepth, and 25 mm from the bottom of each slab. 

• An r2 value obtained after comparing the measured versus predicted temperature differential. 

The r2 values obtained for the calibration sites are summarized in table 95. The average r2 values ranged 

between 0.750 and 0.866. The r2 values obtained for the temperature gradient ranged between 0.539 and 

0.909. The low r2 values were obtained for the JCP section instrumented in Texas. From the r2 values 

obtained during this analysis, it may be concluded that the modified finite-difference model incorporated 

in HIPERPAV II is calibrated sufficiently. The model should be validated to determine the accuracy of 

the temperature prediction for PCC paving applications. 
304 

Table 95. Summary of r2 values obtained during the calibration of the temperature model. 

Instrumented Site Coefficient of Determination (r2) 

State Slab Number 

Figure Numbers 

r

2

 for Temperature 

r

2

 for 

Temperature 

Gradient 

1 196–199 0.854 0.890 

Minnesota 

4 200–203 0.801 0.820 

1 204–207 0.852 0.794 

Arizona 3 208–211 0.750 0.844 

6 212–215 0.853 0.821 

2 216–219 0.866 0.539 

Lufkin, TX 

3 220–223 0.844 0.654 

2 224–227 0.858 0.909 

North Carolina 

3 228–231 0.825 0.840 

E.3 MODEL VALIDATION 

The measured versus predicted temperatures were compared as outlined in the previous section. The 

measured temperatures and the predicted temperatures for all the validation sites are presented in figures 

232 to 267 in section E.6. The goodness of the temperature prediction was calculated in terms of the two 

r2 values documented in the calibration section. The r2 values obtained for the validation sites are 

summarized in table 96. The average r2 values ranged between 0.803 and 0.903. The r2 values obtained 

for the temperature gradient ranged between 0.470 and 0.924. As was the case for the model calibration, 

the lowest r2 values were obtained for the JCP section instrumented in Texas. 

From the r2 values obtained during this analysis, it may be concluded that the finite-difference model 

included in HIPERPAV II provides an accurate prediction of early-age concrete temperatures for PCC 

paving applications. 
305 

Table 96. Summary of r2 values obtained during the validation of the temperature model. 

Instrumented Site Coefficient of Determination (r2) 

State Slab Number 

Figure 

Numbers Temperature Temperature 

Gradient 

2 232–235 0.815 0.848 

Minnesota 

3 236–239 0.814 0.766 

4 240–243 0.820 0.788 

Arizona 

5 244–247 0.879 0.865 

1 248–251 0.864 0.470 

Lufkin, TX 

4 252–255 0.803 0.641 

1 256–259 0.873 0.801 

North Carolina 

4 260–263 0.903 0.924 

Fort Worth, TX 1 264–267 0.859 0.748 

E.4 SUMMARY AND RECOMMENDATIONS 

The early-age temperature development of concrete can be estimated from knowledge of cement 

composition, cement factor, admixtures, thermal characteristics of the concrete, slab thickness, and the 

environmental conditions that occur during paving and curing. Based on the calibration of the 

temperature model, recommendations were made to adjust/modify some models. These include 

modifications to the solar absorptivity constant, heat transfer by convection when plastic sheet are used, 

heat transfer due to evaporative cooling, the maximum solar radiation intensity, AE, and the ultimate 

degree of hydration. Major findings from this investigation are as follows: 

• Adiabatic calorimeter tests provide a means of characterizing concrete hydration with time. 

With the parameters determined through these tests, the temperature prediction model can 

account for the effects that different mixture proportions and constituents have on the heat of 

hydration of concrete. 

• Heat transfer due to evaporative cooling may significantly reduce temperatures in hydrating 

concrete. A model to account for this effect has been developed, and it is recommended that 

this model be further developed to account for actual construction practices. Modeling of the 

moisture condition in the hardened cement paste will be beneficial for this purpose. 

• From the high r2 values shown in tables 95 and 96, and the temperature predictions shown in 

sections E.5 and E.6, it may be concluded that the finite-difference model is able to produce 

good predictions of the early-age concrete temperatures development in concrete paving 

applications. 
306 

•

E.5 TEMPERATURE PREDICTION RESULTS OBTAINED DURING CALIBRATION 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top Middepth 25 mm from bottom Air

Figure 196. Measured concrete and air temperatures for Minnesota, Slab 1. 

 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 197. Measured versus predicted temperatures 25 mm from top of slab for Minnesota, 

Slab 1. 
307 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 198. Measured versus predicted temperatures 25 mm from bottom of slab for Minnesota, 

Slab 1. 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 199. Measured versus predicted temperature gradient for Minnesota, Slab 1. 
308 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top Middepth 25 mm from bottom Air

Figure 200. Measured concrete and air temperatures for Minnesota, Slab 4. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 201. Measured versus predicted temperatures 25 mm from top of slab for Minnesota, 

Slab 4. 
309 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 202. Measured versus predicted temperatures 25 mm from bottom of slab for Minnesota, 

Slab 4. 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 203. Measured versus predicted temperature gradient for Minnesota, Slab 4. 
310 

0

5

10

15

20

25

30

0 12 24 36 48 60

Concrete Age (hrs)

Temperature (oC)

25 mm from top Mid-depth 25 mm from bottom Air

Figure 204. Measured concrete and air temperatures for Arizona, Slab 1. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 205. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 1. 
311 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 206. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, 

Slab 1. 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 207. Measured versus predicted temperature gradient for Arizona, Slab 1. 
312 

-5

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top Middepth 25 mm from bottom Air

Figure 208. Measured concrete and air temperatures for Arizona, Slab 3. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 209. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 3. 
313 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 210. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, 

Slab 3. 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 211. Measured versus predicted temperature gradient for Arizona, Slab 3. 
314 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top Middepth 25 mm from bottom Air

Figure 212. Measured concrete and air temperatures for Arizona, Slab 6. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 213. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 6. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 214. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, 

Slab 6. 
315 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 215. Measured versus predicted temperature gradient for Arizona, Slab 6. 

0

10

20

30

40

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 216. Measured concrete and air temperatures for Lufkin, TX, Slab 2. 
316 

0

10

20

30

40

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 217. Measured versus predicted temperatures 25 mm from top of slab for Lufkin, TX, 

Slab 2. 

0

10

20

30

40

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 218. Measured versus predicted temperatures 25 mm from bottom of slab for Lufkin, TX, 

Slab 2. 
317 

-15

-10

-5

0

5

10

15

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 219. Measured versus predicted temperature gradient for Lufkin, TX, Slab 2. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 220. Measured concrete and air temperatures for Lufkin, TX, Slab 3. 
318 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 221. Measured versus predicted temperatures 25 mm from top of slab for Lufkin, TX, 

Slab 3. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 222. Measured versus predicted temperatures 25 mm from bottom of slab for Lufkin, TX, 

Slab 3. 
319 

-15

-10

-5

0

5

10

15

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 223. Measured versus predicted temperature gradient for Lufkin, TX, Slab 3. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 224. Measured concrete and air temperatures for North Carolina, Slab 2. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 225. Measured versus predicted temperatures 25 mm from top of slab for North Carolina, 

Slab 2. 
320 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 226. Measured versus predicted temperatures 25 mm from bottom of slab for 

North Carolina, Slab 2. 

-15

-10

-5

0

5

10

15

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 227. Measured versus predicted temperature gradient for North Carolina, Slab 2. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 228. Measured concrete and air temperatures for North Carolina, Slab 3. 
321 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Tem perature (oC)

Measured Predicted

Figure 229. Measured versus predicted temperatures 25 mm from top of slab for North Carolina, 

Slab 3. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 230. Measured versus predicted temperatures 25 mm from bottom of slab for 

North Carolina, Slab 3. 
322 

-15

-10

-5

0

5

10

15

0 12 24 36 48 60 72

Concrete Age (h)

Tem perature G radient (oC)

Measured Predicted

Figure 231. Measured versus predicted temperature gradient for North Carolina, Slab 3. 

E.6 TEMPERATURE PREDICTION RESULTS OBTAINED DURING VALIDATION 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top Middepth 25 mm from bottom Air

Figure 232. Measured concrete and air temperatures for Minnesota, Slab 2. 
323 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 233. Measured versus predicted temperatures 25 mm from top of slab for Minnesota, 

Slab 2. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 234. Measured versus predicted temperatures 25 mm from bottom of slab for Minnesota, 

Slab 2. 
324 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 235. Measured versus predicted temperature gradient for Minnesota, Slab 2. 

 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top Middepth 25 mm from bottom Air

Figure 236. Measured concrete and air temperatures for Minnesota, Slab 3. 
325 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 237. Measured versus predicted temperatures 25 mm from top of slab for Minnesota, 

Slab 3. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 238. Measured versus predicted temperatures 25 mm from bottom of slab for Minnesota, 

Slab 3. 
326 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 239. Measured versus predicted temperature gradient for Minnesota, Slab 3. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top Middepth 25 mm from bottom Air

Figure 240. Measured concrete and air temperatures for Arizona, Slab 4. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 241. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 4. 
327 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (hrs)

Temperature (oC)

Measured Predicted

Figure 242. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, 

Slab 4. 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 243. Measured versus predicted temperature gradient for Arizona, Slab 4. 
328 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top Middepth 25 mm from bottom Air

Figure 244. Measured concrete and air temperatures for Arizona, Slab 5. 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 245. Measured versus predicted temperatures 25 mm from top of slab for Arizona, Slab 5. 
329 

0

5

10

15

20

25

30

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 246. Measured versus predicted temperatures 25 mm from bottom of slab for Arizona, 

Slab 5. 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (hrs)

Temperature Gradient (oC)

Measured Predicted

Figure 247. Measured versus predicted temperature gradient for Arizona, Slab 5. 
330 

0

10

20

30

40

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 248. Measured concrete and air temperatures for Lufkin, TX, Slab 1. 

 

0

10

20

30

40

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 249. Measured versus predicted temperatures 25 mm from top of slab for Lufkin, TX, 

Slab 1. 
331 

0

10

20

30

40

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 250. Measured versus predicted temperatures 25 mm from bottom of slab for Lufkin, TX, 

Slab 1. 

-15

-10

-5

0

5

10

15

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 251. Measured versus predicted temperature gradient for Lufkin, TX, Slab 1. 
332 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 252. Measured concrete and air temperatures for Lufkin, TX, Slab 4. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 253. Measured versus predicted temperatures 25 mm from top of slab for Lufkin, TX, 

Slab 4. 
333 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 254. Measured versus predicted temperatures 25 mm from bottom of slab for Lufkin, TX, 

Slab 4. 

-15

-10

-5

0

5

10

15

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 255. Measured versus predicted temperature gradient for Lufkin, TX, Slab 4. 
334 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 256. Measured concrete and air temperatures for North Carolina, Slab 1. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 257. Measured versus predicted temperatures 25 mm from top of slab for North Carolina, 

Slab 1. 
335 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 258. Measured versus predicted temperatures 25 mm from bottom of slab for 

North Carolina, Slab 1. 

-15

-10

-5

0

5

10

15

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 259. Measured versus predicted temperature gradient for North Carolina, Slab 1. 
336 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 260. Measured concrete and air temperatures for North Carolina, Slab 4. 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 261. Measured versus predicted temperatures 25 mm from top of slab for North Carolina, 

Slab 4. 
337 

0

10

20

30

40

50

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 262. Measured versus predicted temperatures 25 mm from bottom of slab for 

North Carolina, Slab 4. 

-15

-10

-5

0

5

10

15

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 263. Measured versus predicted temperature gradient for North Carolina, Slab 4. 

0

10

20

30

40

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

25 mm from top 25 mm from bottom Air

Figure 264. Measured concrete and air temperatures for Fort Worth, TX, Slab 1. 
338 

0

10

20

30

40

50

60

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 265. Measured versus predicted temperatures 25 mm from top of slab for Fort Worth, TX, 

Slab 1. 

0

10

20

30

40

50

60

0 12 24 36 48 60 72

Concrete Age (h)

Temperature (oC)

Measured Predicted

Figure 266. Measured versus predicted temperatures 25 mm from bottom of slab for Fort Worth, 

TX, Slab 1. 

-10

-5

0

5

10

0 12 24 36 48 60 72

Concrete Age (h)

Temperature Gradient (oC)

Measured Predicted

Figure 267. Measured versus predicted temperature gradient for Fort Worth, TX, Slab 1. 
339 

REFERENCES 

1. McCullough, B.F. and Rasmussen, R.O. Fast-Track Paving: Concrete Temperature Control and 

Traffic Opening Criteria for Bonded Concrete Overlays, Volume I: Final Report. FHWA–RD–98–

167. Federal Highway Administration, Washington, DC, 191 pp., October 1999. 

2. Ruiz, J.M., Schindler, A.K., Rasmussen, R.O., Nelson, P.K., and Chang, G.K. Concrete Temperature 

Modeling and Strength Prediction Using Maturity Concepts in the FHWA HIPERPAV Software. CD 

Proceedings of the 7th International Conference on Concrete Pavements, Orlando, FL, September 9–

13, 2001. 

3. Rasmussen, R.O., Ruiz, J.M., Rozycki, D.K., and McCullough, B.F. Constructing High-Performance 

Concrete Pavements Using the FHWA HIPERPAV Systems Analysis Software. CD–ROM. 

Transportation Research Board, Washington, DC, 2002. 

4. Schindler, A.K. Concrete Hydration, Temperature Development, and Setting at Early Ages. Doctoral 

Dissertation, the University of Texas at Austin, Austin, TX, May 2002. 

5. Lerch, W. and Ford, C.L. “Long-Term Study of Cement Performance in Concrete: Chapter 3. 

Chemical and Physical Tests of the Cements.” ACI Journal, Vol. 19, No. 8, pp. 745–795, 1948. 

6. Kjellsen, K.O., Detwiler, R.J., and Gjørv, O.E. “Development of Microstructure in Plain Cement 

Pastes Hydrated at Different Temperatures.” Cement and Concrete Research, Vol. 21, No. 1, pp. 

179–189, 1991. 

7. Bogue, R.H. The Chemistry of Portland Cement. Reinhold Publishing Corporation, New York, NY, 

572 pp., 1947. 

8. Byfors, J. Plain Concrete at Early Ages. Research 3:80, Swedish Cement and Concrete Research 

Institute, Cement och Betong Institutet (CBI), Stockholm, Sweden, 1980. 

9. Scanlon, J.M. and McDonald, J.E. Thermal Properties, Significance of Tests and Properties of 

Concrete and Concrete-Making Materials. Edited by Klieger, P. and Lamonds, J.F., ASTM Special 

Technical Publication No. 169C, Philadelphia, PA, pp. 229–239, August 1994. 

10. Khan, A., Cook, W., and Mitchell, D. “Early-Age Compressive Stress-Strain Properties of Low-, 

Medium-, and High-Strength Concretes.” ACI Materials Journal, Vol. 92, No. 6, November–

December 1995. 

11. De Shutter, G. and Taerwe, L. “Specific Heat and Thermal Diffusivity of Hardening Concrete.” 

Magazine of Concrete Research, Vol. 47, No. 172, pp. 203–208, September 1995. 

12. Van Breugel, K. Simulation of Hydration and Formation of Structure in Hardening Cement-Based 

Materials. Second Edition, Delft University Press, Netherlands, 305 pp., 1999. 

13. Mindess, S. and Young, J.F. Concrete. Prentice-Hall, Inc. Englewood Cliffs, NJ, 1981. 

14. Trinhztfy, H.W., Blaawendraad, J., and Jongendijk, J. Temperature Development in Concrete 

Structures Taking Account of State Dependent Properties. Proceedings from RILEM International 

Conference on Concrete at Early Ages, Vol. 1, Paris, France, pp. 211–218, 1982. 

15. ACI Committee 207, Effect of Restraint, Volume Change, and Reinforcement on Cracking of Massive 

Concrete. American Concrete Institute, Farmington Hills, MI, 1986. 

16. A Guide to Evaluating Thermal Effects in Concrete Pavements. SHRP–C–321, Strategic Highway 

Research Program, National Research Council, Washington, DC, 104 pp., 1993. 

17. Tompson, M.R., Dempsey, B.J., Hill, H., and Vogel, J. Characterizing Temperature Effects for 

Pavement Analysis and Design. Transportation Research Record 1121, pp. 14–22, 1988. 

18. Lytton, R.L., Pufahl, D.E., Michalak, C.H., Liang, H.S., and Dempsey, B.J. An Integrated Model of 

the Climatic Effects on Pavements. FHWA–RD–90–033, Federal Highway Administration, 285 pp., 

November 1989. 

19. Accelerated Rigid Paving Techniques: State-of-the-Art Report (Special Project 201), FHWA–SA–

94–080, Federal Highway Administration, Washington, DC, 255 pp., December 1994. 

20. McAdams, W.H. Heat Transmission. McGraw Hill Series in Chemical Engineering, McGraw Book 

Company, New York, NY, 532 pp., 1954. 
340 

21. Turner, W.C. and Malloy, J.F. Thermal Insulation Properties. McGraw-Hill Book Company, New 

York, NY, 629 pp., 1981. 

22. 1993 ASHRAE Handbook, American Society of Heating, Refrigerating and Air-Conditioning 

Engineers, Inc., Atlanta, GA, 1993. 

23. Heilman, R.H. Surface Heat Transmission. Transactions of the Society of Mechanical Engineers, 

Vol. 51, Part 1, pp. 287–302, 1929. 

24. 4C-Temp&Stress—Temperature and Stress Simulation During Hardening. User Manual, Germann 

Instruments, Evanston, IL, 1998. 

25. CIMS, Computer Active Maturity System. Software and Hardware Manual, Digital Site Systems Inc., 

October 1988. 

26. Sungchul Y. A Temperature Prediction Model in New Concrete Pavement and a New Test Method 

for Concrete Fracture Parameters. Dissertation, Texas A&M University, Austin, Texas, May 1996. 

27. ASTM C 309. Standard Specification for Liquid Membrane-Forming Compounds for Curing 

Concrete. American Society for Testing and Materials, West Conshohocken, PA, 1998. 

28. Incorpera, F.P and DeWitt, D. Fundamentals of Heat and Mass Transfer. Third Edition, J. Wiley & 

Sons, New York, NY, 919 pp., 1990. 

29. Bliss, R.W. “Atmospheric Radiation Near the Surface of the Ground: Summary for Engineers.” 

Solar Energy, Vol. 5, No. 3, pp. 103–120, 1961. 

30. Hottel, H.C. and Egbert, R.B. Radiant Heat Transmission from Water Vapor. Transactions of the 

American Institute of Chemical Engineers, Vol. 38, New York, NY, pp. 531–568, 1942. 

31. Barber, E.S. Calculation of Maximum Pavement Temperatures from Weather Reports. Highway 

Research Board, Bulletin 168, Washington, DC, 1957. 

32. Jonasson, J.-E. and Hedlund, H. An Engineering Model for Creep and Shrinkage in High 

Performance Concrete. RILEM Proceedings PRO 17. Shrinkage of Concrete, Shrinkage 2000. 

Edited by Baroghel-Bouny, V. and Aitchin, P.-C., pp. 507–529, 2000. 

33. Baźant, Z.P. and Baweja, S. “Creep and Shrinkage Prediction Model for Analysis and Design of 

Concrete Structures—Model B3.” Materials and Structures, Vol. 28, pp. 357–365, 1995. 

34. Aïtcin, P.-C. “Demystifying Autogenous Shrinkage.” Concrete International, Vol. 21, No. 11, pp. 

54–56, November 1999 

35. Baźant, Z.P. and Panula, L. “Practical Predictions of Time-Dependent Deformations of Concrete.” 

Materials and Structures, Third RILEM, Vol. 11, No. 65, pp. 307–316, 1978. 

36. Persson, B. Shrinkage of Concrete. Early-Age Cracking in Cementitious Systems. Edited by Bentur, 

A. pp. 102–114. RILEM 2001. 

37. Brooks, J.J. “How Admixtures Affect Shrinkage and Creep.” Concrete International, Vol. 21, No. 4, 

pp. 35–38., April 1999. 

38. Rasmussen, R.O. and Rozycki, D. Characterization and Modeling of Axial Slab-Support Restraint.

Transportation Research Record 1778, Washington, DC, pp. 26–32, 2001. 

39. Friberg B. F. Frictional Resistance Under Concrete Pavements and Restraint Stresses in Long 

Reinforced Slabs. Highway Research Board Proceedings of the 23rd Annual Meeting, Vol. 33, 

Washington, DC, pp. 167–184, 1954. 

40. Timms, A.G. Evaluating Subgrade Friction-Reducing Mediums for Rigid Pavements. Highway 

Research Record 60, pp. 28–38, 1963. 

41. Chia, W.S., McCullough, B.F., and Burns, N.H. Field Evaluation of Subbase Friction 

Characteristics. Research Report 401–5. Center for Transportation Research, September 1986. 

42. Mohamed, A. and Hansen, W. Effect of Nonlinear Temperature Gradient on Curling Stresses in 

Concrete Pavements. Transportation Research Record 1568, pp. 65–71, 1997. 

43. Westman, G. Concrete Creep and Thermal Stresses. Doctoral Thesis, Luleå University of 

Technology, Division of Structural Engineering, 301 pp., 1999. 

44. Baźant, Z.P. and Chern, J.C. “Strain Softening with Creep and Exponential Algorithm.” Journal of 

Engineering Mechanics Division, ASCE, Vol. 111, No. 3, 1985. 
341 

45. Emborg, M., Thermal Stress in Concrete Structures at Early Ages. Doctoral Thesis, Luleå University 

of Technology, Division of Structural Engineering, 285 pp., 1989. 

46. Baźant, Z.P. “Numerical Determination of Long-Range Stress History From Strain History in 

Concrete.” Materials and Structures, (RILEM Paris), Vol. 5, No. 27, pp. 135–141, May–June 1972. 

47. Thornthwaite, C.W. “An Approach Toward a Rational Classification of Climate.” Geographical 

Review. Vol. 38, pp. 55–94, 1948. 

48. Lytton, R.L., Pufahl, D.E., Michalak, C.H., Liang, H.S., and Dempsey, B.J. An Integrated Model of 

the Climatic Effects on Pavements. FHWA–RD–90–033. Federal Highway Administration, 

Washington, DC, November 1989. 

49. National Climatic Data Center. Solar and Meteorological Surface Observation Network, 1961–1990.

Vol. 1, 2, and 3, Version 1.0, September 1993. 

50. The AASHO Road Test, Report 2—Materials and Construction. Special Report 61B. Highway 

Research Board. National Academy of Sciences. National Research Council. Washington, DC, 

1962. 

51. The AASHO Road Test, Report 5—Pavement Research. Special Report 61E. Highway Research 

Board. National Academy of Sciences. National Research Council. Washington, DC, 1962. 

52. DataPave 2.0. Beta Version. Federal Highway Administration, Washington, DC, April 1999. 

53. Jiang, Y.J. and Tayabi, S.D. Analysis of Time Domain Reflectometry Data from LTPP Seasonal 

Monitoring Program Test Sections. Final Report. FHWA–RD–99–115. Federal Highway 

Administration, Washington, DC, July 1999. 

54. CEB-FIP Model Code 1990. Comité Euro-International Du Béton, Redwood Books, Trowbridge, 

Wilshire, Great Britain, 1991. 

55. Melis, L.M., Meyer, A.H., and Fowler, D.W. An Evaluation of Tensile Strength Testing. CTR Project 

432–1F, Center for Transportation Research, University of Texas at Austin, Austin, TX, 1985. 

56. Carrasquillo, P.M. and Carrasquillo, R.L. Improved Concrete Quality Control Procedures Using 

Third Point Loading. CTR Project 1119–1F, Center for Transportation Research, University of Texas 

at Austin, Austin, TX, November 1987. 

57. Kellermann, W.F. “Effect of Size of Specimen, Size of Aggregate and Method of Loading on the 

Uniformity of Flexural Strength Tests.” Public Roads, Federal Highway Administration, Washington, 

DC, 1933. 

58. ACI. “Building Code Requirements for Structural Concrete (ACI 318M–02) and Commentary (ACI 

318RM–02).” ACI Standards. American Concrete Institute, Farmington Hills, MI, 2002. 

59. Légeron, F. and Paultre, P. “Prediction of Modulus of Rupture of Concrete.” ACI Materials Journal, 

Vol. 97, No. 2, pp. 193–200, March–April 2000. 

60. Raphael, J.M. “Tensile Strength of Concrete.” ACI Journal, Proceedings Vol. 81, pp. 158–165, 

March–April 1984. 

61. Popovics, S. Strength and Related Properties of Concrete, A Quantitative Approach. J. Wiley & 

Sons, Inc., New York, NY, 535 pp., 1998. 

62. Neville, A. Properties of Concrete. Fourth Edition, J. Wiley & Sons Inc., New York, NY, 535 pp., 

1999. 

63. Ghafoori, N. and Bucholc, J. “Properties of High-Calcium Dry Bottom Ash Concrete.” ACI 

Materials Journal, Vol. 94, No. 2, March–April 1997. 

64. Huang, Y.H. Pavement Analysis and Design. Prentice Hall. Englewood Cliffs, NJ. 1993. 

65. Westergaard, H.M. “New Formulas for Stresses in Concrete Pavements of Airfields.” Transactions 

of the American Society of Civil Engineers, Vol. 113, pp. 425–444, 1948. 

66. Timoshenko, S. and Lessels, J.M. Applied Elasticity. Westinghouse Technical Night School Press, 

Pittsburgh, PA, pp. 133–141, 1925. 

67. Structural Design Considerations for Pavement Joints. ACI Title 53–1 Report from ACI Committee 

325, Subcommittee III, Journal of the American Concrete Institute, Vol. 28, No. 1, pp. 1–28, July 

1956. 
342 

68. Gere, J.M. and Timoshenko, S.P. Mechanics of Materials. 3rd Ed. PWS–KENT Publishing, Boston, 

MA, 1990. 

69. Ioannides, A.M. and Korovesis, G.T. “Analysis and Design of Doweled Slab-on-Grade Pavement 

Systems.” Journal of Transportation Engineering, Vol. 118, No. 6, pp. 745–768, November–

December 1992. 

70. Colley, B.E. and Humphrey, H.A. Aggregate Interlock at Joints in Concrete Pavements. 

Proceedings of the Highway Research Board 46th Annual Meeting, Report HRR 189, pp. 1–18, 1967. 

71. Skarlatos, M.S. Deflections and Stresses in Concrete Pavements of Airfields with Continuous Elastic 

Joints. Harvard University Research Report under contract W-33-107-eng-4240, U.S. Army Corps of 

Engineers, Ohio River Division Laboratories, Mariemont, OH, June 1949. 

72. Ioannides, A.M. and Hammons, M.I. A Westergaard-Type Solution for the Edge Load Transfer 

Problem. Preprint from the Transportation Research Board 75th Annual Meeting, January 1996. 

73. Ioannides, A.M. and Korovesis, G.T. Aggregate Interlock: A Pure-Shear Load Transfer Mechanism. 

Transportation Research Record 1286, Transportation Research Board, National Research Council, 

Washington, DC, pp. 14–22, 1990. 

74. Nowlen, W.J. “Influence of Aggregate Properties on Effectiveness of Interlock Joints in Concrete 

Pavements.” Bulletin D139, Vol. 10, No. 2, Portland Cement Association, 1968. 

75. Smith, K. D., Mueller, A.L., Darter, M.I., and Peshkin, D.G. Performance of Jointed Concrete 

Pavements. Volume II—Evaluation and Modification of Concrete Pavement Design and Analysis 

Models. FHWA–RD–89–137, Federal Highway Administration, Washington, DC, July 1990. 

76. Yu, H.T., Smith, K.D., Darter, M.I., Jiang, J., and Khazanovich, L. Performance of Concrete 

Pavements Volume III—Improving Concrete Pavement Performance. FHWA–RD–95–111, Federal 

Highway Administration, Washington, DC, 1995. 

77. Darter, M.I. A Comparison Between Corps of Engineers and ERES Consultants, Inc. Rigid Pavement 

Design Procedures. Technical Report Prepared for the U.S. Air Force SAC, Urbana, IL, 1988. 

78. Salsilli, R.A., Barenberg, E.J., and Darter, M.I. Calibrated Mechanistic Design Procedure to Prevent 

Transverse Cracking of Jointed Plain Concrete Pavements. Proceedings of the 5th International 

Conference on Concrete Pavement Design and Rehabilitation, Purdue University, West Lafayette, IN, 

1993. 

79. Darter, M.I. and Barenberg, E.J. Design of Zero-Maintenance Plain Jointed Concrete Pavements 

Volume I—Development of Design Procedures. FHWA–RD–77–111, Federal Highway 

Administration, Washington, DC, 1977. 

80. Treybig, H.J., McCullough, B.F., Smith, P., and Von Quintus, H. Overlay Design and Reflection 

Cracking Analysis for Rigid Pavements—Volume 2, Design Procedures. FHWA–RD–77–67, Federal 

Highway Administration, Washington, DC, 1977. 

81. Lee, Y.H. and Darter, M.I. Loading and Curling Stress Models for Concrete Pavement Design. 

Transportation Research Record No. 1449, Transportation Research Board, National Research 

Council, Washington, DC, 1994. 

82. Lee, Y.H. and Darter, M.I. Modified Portland Cement Association Stress Analysis and Thickness 

Design Procedures. Transportation Research Record No. 1568, Transportation Research Board, 

National Research Council, Washington, DC, 1997. 

83. Lee, Y.H. and Darter, M.I. Mechanistic Design Models of Loading and Curling in Concrete 

Pavements, Airport Pavement Innovations: Theory to Practice. Airfield Pavement Committee, 

Proceedings of the Conference, American Society of Civil Engineers, New York, NY, 1993. 

84. Lee, Y.H., Yen, S.T., Lee, C.T., Bair, J.H., and Lee, Y.M. Development of New Stress Analysis and 

Thickness Design Procedures for Jointed Concrete Pavements. Proceedings of the 6th International 

Conference of Concrete Pavements, Purdue University, West Lafayette, IN,1997. 

85. Smith, K.D., Peshkin D.G., Darter, M.I., and Mueller, A.L. Performance of Jointed Concrete 

Pavements. Volume III—Summary of Research Findings. FHWA–RD–89–138, Federal Highway 

Administration, Washington, DC, November 1990. 
343 

86. Distress Identification Manual for the Long-Term Pavement Performance Project. Strategic 

Highway Research Program. SHRP–P–338. Washington, DC, 1993. 

87. Pilson, C.C. “JCP PSI Ride Model Summary.” Aurora 2000 Technical Memorandum, The Transtec 

Group, Inc., May 1998. 

88. Perera, R.W., Byrum. C., and Kohn, S.D. Investigation of Development of Pavement Roughness. 

FHWA–RD–97–147, Federal Highway Administration, Washington, DC, May 1998. 

89. Hoerner, T.E., Darter, M.I., Khazanovich, L., Titus-Glover, L., and Smith, K.L. Improved Prediction 

Models for PCC Pavement Performance-Related Specifications, Volume I: Final Report. FHWA–

RD–00–130, Federal Highway Administration, Washington, DC, December 2000. 

90. 1-37A Guide for Mechanistic Design of Pavements. Presented at the 79th Transportation Research 

Board Annual Meeting in Washington, DC, 2000. 

91. 1-37A Guide for Mechanistic Design of Pavements. Presented at the 80th Transportation Research 

Board Annual Meeting in Washington, DC, 2001. 

92. Determination of Traffic Information and Data for Pavement Structural Design and Evaluation, 

Interim Report, NCHRP project 1–37A, Development of the 2002 Guide for Design of New and 

Rehabilitated Pavement Structures, December 1999 

93. Won, M., Hankins, K., and McCullough, B.F. A Twenty-Four-Year Performance Review of Concrete 

Pavement Sections Made with Siliceous and Lightweight Coarse Aggregates. Research Report 472–

3. Center for Transportation Research. The University of Texas at Austin, Austin, TX, April 1989. 

94. Simon, M.J., Lagergren, E.S., and Snyder, K.A. Concrete Mixture Optimization Using Statistical 

Mixture Design Methods. Proceedings of the PCI/FHWA International Symposium on High 

Performance Concrete, pp. 230–244, 1997. 

95. Simon, M.J., Snyder, K.A., and Frohnsdorff, G.J. Advances in Concrete Mixture Optimization. 

Concrete Durability and Repair Technology Conference, pp. 21-32, University of Dundee, Scotland, 

UK, September 1999. 

96. Simon, M.J., Lagergren, E.S., and Wathne, L.G. Optimizing High-Performance Concrete Mixtures 

Using Statistical Response Surface Methods. Proceedings of the 5th International Symposium on 

Utilization of High Strength/High-Performance Concrete, Norwegian Concrete Association, Oslo, 

Norway, pp. 1311–1321, 1999. 

97. Simon, M.J., Concrete Mixture Optimization Using Statistical Methods: Final Report. FHWA-RD06-060, Federal Highway Administration, McLean, VA, September 2003. 

98. Meyers, R.H. and Montgomery, DC, Response Surface Methodology: Process and Product 

Optimization Using Designed Experiments. Second Edition, J. Wiley & Sons, New York, NY, 2002. 

99. Ganju, T.N. “Spreadsheeting Mix Designs.” Concrete International. Vol. 18, No. 12, pp. 35–38, 

December 1996. 

100. Friberg, B.F. “Design of Dowels in Transverse Joints of Concrete Pavement.” Journal of 

Transportation Engineering, ASCE, Vol. 105, 1979. 

101. Westergaard, H.M. Analysis of Stresses in Concrete Pavements Due to Variations in Temperature. 

Proceedings of 6th Annual Meeting of Highway Research Board. Vol. 6, pp. 201–217, Washington, 

DC, 1926. 

102. Hetenyi, M. Beams on Elastic Foundation. University of Michigan Press. Ann Arbor, MI. 1946. 

103. Zollinger, D.G. and Barenberg, E.J. Background for Development of Mechanistic Based Design 

Procedure for Jointed Concrete Pavements. FHWA/IL/UI 224. University of Illinois at UrbanaChampaign, IL, May 1989. 

104. PCC Mixture Report (12)—History Data for Contract 40456. Illinois Department of 

Transportation—Bureau of Materials and Physical Research. Springfield, IL, September 2, 1987. 

105. Dossey, T. and McCullough, B.F. Updating and Maintaining the Rigid Pavement Database. Center 

for Transportation Research. Research Report 1342–3F. The University of Texas at Austin, TX, 

November 1994. 
344 

106. Suh, Y.C., Hankins, K., and McCullough, B.F. Early-Age Behavior of Continuously Reinforced 

Concrete Pavement and Calibration of the Failure Prediction Model in the CRCP–7 Program. 

Research Report 1244–3, Center for Transportation Research, The University of Texas at Austin, 

Austin, TX, March 1992. 

107. Darter, M.I., Becker, J.M., Snyder, M.B., and Smith, R.E.. Portland Cement Concrete Pavement 

Evaluation System, COPES, National Cooperative Highway Research Program Report 277, 

Transportation Research Board, National Research Council, Washington, DC, September 1985. 

108. Yu, H.T., K.D. Smith, M.I. Darter, J. Jiang, and L. Khazanovich. Performance of Concrete 

Pavements Volume III—Improving Concrete Pavement Performance. FHWA–RD–95–111, Federal 

Highway Administration, Washington, DC, 1995. 

109. Rada, G.R., Elkins, G.E., Henderson, B., Van Sambeek, R.J., Lopez, Jr., A. LTPP Seasonal 

Monitoring Program: Instrumentation Installation and Data Collection Guidelines. FHWA–RD–94–

110, Federal Highway Administration, Washington, DC, April 1994. 

110. Lee, S.W. and Stoffels, S.M.. Analysis of In Situ Horizontal Joint Movement in Rigid Pavements. 

Transportation Research Record 1778, Transportation Research Board, National Research Council, 

Washington, DC, 2001. 

111. SMP_ATEMP_RAIN_HOUR and SMP_MRCTEMP_AUTO_HOUR Tables, LTPP (CD–ROM) 

NT 2.5, Data Release 9.9, September 10, 1999. 

112. LTPP Manual for Falling Weight Deflectometer Measurements, Operational Field Guidelines.

Federal Highway Administration, McLean, VA, August 2000. 

113. Teller, L.W. and Sutherland, E.C. “The Structural Design of Concrete Pavements: Part 4: The 

Study of the Structural Action of Several Types of Transverse and Longitudinal Joint Designs.” 

Public Roads, Federal Highway Administration, Vol. 17, Nos. 7 and 8, Washington, DC, September 

and October 1936. 

114. Wu, C.L and Tayabji, S.D. Variability of Concrete Pavement Load Transfer Efficiency Data. Paper 

presented at the Transportation Research Board 81st Annual Meeting, Paper No. 02–2448, 

Washington, DC, January 2002. 

115. Teller, L.W. and Cashell, H.D. “Performance of Doweled Joints under Repetitive Loading.” Public 

Roads, Federal Highway Administration, Vol. 30, No. 1, pp. 1–24, April 1958. 

116. Otero, M.A., McCullough, B.F., and Hankins, K. Monitoring of Siliceous River Gravel and 

Limestone Continuously Reinforced Concrete Pavement Test Sections in Houston 2 Years After 

Placement, and Development of a Crack Width Model for the CRCP–7 Program. Research Report 

1244–4, Center for Transportation Research, The University of Texas at Austin, Austin, TX, March 

1992. 

117. Schindler, A.K., Henry, C.P., and McCullough, B.F. Validation of CRCP–8 to Predict Long-Term 

Transverse Crack Spacing Distributions in Continuously Reinforced Concrete Pavements. CD–ROM 

Proceedings, Transportation Research Board 79th Annual Meeting, Washington, DC, January 2000. 

118. Tayabji, S.D., Zollinger, D.G., Vederey, J.R., and Gagnon, J.S. Performance of Continuously 

Reinforced Concrete Pavements: Volume III—Analysis and Evaluation of Field Test Data. FHWA–

RD–94–180, Federal Highway Administration, Washington, DC, 1998. 

119. Tayabji, S.D., Selezneva, O., and Jiang, J. Preliminary Evaluation of LTPP Continuously 

Reinforced Concrete (CRC) Pavement Test Sections. FHWA–RD–99–086, Federal Highway 

Administration, Washington, DC, 1999. 

120. Palmer, R.P. Olsen, M.P.J., and Lytton, R.L. TTICRCP—A Mechanistic Model for the Prediction of 

Stresses, Strains and Displacements in Continuously Reinforced Concrete Pavements. Research 

Report 371–2F, Texas Transportation Institute, The Texas A&M University System, College Station, 

TX, 1988. 

121. Ruiz, J.M., Kim, P.J., Schindler, A.K., and Rasmussen, R.O. Validation of HIPERPAV for 

Prediction of Early-Age Jointed Concrete Pavement Behavior. Transportation Research Record 

1778, Transportation Research Board, Washington, DC, pp. 17–25, 2001. 
345 

122. Schindler A.K., Ruiz J.M., Rasmussen R.O., Chang G.K., Wathne L.G., “Concrete Pavement 

Temperature Prediction and Case Studies with the FHWA HIPERPAV Models,” Cement and 

Concrete Composites, Vol. 26, No. 5, pp. 463-471, Elsevier, 2004. 

123. Pantazopoulou, S.J. and Mills, R.H. “Microstructural Aspects of the Mechanical Response of Plain 

Concrete.” ACI Materials Journal, Vol. 92, No. 6., pp. 605–616, November–December 1995. 

124. Hansen, T.C. “Physical Structure of Hardened Cement Paste—A Classical Approach.” Materials 

and Structures, Vol. 19, No. 114, pp. 423–436, November–December 1986.