Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Simplified Techniques for Evaluation and 

Interpretation of Pavement Deflections 

for Network-Level Analysis

PUBLICATION NO. FHWA-HRT-12-023 DECEMBER 2012
FOREWORD

The objective of this study was to develop an approach for incorporating techniques used to 

interpret and evaluate deflection data for network-level pavement management system (PMS) 

applications. The first part of this research focused on identifying and evaluating existing 

techniques by seeking out those that were simple, reliable, and easy to incorporate into current 

PMS practices, as well as those that produced consistent results. The second part of the research 

detailed the development of guidelines for the application of recommended techniques, along 

with procedures for determining optimum falling weight deflectometer (FWD) test spacing 

and data collection frequency. While there are many viable techniques available for evaluating 

the structural capacity of pavements that use FWD for project-level analysis, many of these 

techniques are time consuming and require an experienced analyst. As a result, using pavement 

deflection testing for network-level analysis has been limited to date. The findings presented in 

this report suggest that it is possible and, in fact, advantageous to define simplified techniques 

for the evaluation and interpretation of pavement deflections for network-level analysis.

Jorge E. Pagán-Ortiz

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.
TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-12-023

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

4. Title and Subtitle

Simplified Techniques for Evaluation and Interpretation of 

Pavement Deflections for Network-Level Analysis

5. Report Date 

December 2012

6. Performing Organization Code

7. Author(s) 

R. Carvalho, R. Stubstad, R. Briggs, O. Selezneva, E. Mustafa, 

and A. Ramachandran

8. Performing Organization Report No.

9. Performing Organization Name and Address

Applied Research Associates, Inc.

7184 Troy Hill Drive, Suite N

Elkridge, MD 21075-7056

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH61-02-C-00138

12. Sponsoring Agency Name and Address

Office of Infrastructure Research and Development

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

13. Type of Report and Period Covered

Final Report 

14. Sponsoring Agency Code

15. Supplementary Notes

The Contracting Officer’s Technical Representative (COTR) was Larry Wiser, HRDI-30.

16. Abstract

The objective of this study was to develop an approach for incorporating techniques used to interpret and evaluate 

deflection data for network-level pavement management system (PMS) applications. The first part of this research 

focused on identifying and evaluating existing techniques by seeking out those that were simple, reliable, and easy to 

incorporate into current PMS practices, as well as those that produced consistent results. The second part of the research 

detailed the development of guidelines for the application of recommended techniques, along with procedures for 

determining optimum falling weight deflectometer (FWD) test spacing and data collection frequency. While there are 

many viable techniques available for evaluating the structural capacity of pavements that use FWD for project-level 

analysis, many of these techniques are time consuming and require an experienced analyst. As a result, using pavement 

deflection testing for network-level analysis has been limited to date. The findings presented in this report suggest that 

it is possible and, in fact, advantageous to define simplified techniques for the evaluation and interpretation of pavement 

deflections for network-level analysis.

17. Key Words

Pavement performance, Rehabilitation, Maintenance, 

Pavement design, Long-term performance, Flexible 

pavements, Rigid pavements

18. Distribution Statement

No restrictions. This document is available to the 

public through the National Technical Information 

Service, Springfield, VA 22161.

19. Security Classification (of this report)

Unclassified

20. Security Classification (of this page)

Unclassified

21. No. of Pages

198

22. Price

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

TABLE OF CONTENTS

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

BACKGROUND ..................................................................................................................... 1

PROJECT OBJECTIVES...................................................................................................... 1

DESIRED OUTCOMES AND PROJECT DELIVERABLES........................................... 2

REPORT ORGANIZATION................................................................................................. 3

CHAPTER 2—LITERATURE REVIEW.................................................................................. 5

INTRODUCTION................................................................................................................... 5

LITERATURE REVIEW APPROACH............................................................................... 5

SUMMARY OF FINDINGS FROM PREVIOUS STUDIES............................................. 6

Agencies Currently Utilizing Deflection Data for Network-Level Applications............. 11

Agencies Utilizing Deflection Data in a Manner Potentially Useful to Enhance 

Network-Level PMS Applications.................................................................................... 15

Identified Techniques for Simplified Evaluation and Analysis........................................ 16

CONCLUSIONS FROM THE LITERATURE REVIEW ............................................... 19

CHAPTER 3—ASSESSMENT OF DATA............................................................................... 21

REVIEW AND ASSESSMENT OF DATA FROM LTPP STUDIES ............................. 21

Data Selection Criteria...................................................................................................... 21

Data Elements Needed for Analyses................................................................................. 21

Analysis Database Development ...................................................................................... 23

Data Review Process......................................................................................................... 23

ASSESSMENT OF DATA TO SUPPORT EVALUATION OF IDENTIFIED 

TECHNIQUES...................................................................................................................... 24

Impact of M&R on Pavement Performance Data ............................................................. 24

Analysis of Deflection Data.............................................................................................. 27

ASSESSMENT OF DATA TO SUPPORT OPTIMUM TEST SPACING AND 

FREQUENCY ....................................................................................................................... 27

LTPP Data to Support Optimum Test Spacing Analysis.................................................. 27

Supplemental Data to Support Optimum Test Spacing Analysis..................................... 27

LTPP Data to Support Optimum Test Frequency Analysis.............................................. 27

LTPP Data to Support Time of Day and Day of Year Analysis....................................... 28

CHAPTER 4—EVALUATION OF APPLICABLE LOAD DEFLECTION

TECHNIQUES............................................................................................................................ 29

ANALYSIS APPROACH..................................................................................................... 30

Binary Logistic Model ...................................................................................................... 30

Stochastic Approach to Evaluate Load Deflection Techniques to Network-Level 

Applications...................................................................................................................... 33

ANALYSIS STEPS............................................................................................................... 35

Data Preparation................................................................................................................ 36

Evaluation of Selected Techniques Based on Observed Performance ............................. 40

Sensitivity of Model to Deflection Parameter .................................................................. 42

Validation Analysis........................................................................................................... 44

Selection of Deflection Technique.................................................................................... 45
iv

THEORETICAL VALIDATION........................................................................................ 45

Mechanistic-Empirical Analysis....................................................................................... 46

Comparison with MEPDG Predicted Performance .......................................................... 48

IMPORTANCE OF LOCAL CALIBRATION ................................................................. 50

SUMMARY OF FINDINGS ................................................................................................ 51

Flexible Pavements........................................................................................................... 52

Rigid Pavements ............................................................................................................... 54

GUIDELINES FOR SELECTING BEST-FITTING TECHNIQUES ............................ 57

1. Data Preparation............................................................................................................ 57

2. Logistic Model Calibration........................................................................................... 58

3. Verification of Accuracy............................................................................................... 58

4. Sensitivity Analysis ...................................................................................................... 59

CHAPTER 5—PROCEDURES FOR OPTIMUM DEFLECTION TEST 

SPACINGS AND FREQUENCY FOR PMS APPLICATIONS ............................................ 61

ANALYSIS OF TEST SPACINGS FOR FWD DATA COLLECTION......................... 62

Modeling the Error Using a Monte Carlo Simulation ...................................................... 62

Comparison to Available Data.......................................................................................... 72

ANALYSIS OF FREQUENCY FOR FWD DATA COLLECTION ............................... 75

Flexible Pavements........................................................................................................... 75

Rigid Pavements ............................................................................................................... 81

CHAPTER 6—GUIDELINES FOR CONSIDERATION OF TIME OF DAY AND 

SEASON OF YEAR FOR OPTIMAL FWD DATA COLLECTION FOR PMS 

APPLICATIONS ........................................................................................................................ 83

SUMMARY OF APPROACHES FROM LITERATURE REVIEW.............................. 83

RESULTS OF LTPP DATA ANALYSIS........................................................................... 84

DEFLECTION ADJUSTMENT PROCEDURES............................................................. 84

RECOMMENDATIONS FOR TIME OF DAY FOR DEFLECTION 

MEASUREMENTS AT NETWORK LEVEL................................................................... 86

RECOMMENDATIONS FOR SEASON OF YEAR FOR MEASUREMENTS AT 

NETWORK LEVEL............................................................................................................. 87

APPLICATIONS AND LIMITATIONS............................................................................ 87

CHAPTER 7—PRACTICAL EXAMPLE ............................................................................... 89

INTRODUCTION................................................................................................................. 89

REVIEW OF RECOMMENDED APPLICATION .......................................................... 89

MDSHA EXAMPLE............................................................................................................. 90

Overview on MDSHA PMS ............................................................................................. 90

Sample of MDSHA Network............................................................................................ 92

Incorporation of Structural Analysis on MDSHA PMS ................................................... 93

CONCLUSIONS ................................................................................................................... 99

CHAPTER 8—CONCLUSIONS AND RECOMMENDATIONS ....................................... 101

SIMPLIFIED TECHNIQUES FOR EVALUATION AND INTERPRETATION 

OF PAVEMENT DEFLECTIONS FOR NETWORK-LEVEL ANALYSIS................ 101

OPTIMUM DEFLECTION TEST SPACINGS AND FREQUENCY FOR PMS 

APPLICATIONS ................................................................................................................ 103

Test Spacing.................................................................................................................... 103
v

Frequency........................................................................................................................ 103

Time of Day and Season of Year.................................................................................... 104

EXAMPLE OF INCORPORATING STRUCTURAL ANALYSIS ON PMS.............. 104

APPENDIX A............................................................................................................................ 107

APPENDIX B ............................................................................................................................ 115

PRE-SCREENING OF DEFLECTION PARAMETERS FOR FLEXIBLE 

PAVEMENTS ..................................................................................................................... 115

PRE-SCREENING OF DEFLECTION PARAMETERS FOR RIGID 

PAVEMENTS ..................................................................................................................... 121

FLEXIBLE PAVEMENT STRUCTURAL ANALYSIS................................................. 132

Models Based on Roughness Performance..................................................................... 132

Models Based on Rutting Performance .......................................................................... 133

Models Based on Fatigue Cracking Performance........................................................... 134

RIGID PAVEMENT STRUCTURAL ANALYSIS FOR 9,000 LB (4,086 KG) 

FWD LOAD......................................................................................................................... 135

Models Based on Roughness Performance (9,000 lb (4,086 kg)) .................................. 135

Models Based on Faulting at Joints Performance (9,000 lb (4,086 kg)) ........................ 137

Models Based on Transverse Cracking Performance (9,000 lb (4,086 kg))................... 139

RIGID PAVEMENT STRUCTURAL ANALYSIS FOR 12,000-LB (5,448-KG) 

FWD LOAD......................................................................................................................... 141

Models Based on Roughness Performance (12,000 lb (5,448 kg)) ................................ 141

Models Based on Faulting at Joints Performance (12,000 lb (5,448 kg)) ...................... 143

Models Based on Transverse Cracking Performance (12,000 lb (5,448 kg))................. 145

APPENDIX C............................................................................................................................ 147

FLEXIBLE PAVEMENT STRUCTURAL ANALYSIS................................................. 147

Models Based on Rutting Performance for Flexible Pavements.................................... 147

Models Based on Fatigue Cracking Performance for Flexible Pavements..................... 149

RIGID PAVEMENT STRUCTURAL ANALYSIS FOR 9,000-LB (4,086-KG) 

FWD LOAD......................................................................................................................... 150

Models Based on Roughness Performance for Rigid Pavements (9,000 lb 

(4,086 kg))....................................................................................................................... 150

Models Based on Faulting at Joints Performance for Rigid Pavements (9,000 lb 

(4,086 kg))....................................................................................................................... 151

Models Based on Transverse Cracking Performance for Rigid Pavements 

(9,000 lb (4,086 kg))....................................................................................................... 152

RIGID PAVEMENT STRUCTURAL ANALYSIS FOR 12,000-LB (5,488-KG) 

FWD LOAD......................................................................................................................... 154

Models Based on Roughness Performance for Rigid Pavements (12,000 lb 

(5,445 kg))....................................................................................................................... 154

Models Based on Faulting at Joints Performance for Rigid Pavements 

(12,000 lb (5,445 kg))..................................................................................................... 155

Models Based on Transverse Cracking Performance for Rigid Pavements 

(12,000 lb (5,445 kg))..................................................................................................... 156
vi

APPENDIX D............................................................................................................................ 159

MECHANISTIC-EMPIRICAL ANALYSIS OF FLEXIBLE PAVEMENTS.............. 159

Comparison with MEPDG Predicted Performance ........................................................ 161

MECHANISTIC-EMPIRICAL ANALYSIS OF RIGID PAVEMENTS...................... 163

Comparison with MEPDG Predicted Performance ........................................................ 165

APPENDIX E ............................................................................................................................ 167

APPENDIX F ............................................................................................................................ 175

REFERENCES.......................................................................................................................... 181
vii

LIST OF FIGURES

Figure 1. Equation. Calculation of RoC........................................................................................ 14

Figure 2. Equation. Calculation of BLI ........................................................................................ 14

Figure 3. Equation. Calculation of MLI........................................................................................ 14

Figure 4. Equation. Calculation of LLI......................................................................................... 14

Figure 5. Equation. Calculation of CIi .......................................................................................... 16

Figure 6. Equation. Calculation of Fi............................................................................................ 16

Figure 7. Equation. Calculation of Si ............................................................................................ 17

Figure 8. Equation. Calculation of Ii............................................................................................. 17

Figure 9. Equation. Calculation of RA ......................................................................................... 17

Figure 10. Equation. Calculation of TA........................................................................................ 17

Figure 11. Equation. Calculation of SNeff...................................................................................... 17

Figure 12. Equation. Calculation of d0.......................................................................................... 17

Figure 13. Equation. Calculation of Mr ........................................................................................ 18

Figure 14. Equation. Calculation of E0 ......................................................................................... 18

Figure 15. Equation. Calculation of Esg ........................................................................................ 18

Figure 16. Equation. Calculation of n........................................................................................... 18

Figure 17. Equation. Calculation of C .......................................................................................... 18

Figure 18. Equation. Calculation of E0(r) ...................................................................................... 19

Figure 19. Equation. Calculation of ........................................................................................ 19

Figure 20. Graph. Variation of roughness in section 06-0509...................................................... 26

Figure 21. Equation. General formulation of the logistic model .................................................. 30

Figure 22. Equation. General linear formulation for the exponent term of the logistic model .... 30

Figure 23. Graph. Typical logistic model probability function of a predictor variable X............ 31

Figure 24. Graph. Example of an ROC curve............................................................................... 32

Figure 25. Graph. Example of logistic model probability function of a predictor variable 

X used to create a structural decision matrix................................................................................ 34

Figure 26. Graph. Example of performance extrapolation based on historical data..................... 39

Figure 27. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

I2 for flexible pavements............................................................................................................... 43

Figure 28. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

Hogg for flexible pavements......................................................................................................... 44

Figure 29. Equation. Calculation of I2 .......................................................................................... 45

Figure 30. Graph. Deflection parameter I2 as a function of SN for a flexible pavement 

with HMA modulus of 500,000 psi (3,445,000 kPa).................................................................... 47

Figure 31. Graph. Sensitivity of deflection parameter I1 to slab thickness................................... 48

Figure 32. Graph. Sensitivity of I1 structural logistic model probability based on fatigue 

cracking performance to MEPDG predicted fatigue cracking for flexible pavements................. 49

Figure 33. Graph. Sensitivity of I1 structural logistic model probability based on 

roughness performance to MEPDG predicted roughness for rigid pavements............................. 50

Figure 34. Equation. Calculation of CI3........................................................................................ 52

Figure 35. Equation. Calculation of I1 .......................................................................................... 53

Figure 36. Equation. Calculation of C15 ....................................................................................... 54

Figure 37. Equation. Calculation of CI4........................................................................................ 55

Figure 38. Illustration. Monte Carlo simulation ........................................................................... 63

σ(r)
viii

Figure 39. Illustration. Deflection measurement pairings based on 0.1-, 0.2-, and 0.3-mi 

(0.161-, 0.322-, and 0.483-kg) spacings ....................................................................................... 64

Figure 40. Graph. Expected average error as function of spacing for 10-mi-(16.1-km)-long 

sections.......................................................................................................................................... 65

Figure 41. Graph. Expected average errors for 10-mi- (16.1-km)-long section at different 

spacings and probability levels..................................................................................................... 66

Figure 42. Graph. Normal distribution ......................................................................................... 66

Figure 43. Graph. Average error curves for different section lengths.......................................... 67

Figure 44. Graph. Values of a and b from the seven average error curves .................................. 67

Figure 45. Equation. Average expected error due to sampling..................................................... 68

Figure 46. Graph. Standard deviation of average error curves for different section lengths........ 68

Figure 47. Graph. Values of c and d from the seven standard deviation curves .......................... 69

Figure 48. Equation. Standard deviation of the expected error due to sampling.......................... 69

Figure 49. Graph. Observed average error (data points) plotted with the computed average 

error (lines).................................................................................................................................... 70

Figure 50. Graph. Observed standard deviation (data points) plotted with the computed 

average error (lines)...................................................................................................................... 70

Figure 51. Graph. Calculated errors for a 10-mi- (16.1-km)-long section with different 

means and standard deviations of errors....................................................................................... 71

Figure 52. Equation. Calculation of COV shift factor.................................................................. 71

Figure 53. Graph. Maximum and minimum section means and weighted mean deflection 

for all sections in each State.......................................................................................................... 73

Figure 54. Graph. Average error for each spacing........................................................................ 73

Figure 55. Graph. Comparison between measured error and predicted error for all 

New Mexico sections at 0.2-mi (0.322-km) spacing .................................................................... 74

Figure 56. Graph. Comparison between measured error and predicted error for all 

New Mexico sections at 0.5-mi (0.805-km) spacing .................................................................... 74

Figure 57. Graph. Comparison between measured error and predicted error for all 

New Mexico sections at 1-mi (1.61-km) spacing ......................................................................... 75

Figure 58. Graph. Plot of log (D1) versus temperature for SHRP section 501002....................... 76

Figure 59. Equation. Deflection adjustment by temperature ........................................................ 77

Figure 60. Graph. Center deflection measurements versus test date—adjusted and 

unadjusted ..................................................................................................................................... 77

Figure 61. Graph. Temperature-adjusted center deflections versus test date for SHRP 

section 501002 .............................................................................................................................. 78

Figure 62. Graph. Specificity of fatigue cracking models for flexible pavements....................... 84

Figure 63. Graph. Specificity of rutting models for flexible pavements...................................... 85

Figure 64. Graph. Distribution of prescribed treatment for the first intervention ........................ 95

Figure 65. Graph. Cost distribution over the analysis period ....................................................... 98

Figure 66. Equation. Calculation of LTEA................................................................................. 136

Figure 67. Graph. Sensitivity of rutting acceptable probability to deflection parameter 

CI3 for flexible pavements.......................................................................................................... 147

Figure 68. Graph. Sensitivity of rutting acceptable probability to deflection parameter 

D1 for flexible pavements ........................................................................................................... 148

Figure 69. Graph. Sensitivity of rutting acceptable probability to deflection parameter 

Hogg for flexible pavements....................................................................................................... 148
ix

Figure 70. Graph. Sensitivity of fatigue cracking acceptable probability to deflection 

parameter I1 for flexible pavements............................................................................................ 149

Figure 71. Graph. Sensitivity of fatigue cracking acceptable probability to deflection 

parameter Hogg for flexible pavements...................................................................................... 149

Figure 72. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

CI5 for rigid pavements (9,000 lb (4,086 kg)) ............................................................................ 150

Figure 73. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

I1 for rigid pavements (9,000 lb (4,086 kg))............................................................................... 150

Figure 74. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

LTEA for rigid pavements (9,000 lb (4,086 kg))........................................................................ 151

Figure 75. Graph. Sensitivity of faulting at joints acceptable probability to deflection 

parameter D6 for rigid pavements (9,000 lb (4,086 kg))............................................................. 151

Figure 76. Graph. Sensitivity of faulting at joints acceptable probability to deflection 

parameter LTEA for rigid pavements (9,000 lb (4,086 kg))....................................................... 152

Figure 77. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter CI4 for rigid pavements (9,000 lb (4,086 kg)) ........................................................... 152

Figure 78. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter D1 for rigid pavements (9,000 lb (4,086 kg))............................................................. 153

Figure 79. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter LTEA for rigid pavements (9,000 lb (4,086 kg))....................................................... 153

Figure 80. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

CI4 for rigid pavements (12,000 lb (5,445 kg)) .......................................................................... 154

Figure 81. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

I1 for rigid pavements (12,000 lb (5,445 kg))............................................................................. 154

Figure 82. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

LTEA for rigid pavements (12,000 lb (5,445 kg))...................................................................... 155

Figure 83. Graph. Sensitivity of faulting at joints acceptable probability to deflection 

parameter D6 for rigid pavements (12,000 lb (5,445 kg))........................................................... 155

Figure 84. Graph. Sensitivity of faulting at joints acceptable probability to deflection 

parameter LTEA for rigid pavements (12,000 lb (5,445 kg))..................................................... 156

Figure 85. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter CI4 for rigid pavements (12,000 lb (5,445 kg)) ......................................................... 156

Figure 86. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter D1 for rigid pavements (12,000 lb (5,445 kg))........................................................... 157

Figure 87. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter LTEA for rigid pavements (12,000 lb (5,445 kg))..................................................... 157

Figure 88. Equation. Computation of SN ................................................................................... 159

Figure 89. Equation. Computation of the layer coefficient a2 for base course ........................... 159

Figure 90. Graph. Deflection parameter I2 as a function of SN for a flexible pavement 

with HMA modulus of 500,000 psi (3,445,000 kPa).................................................................. 160

Figure 91. Graph. Deflection parameter CI3 as a function of SN for a flexible pavement 

with HMA modulus of 500,000 psi (3,445,000 kPa).................................................................. 160

Figure 92. Graph. Deflection parameter I1 as a function of SN for a flexible pavement 

with HMA modulus of 500,000 psi (3,445,000 kPa).................................................................. 161

Figure 93. Equation. Calculation of number of load repetitions to fatigue failure..................... 161

Figure 94. Equation. Calculation of correction for different asphalt layer thickness effects ..... 162
x

Figure 95. Equation. Calculation of laboratory to field adjustment factor................................. 162

Figure 96. Equation. Calculation of parameter M....................................................................... 162

Figure 97. Equation. Fatigue cracking prediction....................................................................... 162

Figure 98. Equation. Calculation of permanent deformation ..................................................... 162

Figure 99. Equation. Calculation of k1........................................................................................ 162

Figure 100. Equation. Calculation of C1 and C2 ......................................................................... 162

Figure 101. Graph. Sensitivity of CI3 structural logistic model probability based on 

rutting performance to MEPDG predicted rutting for flexible pavements................................. 163

Figure 102. Graph. Sensitivity of deflection parameter D6 to slab thickness............................. 164

Figure 103. Graph. Sensitivity of deflection parameter CI4 to slab thickness............................ 164

Figure 104. Graph. Sensitivity of D6 structural logistic model probability based on faulting 

performance to MEPDG predicted faulting for rigid pavements................................................ 165

Figure 105. Graph. Sensitivity of CI4 structural logistic model probability based on slab 

cracking performance to MEPDG predicted slab cracking for rigid pavements........................ 166

Figure 106. Graph. Comparison between measured error and predicted error for all 

Kansas sections at 0.2-mi (0.322-km) spacing ........................................................................... 172

Figure 107. Graph. Comparison between measured error and predicted error for all 

Kansas sections at 0.5-mi (0.805-km) spacing ........................................................................... 172

Figure 108. Graph. Comparison between measured error and predicted error for all 

Kansas sections at 1-mi (1.61-km) spacing ................................................................................ 173

Figure 109. Graph. Comparison between measured error and predicted error for all 

Oregon sections at 0.2-mi (0.322-km) spacing........................................................................... 173

Figure 110. Graph. Comparison between measured error and predicted error for all 

Oregon sections at 0.5-mi (0.805-km) spacing........................................................................... 174

Figure 111. Graph. Comparison between measured error and predicted error for all 

Oregon sections at 1-mi (1.61-km) spacing................................................................................ 174
xi

LIST OF TABLES

Table 1. Summary of useful practices for FWD use in network-level analyses............................. 7

Table 2. Structural condition associated with deflection bowl parameters .................................. 15

Table 3. LTPP database tables used to support data collection .................................................... 23

Table 4. LTPP data availability to support evaluation of identified techniques........................... 24

Table 5. Data assessment summary after multiple section analysis ............................................. 27

Table 6. FWD data availability for SMP sites.............................................................................. 28

Table 7. Example of structural decision matrix ............................................................................ 34

Table 8. Input continuous data summary for flexible pavement sections..................................... 37

Table 9. Input discrete data summary for flexible pavement sections.......................................... 37

Table 10. Input continuous data summary for rigid pavement sections....................................... 38

Table 11. Input discrete data summary for rigid pavement sections ............................................ 38

Table 12. Structural distresses in flexible and rigid pavements.................................................... 38

Table 13. Distress threshold for flexible and rigid pavments....................................................... 39

Table 14. Traffic characteristics used for sampling...................................................................... 40

Table 15. Statistics of calibrated models based on roughness performance of flexible 

pavements ..................................................................................................................................... 42

Table 16. Example of validation results for the structural logistic model based on 

roughness for flexible pavements ................................................................................................. 45

Table 17. Variables in the I2 final model (based on roughness)................................................... 45

Table 18. Summary of the mechanistic analysis inputs for flexible pavements........................... 46

Table 19. Summary of the mechanistic analysis inputs for rigid pavements................................ 47

Table 20. Benefits of local calibration.......................................................................................... 51

Table 21. Variables in the I2 final model for flexible pavements based on roughness 

performance .................................................................................................................................. 52

Table 22. Variables in the CI3 final model for flexible pavements based on rutting 

performance .................................................................................................................................. 52

Table 23. Variables in the I1 final model for flexible pavements based on fatigue cracking 

performance .................................................................................................................................. 53

Table 24. Variables in the CI5 final model for rigid pavements based on roughness 

performance (9,000 lb (4,086 kg))................................................................................................ 54

Table 25. Variables in the CI4 final model for rigid pavements based on roughness 

performance (12,000 lb (5,448 kg)).............................................................................................. 55

Table 26. Variables in the D6 final model for rigid pavements based on faulting at joints 

performance (9,000 lb (4,086 kg))................................................................................................ 55

Table 27. Variables in the D6 final model for rigid pavements based on faulting at joints 

performance (12,000 lb (5,448 kg)).............................................................................................. 56

Table 28. Variables in the CI4 final model for rigid pavements based on transverse slab 

cracking performance (9,000 lb (4,086 kg))................................................................................. 56

Table 29. Variables in the CI4 final model for rigid pavements based on transverse slab 

cracking performance (12,000 lb (5,448 kg))............................................................................... 57

Table 30. Errors in percentage for 90 percent reliability based on various section lengths, 

sample spacings, and COV of 33 percent ..................................................................................... 72

Table 31. Deflection data for New Mexico, Oregon, and Kansas................................................ 72

Table 32. Annual change in D1 by SHRP test section .................................................................. 79
xii

Table 33. Rate of deflection change by traffic level..................................................................... 80

Table 34. Rate of deflection change by subgrade type ................................................................. 80

Table 35. Rate of deflection change by AC thickness.................................................................. 80

Table 36. Rate of deflection change by climate classification...................................................... 81

Table 37. Statistics for flexible pavement fatigue cracking models: D1 versus D1 adjusted........ 85

Table 38. Statistics for flexible pavement rutting models: D1 versus D1 adjusted ....................... 85

Table 39. Statistics for flexible pavement IRI as a function of season......................................... 87

Table 40. MDSHA pavement classification based on IRI values................................................. 91

Table 41. MDSHA PMS treatment decision matrix ..................................................................... 92

Table 42. Summary statistics of MDSHA sections used in the example...................................... 93

Table 43. Summary statistics of MDSHA sections used in the example 

(percent distribution of sections) .................................................................................................. 93

Table 44. Structural decision matrix based on roughness and rutting performance..................... 94

Table 45. Adjustment of MDSHA treatment option based on structural analysis........................ 95

Table 46. Results from the PMS optimization considering the structural analysis...................... 97

Table 47. Impact on costs from the PMS optimization considering the structural analysis......... 98

Table 48. Useful practices for FWD use in network-level analyses........................................... 107

Table 49. Pre-screening of deflection variables for roughness-based logistic model for 

flexible pavements...................................................................................................................... 115

Table 50. Pre-screening of deflection variables for rutting-based logistic model for 

flexible pavements...................................................................................................................... 117

Table 51. Pre-screening of deflection variables for fatigue cracking-based logistic 

model for flexible pavements...................................................................................................... 119

Table 52. Pre-screening of deflection variables for drop 2 roughness-based logistic 

model for rigid pavements.......................................................................................................... 121

Table 53. Pre-screening of deflection variables for drop 2 faulting at joints-based logistic 

model for rigid pavements.......................................................................................................... 123

Table 54. Pre-screening of deflection variables for drop 2 transverse cracking-based 

logistic model for rigid pavements ............................................................................................. 125

Table 55. Pre-screening of deflection variables for drop 3 roughness-based logistic 

model for rigid pavements.......................................................................................................... 127

Table 56. Pre-screening of deflection variables for drop 3 faulting at joints-based logistic 

model for rigid pavements.......................................................................................................... 129

Table 57. Pre-screening of deflection variables for drop 3 transverse cracking-based 

logistic model for rigid pavements ............................................................................................. 131

Table 58. Statistics of calibrated models based on roughness performance of flexible 

pavements—all models............................................................................................................... 132

Table 59. Statistics of calibrated models based on rutting performance of flexible 

pavements—all models............................................................................................................... 133

Table 60. Variables in the CI3 final model (based on rutting).................................................... 133

Table 61. Variables in the Hogg final model (based on rutting) ................................................ 133

Table 62. Variables in the D1 final model (based on rutting)..................................................... 134

Table 63. Statistics of calibrated models based on fatigue cracking performance of flexible 

pavements ................................................................................................................................... 134

Table 64. Variables in the I1 final model (based on fatigue cracking) ....................................... 134

Table 65. Variables in the Hogg final model (based on fatigue cracking) ................................. 134
xiii

Table 66. Statistics of calibrated models based on roughness performance of rigid 

pavements (9,000 lb (4,086 kg))................................................................................................. 135

Table 67. Variables in the CI5 final model (based on roughness) (9,000 lb (4,086 kg))............ 135

Table 68. Variables in the I1 final model (based on roughness) (9,000 lb (4,086 kg))............... 135

Table 69. Variables in the LTEA final model (based on roughness) (9,000 lb (4,086 kg))....... 135

Table 70. Statistics of calibrated models based on roughness performance of rigid 

pavements for alternative FWD test locations (9,000 lb (4,086 kg)).......................................... 136

Table 71. Variables in the D1 final model for FWD testing at edge corner slab 

(based on roughness) (9,000 lb (4,086 kg))................................................................................ 136

Table 72. Variables in the D1 final model for FWD testing at edge midslab 

(based on roughness) (9,000 lb (4,086 kg))................................................................................ 136

Table 73. Statistics of calibrated models based on faulting at joints of rigid pavements 

(9,000 lb (4,086 kg))................................................................................................................... 137

Table 74. Variables in the D6 final model (based on faulting at joints) (9,000 lb (4,086 kg))... 137

Table 75. Variables in the LTEA final model (based on faulting at joints) (9,000 lb 

(4,086 kg))................................................................................................................................... 137

Table 76. Statistics of calibrated models based on faulting at joints of rigid pavements 

(9,000 lb (4,086 kg))................................................................................................................... 138

Table 77. Variables in the D1 final model for FWD testing at edge corner slab 

(based on faulting at joints) (9,000 lb (4,086 kg))...................................................................... 138

Table 78. Variables in the D1 final model for FWD testing at edge midslab 

(based on faulting at joints) (9,000 lb (4,086 kg))...................................................................... 138

Table 79. Statistics of calibrated models based on transverse cracking of rigid 

pavements (9,000 lb (4,086 kg))................................................................................................. 139

Table 80. Variables in the CI4 final model (based on transverse cracking) 

(9,000 lb (4,086 kg))................................................................................................................... 139

Table 81. Variables in the D1 final model (based on transverse cracking) 

(9,000 lb (4,086 kg))................................................................................................................... 139

Table 82. Variables in the LTEA final model (based on transverse cracking) 

(9,000 lb (4,086 kg))................................................................................................................... 140

Table 83. Statistics of calibrated models based on transverse cracking of rigid pavements 

(9,000 lb (4,086 kg))................................................................................................................... 140

Table 84. Variables in the D1 final model for FWD testing at edge corner slab 

(based on transverse cracking) (9,000 lb (4,086 kg)) ................................................................. 140

Table 85. Variables in the D1 final model for FWD testing at edge midslab 

(based on transverse cracking) (9,000 lb (4,086 kg)) ................................................................. 140

Table 86. Statistics of calibrated models based on roughness of rigid pavements 

(12,000 lb (5,448 kg))................................................................................................................. 141

Table 87. Variables in the CI4 final model (based on roughness) (12,000 lb (5,448 kg)).......... 141

Table 88. Variables in the I1 final model (based on roughness) (12,000 lb (5,448 kg))............. 141

Table 89. Variables in the LTEA final model (based on roughness) (12,000 lb (5,448 kg))..... 141

Table 90. Statistics of calibrated models based on roughness of rigid pavements 

(12,000 lb (5,448 kg))................................................................................................................. 142

Table 91. Variables in the D1 final model for FWD testing at edge corner slab 

(based on roughness) (12,000 lb (5,448 kg)).............................................................................. 142
xiv

Table 92. Variables in the D1 final model for FWD testing at edge midslab 

(based on roughness) (12,000 lb (5,448 kg)).............................................................................. 142

Table 93. Statistics of calibrated models based on faulting at joints of rigid pavements 

(12,000 lb (5,448 kg))................................................................................................................. 143

Table 94. Variables in the D6 final model (based on faulting at joints) (12,000 lb 

(5,448 kg))................................................................................................................................... 143

Table 95. Variables in the LTEA final model (based on faulting at joints) (12,000 lb 

(5,448 kg))................................................................................................................................... 143

Table 96. Statistics of calibrated models based on faulting at joints of rigid pavements 

(12,000 lb (5,448 kg))................................................................................................................. 144

Table 97. Variables in the D1 final model for FWD testing at edge corner slab 

(based on faulting at joints) (12,000 lb (5,448 kg)).................................................................... 144

Table 98. Variables in the D1 final model for FWD testing at edge midslab 

(based on faulting at joints) (12,000 lb (5,448 kg)).................................................................... 144

Table 99. Statistics of calibrated models based on transverse cracking of rigid pavements 

(12,000 lb (5,448 kg))................................................................................................................. 145

Table 100. Variables in the CI4 final model (based on transverse cracking) 

(12,000 lb (5,448 kg))................................................................................................................. 145

Table 101. Variables in the D1 final model (based on transverse cracking) 

(12,000 lb (5,448 kg))................................................................................................................. 145

Table 102. Variables in the LTEA final model (based on transverse cracking) 

(12,000 lb (5,448 kg))................................................................................................................. 146

Table 103. Statistics of calibrated models based on transverse cracking of rigid pavements 

(12,000 lb (5,448 kg))................................................................................................................. 146

Table 104. Variables in the D1 final model for FWD testing at edge corner slab 

(based on transverse cracking) (12,000 lb (5,448 kg)) ............................................................... 146

Table 105. Variables in the D1 final model for FWD testing at edge midslab 

(based on transverse cracking) (12,000 lb (5,448 kg)) ............................................................... 146

Table 106. Information about the different States used in the analysis...................................... 167

Table 107. Errors in percentage for 50, 70, and 80 percent reliability for section lengths 

up to 10 mi (16.1 km) ................................................................................................................. 170

Table 108. Errors in percentage for 90, 95, and 99.5 percent reliability for section lengths 

up to 10 mi (16.1 km) ................................................................................................................. 171

Table 109. Description of the Maryland sections used in the example ...................................... 175

Table 110. FWD test data for all of the Maryland sites.............................................................. 178
1

CHAPTER 1—INTRODUCTION

BACKGROUND

The concept of a pavement management system (PMS) was developed following the 

American Association of State Highway Officials (AASHO) successful Road Test in the 1950s. 

Pavement performance was first characterized at the AASHO Road Test, providing the necessary 

information to compare design alternatives and expectations over the service life of flexible and 

rigid pavement structures. A link was established between performance and planning, designing, 

constructing, and maintaining pavements, and the concept of PMS was defined accordingly.

Surface distress measurements and roughness are the main components in determining a 

pavement’s existing condition. These quantities can be used for predicting future performance 

and programming maintenance and construction/reconstruction activities, despite the fact that 

structural capacity has a major effect on how the pavement will perform in the future (i.e., rate of 

deterioration, types and severity of distresses, etc.). Therefore, it is important to consider the 

existing structural capacity of pavements and current surface distresses to predict the pavements’ 

future condition with reasonable accuracy.

There are several techniques available to evaluate the structural capacity of pavements, 

most of which were developed for project-level applications (i.e., provide structural quality 

assessments for designing pavement rehabilitation or reinforcement). Many of these techniques 

are time consuming, and some require an experienced analyst. They generally provide more 

detail than is necessary for decision trees, making them less attractive and less cost effective for 

network-level applications. As a result, using pavement deflection testing for network-level 

analysis has been limited, even within agencies that extensively use a falling weight 

deflectometer (FWD) for project-level analysis.

However, some of these project-level techniques can be adapted to assist with network-level 

PMS applications. The key is to improve each technique in such a way that a simple parameter 

(or set of parameters) can be computed to describe the overall structural capacity of a uniform

pavement section. Applicable techniques to assess pavement structural condition should 

improve the accuracy of PMS through enhanced project scoping and timing, potentially saving 

transportation agencies considerable funds and reducing construction delays (and therefore user 

costs) from poorly timed or ineffective projects. States including Texas, Kansas, New Jersey, 

Virginia, and Alaska have successfully incorporated structural indices in network-level 

applications. Such techniques are also used in countries such as South Africa, Finland, 

Denmark, France, and Australia.

PROJECT OBJECTIVES

The primary objectives of this study were to identify, develop, verify, and recommend simplified 

deflection-based analytical techniques suitable for rapid automated screening of pavement 

structural capacity for inclusion in a network-level PMS. These techniques have been derived 

from information gathered from the Long-Term Pavement Performance (LTPP) database and 

from other highway agencies currently using structural information in their PMS.

(1) The success 
2

of this study hinges on identifying solutions that can be implemented readily in national, State, 

and local municipality systems.

Another objective of the study was to develop and recommend data collection procedures that 

maximize testing productivity and minimize risk while still providing adequate information for 

use in a typical PMS. Test point spacing and frequency of data collection are the two primary 

parameters of interest.

It is intended that the results of this study are applicable to agencies that do not use deflection 

testing in their PMS but still use nondestructive deflection testing as part of their project-level 

analysis and design activities.

DESIRED OUTCOMES AND PROJECT DELIVERABLES

The following list describes the project’s desired outcomes and deliverables:

• The development of a rational approach to evaluate deflection techniques capable of 

assessing pavement structural capacity for network-level analyses.

• The recommendation of practical and efficient techniques for evaluating deflection data 

for network-level analyses.

• Statistical procedures for determining the optimum test spacing and frequency of 

deflection measurements for network-level applications.

• Guidelines for considering the best time of day and/or period of the year for deflection 

data collection and procedures for incorporating historical data into the network-level 

deflection analysis.

• A prototype version of software that is capable of computing deflection-based parameters 

for network-level PMS applications using selected, simplified techniques.

• A final report describing the analysis approach, findings, and recommendations from 

the study.

• A stand-alone guide with step-by-step instructions for using deflection interpretation 

techniques for network-level analyses.
3

REPORT ORGANIZATION

This report documents the findings from phase 1 and phase 2 of the project. The information 

presented in this report is organized in the following chapters:

• Chapter 1 includes an introduction to the study, as well as background information, 

project objectives, desired outcomes, and project deliverables.

• Chapter 2 provides a literature review, including a summary of findings from previous 

studies and a list of the techniques for simplified load deflection data evaluation 

and analysis.

• Chapter 3 provides an assessment of LTPP data to support this investigation, including an 

evaluation of the need for supplemental data from other sources.

• Chapter 4 includes the methodology for evaluating and selecting applicable techniques 

for simplified evaluation and analysis.

• Chapter 5 includes the methodology for determining the optimum test spacing and 

frequency for network-level analyses.

• Chapter 6 includes guidelines for consideration of time of day and season of year for 

optimal data collection.

• Chapter 7 provides a practical example of how to apply the outcome of this research in 

existing PMS.

• Chapter 8 provides the conclusions and recommendations.

5

CHAPTER 2—LITERATURE REVIEW

INTRODUCTION

An essential part of this project was to conduct an extensive literature search. While FWD load

deflection data have long been used to carry out project-level analyses, using these data to 

conduct network-level surveys is performed less frequently. Nevertheless, the existing literature 

shows that several agencies are already using FWD data in their network-level pavement 

analysis procedures.

Some agencies have also developed procedures that may assist in the development of a 

simplified approach to using deflection data in a network-level analysis that links pavement 

structural parameters, determined through the use of FWD data to pavement performance.

A review of all available literature was duly conducted, including obtaining information from 

agencies outside the Unites States, to ascertain which agencies use deflection data, which 

approach they employ, and whether these particular approaches may be useful in the present 

study. All deflection parameters (measured or computed) included in this report refer to the 

Strategic Highway Research Program (SHRP) seven sensor positions.

(2)

LITERATURE REVIEW APPROACH

Relevant literature references were reviewed on the following subjects to achieve the literature 

review objectives:

• Network versus project-level structural analysis: Searched for differences and 

similarities in deflection data collection, such as parameters used, spacing, frequency,

and loading.

• Data collection: Searched and compiled information regarding data collection (sampling 

or systematic), section length, and spacing between tests.

• Data sources: Investigated the source of deflection data and what the data are used for in 

terms of network-level surveys, project-level surveys, or both.

• Data interpretation: Compiled information about how the data were analyzed 

(deterministic, probabilistic, combination, etc.).

• Required structural information: Identified which parameters were required and 

utilized for network-level structural analysis, such as the following:

o Center deflection (D0): The deflection at the center of the applied load.

o Curvature index (D0 ‒ Di): The difference between the center deflection and the 

deflection at a prescribed offset from the load center.

o Load-normalized and temperature-corrected center deflection ( D0 ).
6

o Radius of curvature (RoC).

o Various “AREA” values of the deflection basin.

o Closed-form and two-layer solutions.

• Relationship to performance: Searched for literature that reports practices and 

research on incorporating structural evaluation of pavements based on deflections 

and performance measures.

• PMS implementation: Compiled information on studies about implementation of 

deflection-based parameters on PMS.

• Report findings on each subject: Compiled relevant information from references 

grouped by key topics in tabular form.

It is crucial to establish a reasonable body of knowledge on these topics to address the following:

• Establish the objectives of a structural network-level analysis.

• Determine the necessary structural information.

• Decide which conditions pavement deflections are useful for providing the required 

information for a network-wide structural evaluation, 

• Determine performance indicators are currently used to link structural condition or 

integrity to the level of pavement distresses observed in the field.

SUMMARY OF FINDINGS FROM PREVIOUS STUDIES

Table 1 provides a summary of potentially relevant agency practices for FWD data collection 

and use for network-level analyses identified during the literature review study (see the complete 

table of references in appendix A).
Table 1. Summary of useful practices for FWD use in network-level analyses.

Agency and 

Publication

Test Point 

Spacing

FWD Test 

Frequency

FWD 

Sensor 

Positions

Limiting 

Factors Basic Details of the PMS Approach

California Department 

of Transportation 

(Caltrans); “Test to 

Determine Overlay and 

Maintenance 

Requirements by 

Pavement Deflection 

Measurements”(3)

N/A N/A N/A None; currently 

used for 

flexible and 

composite 

pavements only

Uses center deflection only, plus existing

asphalt concrete (AC) or AC + portland 

cement concrete (PCC) layer thickness.

Federal Highway 

Administration 

(FHWA); Review of the 

LTPP Backcalculation 

Results(4)

N/A N/A N/A None; may be 

used for 

flexible, 

composite, and 

rigid pavements 

alike

Uses Hogg model for subgrade modulus 

calculation. While it is possible that surface 

course stiffness can be derived using a 

related approach reported to FHWA by the 

authors, this is probably too complex and 

not worth the effort.

National Cooperative 

Highway Research 

Program (NCHRP);

Project 10-48:

Assessing Pavement 

Layer Condition Using 

Deflection Data(5)

Probably not 

studied

Probably not 

studied

SHRP 

positions, 

generally

None; all 

pavement types 

studied using 

LTPP database 

(flexible, rigid, 

and composite)

Uses easy-to-obtain deflection basin 

parameters and relates these parameters to 

observed pavement distresses.

FHWA; Temperature 

Predictions and 

Adjustment Factors for 

Asphalt Pavement 

(FHWA-RD-98-085)

(6)

N/A N/A N/A N/A The adjustment for asphalt pavements for 

temperature-at-depth and center deflection 

adjustments for pavement temperature may 

be used to assist in the present study.

7
Agency and 

Publication

Test Point 

Spacing

FWD Test 

Frequency

FWD 

Sensor 

Positions

Limiting 

Factors Basic Details of the PMS Approach

Kansas Department of 

Transportation

(KDOT); “NetworkLevel Pavement 

Deflection Testing 

and Structural 

Evaluation”

(7)

A minimum of 

three tests per 

mile; five is 

preferred

One-third of 

network per 

year; however,

one-fifth of 

network may 

be adequate

Unknown; 

probably 

unimportant

Flexible 

pavements only

Used data from one Kansas district on AC 

surfaces only (non-interstate), which is a

similar approach to the current study. Based 

on the 1993 American Association of State 

Highway and Transportation Officials 

(AASHTO) Guide for Design of Pavement 

Structures.

(8) The FWD, especially the 

center deflection value, added considerably 

to predictive capability of method used. 

Based on the concept of pavement 

structural evaluation (PSE). PSE was found 

to be twice as important to predict 

pavement performance as any other 

observable parameter. Recommended the 

use of Bayesian statistical models.

Alaska Department of 

Transportation 

(AkDOT); Modeling 

Flexible Pavement 

Reponse and 

Performance(9)

0.1 mi After repaving SHRP 

positions

No limits Deflections are converted to layer moduli, 

which are then used to obtain stress/strain 

values under a standard equivalent singleaxle load (ESAL). Transfer functions relate 

stress/strain to cracking in bound layers and 

permanent deformation in unbound layers.

Texas Department of 

Transportation 

(TxDOT); 

Incorporating a 

Structural Strength 

Index into the Texas 

Pavement Evaluation 

System (FHWA/TX88/409-3F)

(10)

0.5 mi One 

recommended 

per year

1 ft Flexible 

pavements less 

than 5.5 inches 

AC thickness

Structural strength index (SSI) varies from 

zero to 100 (weak to strong). Based on 

normalized basin parameters, such as outer 

deflections, surface curvature index (SCI), 

and center deflection under a 9,000-lb load. 

Can characterize subgrades and pavement 

structure independently in terms of relative 

stiffness. System based on statistical 

evaluation of deflections statewide.

8
Agency and 

Publication

Test Point 

Spacing

FWD Test 

Frequency

FWD 

Sensor 

Positions

Limiting 

Factors Basic Details of the PMS Approach

TxDOT; Network-Level 

Deflection Data 

Collection for Rigid 

Pavement(11)

0.5 mi N/A 1 ft Rigid 

pavements

Not very useful from an analytical 

standpoint; mostly gives recommendations 

regarding field test procedures, estimated 

costs for testing and analysis, and reference 

to maximum allowable deflections for rigid 

pavements for network testing.

Virginia Department of 

Transportation

(VDOT); NetworkLevel Pavement 

Evaluation of 

Virginia’s Interstate 

System Using the 

Falling Weight 

Deflectometer (Report

VTRC 08-R18)

(12)

0.2 mi 4–5-year cycle SHRP 

positions

None Flexible pavements were analyzed by 

calculating the subgrade resilient modulus, 

the effective pavement modulus, and the 

effective structural number (SN). Rigid and 

composite pavements were analyzed by 

calculating the area under the deflection 

basin and the static modulus of subgrade 

reaction (k-value).

National Laboratory for 

Civil Engineering; Use 

of Deflections at 

Network Level in 

England for 

Programming and 

Other Purposes(13)

N/A; Used 

deflectograph, 

complemented 

by FWD

3–5 years N/A Flexible 

pavements only

Used Transport and Road Research 

Laboratory (TRRL) equations to calculate 

residual life and strengthening requirements 

based on deflection. The conclusion was 

that deflection does not increase with time 

and in some cases actually decreases due to 

an increase in pavement materials stiffness 

due to aging, etc. This approach was used 

until 2000.

9
Agency and 

Publication

Test Point 

Spacing

FWD Test 

Frequency

FWD 

Sensor 

Positions

Limiting 

Factors Basic Details of the PMS Approach

South Africa; 

“Benchmarking the 

Structural Condition of 

Flexible Pavements 

with Deflection Bowl 

Parameters”(14)

0.2 km N/A 300 mm 

typical

Flexible 

pavements only

Pavement is divided into three zones based 

on depth. Uses basin parameters to 

characterize base, middepth, and subgrade 

structural condition such as “sound,” 

“warning,” or “severe.”

Association of 

Australian and New 

Zealand Road 

Transport and Traffic 

Authorities; Use of 

FWD in the Network 

Level Pavement 

Condition Survey(15)

N/A N/A 0, 900, and 

1,500 mm

Flexible and 

semi-rigid 

pavements

Uses adjusted SN as indicator for pavement 

bearing capacity. SN is calculated based on 

d0, d900, and d1500, in which d represents 

deflection and i is the distance from the 

center of the plate (0, 900 and 1,500 mm).

N/A = Not available.

1 mi = 1.61 km

1 inch = 25.4 mm

1 ft = 0.305 m

1 lb = 0.454 kg

10
11

Agencies Currently Utilizing Deflection Data for Network-Level Applications

Findings from the literature indicate that only five agencies use, or are planning to use, load 

deflection data directly within their PMS.

United Kingdom

The United Kingdom uses traveling deflectograph data, not FWD or dynamic load 

deflection data; therefore, these data are not applicable to the present study.

(13,16) The traveling 

deflectograph does not correlate well with the FWD (or even the rolling wheel deflectometer 

(RWD)) due to the large differences in loading time and the Benkelman beam style apparatus 

involved, among other salient factors. While researchers in the United Kingdom have tried to 

supplement their traveling deflectograph data with FWD data, they discovered that the two do 

not correlate well, as expected; therefore, the FWD was dropped in favor of the traveling

deflectograph. Interestingly, the old Caltrans traveling deflectograph, which was similar to the 

UK device, was dropped at least 30 years ago, first in favor of the Dynaflect® and later the FWD.

Alaska

AkDOT uses a multiyear cycle for deflection readings based on ongoing pre-and postrehabilitation projects. Their PMS approach using FWD data was only recently initiated.

(9) It

cannot be considered a simple process since back-calculation of sorts is currently used to 

determine remaining life. How well AkDOT’s FWD evaluation procedure actually translates to 

pavement distresses, and therefore to pavement life expectancy, remains to be seen. Alaska’s 

application of load deflection data within their PMS is relatively new. Accordingly, a few more 

years’ worth of data will be needed to evaluate structural versus performance correlations. At the 

time this report was written, AkDOT gathered over 300 mi (483 km) of FWD data on the Parks 

Highway. These data were subsequently used as an example of how to incorporate the simplified 

methodology developed herein and will be shown later in this report. 

Conversely, the methodology used to calculate the subgrade “seed” modulus using the AkDOT 

procedure is straightforward and immediately useable as a stand-alone parameter. Therefore, it

can be used to correlate the subgrade modulus from the LTPP FWD database to see how well 

that particular approach (i.e., a nonlinear subgrade modulus model) relates to the various 

performance indicators in the mature LTPP database. The AkDOT procedure currently applies to 

flexible pavements only; however, rigid pavements may be investigated using the same subgrade 

modulus closed-form back-calculation process.

Texas

TxDOT currently uses deflection data in their PMS for flexible pavements only (district 

optional). (See references 10, 11, 17, and 18.) The publication Incorporating a Structural 

Strength Index into the Texas Pavement Evaluation System has been in use since its publication 

in 1988 in some of Texas’s districts.

(10) It is currently used for relatively thin asphalt-surfaced 

pavements in 4 of 13 districts in Texas—Fort Worth, Houston, San Antonio, and Pharr. It is 

expected that the entire State will soon use the newer process shown in table 1.

(10)
12

In an older TxDOT method, network-level deflection basins were collected at selected locations 

in the State to determine averages and ranges for a variety of pavement thicknesses and subgrade 

types. Basin parameters were developed and used in lieu of a back-calculation approach due to 

the lack of pavement structural data (i.e., number of layers, layer thicknesses, and material 

types). The greatest drawback to this approach is that it does not provide an indication of 

remaining structural life or bearing capacity. This approach essentially uses two basin 

parameters: SCI and W7, which is the deflection measured 6 ft (1.83 m) from the FWD load 

center. SCI is the difference between the deflections measured at the center of the load plate and 

the deflection measured 12 inches (304.8 mm) from the load plate. From these two parameters, 

an SSI is determined from one of three tables: one for surface treated pavements, one for thin 

asphalt pavements, and one for intermediate and thick asphalt pavements. SSI is further adjusted 

for traffic and rainfall levels to arrive at a final SSI. SSI ranges from 100 for a 100 percent 

structurally adequate pavement to zero for a 100 percent structurally inadequate pavement

(meaning zero percent adequacy). This approach allows the user to determine where the 

inadequacies lie, whether within the subgrade or somewhere within the pavement structural 

section itself, above the subgrade.

Virginia

VDOT recently began using deflection data in their PMS, covering the entire network on a 

4- to 5-year cycle for both flexible and rigid pavements.

(12) The procedure is simple and 

straightforward. However, since it is relatively new, the current study will have to evaluate 

the relationship of Virginia’s structural determination procedures to pavement performance 

data in the LTPP database.

In developing the VDOT method, a two-phase evaluation of a proposed network-level structural 

evaluation technique was carried out in 2007 and 2008. Both phases were restricted to interstate 

pavements. In phase I, only I-64 and I-77 were included in the study. The results looked 

promising, so phase II was initiated on the remainder of Virginia’s interstate system. A final 

report was published in 2008, which concluded that network-level deflection testing could be 

used to address network needs in terms of rehabilitation strategies and funding management 

decisions.

(12) The author further suggested that the network-level structural analysis should be 

expanded to include Virginia’s primary network.

Pavement types in the study included flexible, rigid, and composite pavement structures. For 

flexible pavements, the analysis was conducted according to the 1993 AASHTO Guide for 

Design of Pavement Structures.

(8) For rigid and composite pavements, the analysis was 

conducted according to the 1998 Supplement to the AASHTO Guide for Design of Pavement 

Structures: Part II—Rigid Pavement Design and Rigid Pavement Joint Design.

(19)

For flexible pavements, the resilient modulus (Mr) is first calculated according to the 1993 

AASHTO Guide for Design of Pavement Structures.

(8) The effective pavement modulus (Ep) is 

calculated from the center deflection and subgrade modulus, also according to AASHTO 

procedures. Finally, an effective structural number (SNeff) is determined from Ep and the total 

pavement thickness above the subgrade.

(8)
13

For rigid and composite pavements, the deflection basin AREA and the static modulus of 

subgrade reaction, k, are used to quantify overall structural condition.

A cumulative distribution curve of SNeff and Mr was developed for all flexible pavements in the 

study. Similar curves were developed for center deflections and deflection basin AREA for rigid 

pavements. These distribution curves are used to identify structurally weak areas of the network 

for further project-level investigation.

One factor that contributed to the overall success of this approach is the availability of pavement 

layer data (thicknesses, material types, etc.) in VDOT’s Highway Traffic Record Information 

System database.

(20) Also noted were rather high subgrade Mr in the cumulative distribution 

curves. The 50th percentile value of the subgrade stiffness was around 12,500 psi (86,125 kPa). 

This may have been due in part to the presence of rigid or semi-rigid layers in the subgrade,

which the AASHTO method does not address, and in part due to the typical non-linear behavior 

of cohesive subgrades (with a lower effective modulus under the load than at increasing 

distances from the load). The 1993 AASHTO Guide for Design of Pavement Structures

equations utilize the outer deflection sensors to characterize the subgrade modulus, not the

true effective modulus of the subgrade under the load.(8)

South Africa

The Republic of South Africa uses FWD testing at 656-ft (200-m) intervals to ascertain the 

bearing capacity of three roadway “zones” or layers (surface, base, and subgrade). The 

methodology relies on direct deflection basin parameters, not back-calculation.

(14) A 

benchmarking technique was developed to relate direct deflection values and basin parameters 

to the structural condition of the pavement at both the project and network levels. This 

benchmarking technique can be used in the absence of detailed information regarding 

pavement composition.

The South African method correlates FWD deflections to structural layers or zones within the 

pavement structure. These zones are numbered 1 through 3, where zone 1 corresponds to the 

materials closest to the load plate within the pavement structure, extending out to 11.7 inches 

(300 mm) in terms of the deflection basin (and probably somewhat less in terms of depth within 

the structure). In zone 2, the inflection point in the deflection basin occurs and generally lies 

from < 1 to 2 ft (< 0.305 to 0.61 m) in depth below the pavement surface. Zone 3 extends from 

approximately 2 to 6.5 ft (0.61 to 1.98 m) from the center of the load plate and thus represents 

the deepest layers in the pavement structure—primarily the subgrade.

In the South African method, the following deflection parameters and associated pavement 

structural zones are represented:

• D0, or the maximum deflection as measured at the center of loading (also known as center 

deflection) is correlated to all three zones, since it represents the response of the entire 

pavement structure.

• RoC is correlated to zone 1 (the upper pavement layers) and is derived using the equation 

in figure 1.
14

• The base layer index (BLI) is correlated to zone 1 and is calculated using the equation 

in figure 2.

• The middle layer index (MLI) is correlated to zone 2 and is calculated using the equation 

in figure 3.

• The lower layer index (LLI) is correlated to zone 3 and is calculated using the equation 

in figure 4.

( ) 















− = 2 (1 / ) 0 200 0

2

D D D

L RoC

Figure 1. Equation. Calculation of RoC.

Figure 2. Equation. Calculation of BLI.

Figure 3. Equation. Calculation of MLI.

Figure 4. Equation. Calculation of LLI.

Where:

L = Diameter of the load plate of the FWD (mm).

D0 = Deflection at center of load plate (mm).

D200 = Deflection at 8 inches (200 mm) from the center of the load plate (mm). 

D300 = Deflection at 12 inches (300 mm) from the center of the load plate (mm). 

D600 = Deflection at 24 inches (600 mm) from the center of the load plate (mm). 

D900 = Deflection at 36 inches (200 mm) from the center of the load plate (mm).

These deflection bowl parameters are related to a structural condition rating according to the 

structural condition and the type of base layer, as described in table 2, extracted from Horak’s 

“Benchmarking the Structural Condition of Flexible Pavements with Deflection Bowl 

Parameters.”

(14)

The basin parameters LLI, MLI, and BLI are plotted against stationing for a particular roadway 

to facilitate the structural assessment procedure. This plot of structural condition is often used in 

conjunction with visual assessments to determine the type of rehabilitation required to restore the 

pavement to a good condition.

BLI = D0 - D300

MLI = D300 - D600

LLI = D600 - D900
15

Table 2. Structural condition associated with deflection bowl parameters.

(14)

Base Type

Structural 

Condition 

Rating

Deflection Bowl Parameters

D0

( )

RoC

(m)

BLI

( )

MLI

( )

LLI

( )

Granular base

Sound < 500 > 100 < 200 < 100 < 50

Warning 500–750 50–100 200–400 100–200 50–100

Severe > 750 < 50 > 400 > 200 > 100

Cementitious 

base

Sound < 200 > 150 < 100 < 50 < 40

Warning 200–400 80–150 100–300 50–100 40–80

Severe > 400 < 80 > 300 > 100 > 80

Bituminous 

base

Sound < 400 > 250 < 200 < 100 < 50

Warning 400–600 10–250 200–400 100–150 50–80

Severe > 600 < 100 > 400 > 150 > 80

Note: These criteria can be adjusted to improve sensitivity of benchmarking.

1 mil = 25.4

1 ft = 0.305 m

The surface modulus is calculated at the various sensors and plotted against distance from the 

load plate to assess nonlinearity. The standard Boussinesq equations are used for this purpose. 

Points where the surface modulus increases with increasing distance from the load center are 

regarded as “stress softening.” If the surface modulus is similar for all measured deflections, the 

subgrade is regarded as linear-elastic. Decreasing surface modulus with increasing distance from 

the load center indicates a “stress stiffening” subgrade.

Agencies Utilizing Deflection Data in a Manner Potentially Useful to Enhance NetworkLevel PMS Applications

In addition to the previously listed agencies that already utilize load deflection data within their 

PMS, the following agencies use deflection data with potential network-level PMS applications:

• Caltrans: Currently uses deflection data for project-level pavement analysis and design

only; however, the design method is simple and straightforward and was therefore tried

during phase 2 of this study as a potential network-level PMS tool.

(3)

• KDOT: This approach is simple and straightforward. If the equations can be used to 

regress against LTPP performance measures, this could have been tried; however, since

KDOT used this approach for flexible pavements only and only in one district for a trial 

project, the methodology was not further investigated.

(7)

The following publications do not describe deflection data applications of specific agencies, but 

they are relevant to the scope of this project:

• NCHRP Project 10-48: This study was similar to the current study, and it utilized 

the LTPP database.

(1) Equations cover flexible, composite, and rigid pavements as 

deflections relate to performance.

(5)

μm μm μm μm

μm
16

• Temperature Predictions and Adjustment Factors for Asphalt Pavement (FHWA-RD98-085): This study applies to asphalt temperature corrections and mid-depth temperature 

determinations for asphalt pavements only (not needed for concrete but likely applicable 

if needed).

(6) The equations found in this publication are potentially useful for 

performance measures that relate FWD center deflection to pavement performance.

However, after regressing against both temperature-corrected and temperatureuncorrected values of center deflection (D1) (or their inverse), it was determined that no 

improvement in any of the logistic models resulted.

(6)

• Use of FWD in the Network Level Pavement Condition Survey: This study utilizes 

center deflection and measures of curvature, along with roughness, rutting, and skid

resistance.

(15) Center deflection (or its inverse) was utilized during this research, with 

some (but not universal) success. The results are presented later in this report.

Identified Techniques for Simplified Evaluation and Analysis

Based on the literature review and summary of useful practices presented in table 1, a list of 

deflection techniques was created. Several techniques were considered to be applicable to the 

scope of this project and were selected for further analysis. The following techniques and 

equations were selected when applicable:

1. D1, measured at the center of the load plate in millimeters. (See references 14, 3, 7, 15, 

and 21.)

2. Direct deflection basin, D1 through D7, where Di is the deflection measured at sensor i = 1 

through 7 according to SHRP’s seven sensor positions.

(2,21)

3. Curvature index (CI) (see figure 5).

(14,15,21)

CIi = Di − Di+1

Figure 5. Equation. Calculation of CIi.

Where Di is the deflection measured at sensor i = 1 through 7.

4. Shape indicator (F) (see figure 6).

(21)















 − = − +

i

i i

i D

D D F 1 1

Figure 6. Equation. Calculation of Fi.

Where i is the sensor 1 through 7.
17

5. Slope variance (S) (see figure 7).

(21)

i D Di S = 1 −

Figure 7. Equation. Calculation of Si.

Where i is the sensor 1 through 7.

6. Reciprocal indicator (I) (see figure 8).

(21)

i

i D

I 1 =

Figure 8. Equation. Calculation of Ii.

Where i is the sensor 1 through 7.

7. Rectangular area indicator (RA) (see figure 9).

(21)

i

i

i

i

D

D

RA

7

1

= Σ = =

Figure 9. Equation. Calculation of RA.

Where i is the sensor 1 through 7.

8. Trapezoidal area indicator (TA) (see figure 10).

(21)

i

i

i

i

D

D D D

TA

26

1 7 2

= + + Σ = =

Figure 10. Equation. Calculation of TA.

Where i is the sensor 1 through 7.

9. SNeff (see figure 11).

(17,18,7)

( )

1 / 3 0.0045 eff D Ep SN = ⋅ ⋅

Figure 11. Equation. Calculation of SNeff.

Where D is the total pavement layer thickness above the subgrade (mm) and Ep is the 

effective pavement modulus, computed using the equation in figure 12.



















































 



 



 − +

+

















+

= ⋅ ⋅

−

p

r

p

r

E

a

D

M

E

a

D M

d p a

2

1

2

2

3

0

1 1

1

1 1.5

Figure 12. Equation. Calculation of d0.
18

Where d0 is deflection at the center of the load plate (mm), P is load plate pressure (MPa), 

a is load plate radius (mm), D is pavement layers thickness above subgrade (mm), and Mr is

the resilient modulus, given by the following expression:

d r

P M

r

r

2.4 =

Figure 13. Equation. Calculation of Mr.

Where Mr is resilient modulus (MPa), P is applied load (kN), dr is deflection at a distance r

from the center of the load (mm). r is chosen as the distance to the seventh sensor.

10. Deterministic-empirical back-calculation model (closed form solution) for effective subgrade 

modulus (Hogg model).

(4)

















∆ 





 







−

+ − = l

p

S

S

E I

0

0

0

0 0

0 2(1 )

(1 )(3 4 )

μ

μ μ

Figure 14. Equation. Calculation of E0.

Where E0 is subgrade modulus (effective) (MPa), μ0 is Poisson’s ratio for subgrade, S0 is the 

theoretical point load stiffness (MPa), S is the pavement stiffness (MPa), P is applied load

(kPa), ∆0 is the deflection at center of load plate (mm), L is the characteristic length (mm), 

and I is the influence factor.

(4)

11. Radius of curvature, shown in figure 1 (page 14) for completeness.

(14)

12. Elmod, nonlinear subgrade parameters.

(22)

n

Esg C 



 



 = σ'

σ

Figure 15. Equation. Calculation of Esg.

( )





 





















=

1

2 2log

log

0( 2)

0 1

r

r

E

E

n r

r

Figure 16. Equation. Calculation of n.

n

r

n

r

E r E r C















 − 















− =

' '

( 1) ( 2)

0( 1) 0( 2)

σ

σ

σ

σ

Figure 17. Equation. Calculation of C.
19

( )

(1 )

2

0( )

r

r r d

u P E

π

− =

Figure 18. Equation. Calculation of E0(r).

θ

π

σ 3

( ) 2 cos

2

3

R

P r =

Figure 19. Equation. Calculation of .

Where:

Esg = Subgrade modulus (kPa).

C = A layer constant, n is a layer constant representing the nonlinearity of the subgrade.

σ = Principle stress (MPa).

σ’ = Reference stress (14.5 psi (0.1 MPa)).

E0(r) = Surface modulus at distance r from load center (MPa).

r = Horizontal distance from load center (mm).

z = Vertical depth with respect to the pavement surface (mm).

= Principle stress at depth z (assuming z = r).

μ = Poisson’s Ratio, d(r) is deflection at distance r from load center (mm).

P = Applied load on pavement surface (MPa).

R = Distance to evaluation point (R2

= r

2 + z2

).

Θ = Angle with respect to vertical axis through load center.

In addition to the parameters mentioned, the load transfer efficiency (LTE) value was calculated 

for rigid pavements. There are two ways of calculating LTE—in one method, the FWD test is 

performed at the slab before the joint (joint approach), and in the second method, the FWD test is 

performed at the slab after the joint (joint leave). An analysis of both was conducted, and the 

values were close to each other. Therefore, for simplification, only one LTE value was chosen. 

The option was for the first method with LTE at the joint approach because it does not require 

any modification on the configuration of the FWD. The LTE at joint approach is referred to 

as “LTEA” in this report and was calculated as the ratio of the deflection at the third sensor 

(12 inches (304.8 mm) from the center of the load) and the deflection at the center of the load.

CONCLUSIONS FROM THE LITERATURE REVIEW

Several successful techniques for use in network-level PMS applications were identified through 

the literature search. A few highway agencies have been using deflections as part of their 

network condition assessment. Among those, Texas, Virginia, and South African approaches 

were selected for further investigation in succeeding tasks with little or no modification. In 

addition, there were several techniques that could be utilized in the present study even though 

these techniques were not used in a network-level PMS. Combining all sources available, a list 

of potential applicable techniques that are relevant to the scope of this project was created as a 

result of the literature review and is shown in table 1. These deflection techniques formed the 

basis for the analyses carried out in this project.

σ(r)

σ(r)

21

CHAPTER 3—ASSESSMENT OF DATA

REVIEW AND ASSESSMENT OF DATA FROM LTPP STUDIES

Data Selection Criteria

The goal of this task was to review data from LTPP studies that are relevant to the scope of this 

study. Of particular interest was the assessment of LTPP sites that had sufficient deflection 

information, site characteristics (structure, climate conditions, traffic, and age), and historical 

performance data consisting of load-related distresses and roughness levels. Data from both 

General Pavement Studies (GPS) and Specific Pavement Studies (SPS) were considered. SPS 

sites are particularly valuable due to the extensive material testing and performance data 

concurrently available. In addition, sites from the Seasonal Monitoring Program (SMP) provided

useful information for studying environmental effects, as well as the timing and frequency of 

deflection testing for network-level coverage.

One objective of a PMS is to establish long-term maintenance and rehabilitation (M&R) 

strategies for the network. Therefore, only those pavement sections for which the database 

included at least 5 years’ worth of data were included in the analysis database.

Data Elements Needed for Analyses

The following data elements were identified as necessary for the analysis:

• Performance data:

o AC surfaces.

o Rutting.

o International Roughness Index (IRI).

o Fatigue cracking.

o Transverse cracking.

o Longitudinal cracking.

o Alligator cracking.

o PCC surfaces.

o IRI.

o PCC faulting at joints.

o PCC faulting at cracks.
22

o Transverse cracking.

o Longitudinal cracking.

o Durability cracking.

o Number of corner breaks.

• Pavement structure:

o Pavement layer type.

o Representative thickness for a layer in a section.

o Type of material (AC, PCC, etc.).

• Pavement deflection data:

o Peak deflection values.

o Drop height.

o Peak load (peak load equals peak plate pressure).

o Lane number.

o Lane location.

o Measured pavement surface temperature.

o Time of day.

• Climatic data:

o Average temperature.

o Average precipitation.
23

Table 3 provides a summary of data types that were assessed in this investigation, along with the 

corresponding LTPP data tables containing the required data elements.

Table 3. LTPP database tables used to support data collection.

Type of Data Data Element Chosen Relevant LTPP Tables

Traffic • Average annual daily 

truck traffic (AADTT)

• Vehicle classifications

TRF_MONITOR_VEHICLE_DISTRIB

Climate Temperature CLM_VWS_TEMP_MONTH

Precipitation CLM_VWS_PRECIP_MONTH

FWD 

deflection 

surveys

Deflection data MON_DEFL_DROP_DATA

Test location MON_DEFL_LOC_INFO

Test temperature MON_DEFL_TEMP_VALUE

MON_DEFL_TEMP_DEPTHS

FWD sensors MON_DEFL_DEV_SENSORS

Performance Rutting MON_T_PRF_INDEX_SECTION

Longitudinal profile MON_PROFILE_MASTER

Hot mix asphalt (HMA)

surface distresses

MON_DIS_AC_REV

PCC faulting MON_DIS_JPCC_FAULT_SECT

PCC surface distresses MON_DIS_JPCC_REV

Structure • Layer type (material)

• Layer thickness

TST_L05B

General 

information

• Construction history

• LTPP assignment date

• Experiment type

EXPERIMENT_SECTION

Analysis Database Development

The LTPP Standard Data Release (SDR) 23 database (the most up-to-date version at the time this 

study was conducted) was examined for the identified data elements to determine the extent of

data availability.

(1) Data were extracted from the LTPP database, imported into a Microsoft 

Access® analysis database, and stored in various data tables. These tables were set up according 

to the principles of the relational databases so that they could be manipulated and linked together 

for various analysis purposes.

Data Review Process

Data for the sites that satisfied the data selection criteria were reviewed for quality, 

reasonableness, and availability in light of supporting the evaluation of identified 

deflection techniques.

The first step in the data review process was to eliminate test sections that had less than 5 years 

of performance and/or deflection data from the beginning of the monitoring period. In the 

sequence, quality and reasonableness were evaluated for all sections selected. The performance 

plots and deflections versus time were then visually inspected. Outliers and unreasonable trends 
24

were identified for a more detailed evaluation. A summary of the data assessment results is 

presented in the following sections.

Outliers identified in performance trends were marked for possible exclusion from the datasets. 

Ultimately, whether an outlier was excluded depended on its influence on the performance trend 

over the years that data were collected and its impact on predicting future performance. Details 

of this approach are provided in chapter 4 of this report.

ASSESSMENT OF DATA TO SUPPORT EVALUATION OF IDENTIFIED 

TECHNIQUES

All deflection data collected during the experiment were obtained from the LTPP SDR 23 

database and assessed.

(1) In total, there were 1,027 sections in the SPS and GPS experiments with 

5 or more years of performance and deflection data available. These sections include all 

pavement types—flexible, rigid, and composite. These sections may or may not have been 

rehabilitated during the course of data collection. Table 4 lists the experiments, number of 

sections available with deflection and performance data, and average period of time of 

data coverage.

Table 4. LTPP data availability to support evaluation of identified techniques.

Pavement 

Type

Experiment 

Type

Number of 

Sections with 

FWD Data

Distress Data 

Availability

(average years)

Flexible

GPS-1 233 12.8

GPS-2 146 13.4

GPS-6A 62 11.6

SPS-5 152 12.7

Total 593

Rigid

SPS-6 51 11.0

GPS-3 133 14.5

GPS-4 69 13.1

GPS-9 21 13.3

Total 274

Composite

GPS-7A 35 10.9

SPS-6 125 12.7

Total 160

Impact of M&R on Pavement Performance Data

In addition to verifying performance requirements and deflection availability, it was also 

important to consider any M&R work on the LTPP lane of the analysis sections. When one 

section is rehabilitated, performance invariably improves, and this affects the outcome of the 

analysis. Of the 1,027 sections selected, 47 of the flexible sections, 105 of the rigid sections, and 

97 of the composite sections had been rehabilitated (almost 25 percent of all sections). An 

approach to identify these sections and split them based on the rehabilitation work performed 

(i.e., change in structure and reduction of distress level) was developed. The main reason for 

performing this type of analysis was the possibility of increasing the number of available 
25

representative pavement sections, especially for the more sparsely populated rigid and composite 

pavement types.

The multiple section analysis was designed to enhance the chances of using sections with 

rehabilitation work performed during the monitoring period. Usually, any rehabilitation work 

done on the pavement is indicated in the LTPP database by a change in construction number. 

This is an event number used to relate changes in pavement structure with other time-dependent 

data elements. This field is set to “1” when a test section is accepted into the LTPP program and 

is incremented with each M&R activity.

The first step was to plot the performance data as a function of time for all sections. A simple 

macro-based code was written to expedite this process. The analysis of performance change is 

required because sometimes the M&R work is done outside the LTPP lane (e.g., at the shoulder) 

with no implication on LTPP lane performance.

For this analysis, the IRI was the performance measure used to determine the cutoff date to split 

the section based on recorded M&R activities. IRI is sensitive to M&R work performed on the 

pavement, and IRI measurements are more frequent in the LTPP distress survey campaign, 

which enhances the chances of finding sections that can be successfully split and still provide 

enough data for analysis.

Figure 20 shows section 06-0509, which illustrates how the section split was done based on 

rehabilitation work executed on the pavement. This example is a flexible pavement section 

located on I-40 in California, and the figure shows the variation of roughness over time. There 

were two rehabilitation interventions executed during the time the section was monitored. Three 

distinct pavement structures are identified. The first subsection (A) corresponds to the pavement 

from the original construction. The first split creates another subsection (B) with a new structure 

due to partial milling of the existing pavement and placing a hot mix recycled asphalt concrete 

overlay. The second split creates the third pavement subsection (C) due to a single layer of 

surface treatment applied to the existing surface. These two splits yield the following subsections 

and pavement structures:

• Structure A has a construction number index of 1, corresponding to the following original 

pavement structure:

o Untreated subgrade.

o Unbound (granular) subbase.

o Bound (treated) base.

o HMA concrete.
26

• Structure B has a construction number index of 2, corresponding to partial milling of the 

existing surface layer in A, followed by filling and overlay using a hot recycled asphalt 

concrete mix.

• Structure C has a construction number index of 3, which corresponds to another HMA

concrete overlay placed on top of B.

1 inch = 25.4 mm

1 mi = 1.61 km

Figure 20. Graph. Variation of roughness in section 06-0509.

After the multiple section analysis was concluded, each of the three new subsections was 

reevaluated based on the 5-year performance criterion. The first subsection (A) was excluded 

from the analysis because it had less than 5 years of performance data. Subsections B and C both 

had more than 5 years of performance data and were therefore included in the project’s dataset.

This process was carried out on all LTPP sections selected to support the evaluation of simplified 

deflection-based analysis techniques. Table 5 shows the final data assessment summary after 

performing the multiple section analysis. Notice that if the sections that received one or more 

M&R procedures after being assigned to the LTPP database were excluded altogether from the 

dataset, the total number of available sections would have been 827. After splitting the sections 

and including the subsections with 5 years or more of performance data, the total number of 

available sections increased to 1,033. Accordingly, the multisection analysis minimized the loss 

of LTPP data points available for the study.
27

Table 5. Data assessment summary after multiple section analysis.

Pavement Type Total Sections 

Selected Sections After 

Multiple Section Analysis

Flexible 573 623

Rigid joint plain 

concrete pavement 

(JPCP) 127 175

Rigid joint reinforced 

concrete pavement 64 79

Composite 63 156

Total 827 1,033

Note: Total sections include sections before multiple section split and excluded 

rehabilitated sections.

Analysis of Deflection Data

Deflection data were analyzed for quality and reasonableness. Prior LTPP studies investigated 

the quality of deflection data, and the recommendations and final tables originating from these 

studies were used as the source of data mining for this project.

(23) After the data were extracted 

into spreadsheets, each deflection-based technique or parameter was computed. Table 1 lists the 

deflection techniques investigated in this project.

ASSESSMENT OF DATA TO SUPPORT OPTIMUM TEST SPACING AND 

FREQUENCY

LTPP Data to Support Optimum Test Spacing Analysis

As part of phase I, the applicability of LTPP data for this type of analysis was verified. One of 

the concerns with LTPP data was the limited length of the LTPP sections (generally 500 ft

(152.5 m)), which is not ideal for a statistical analysis of optimum test point spacing on the 

network level. A theoretical statistical study was conducted to evaluate the implications of 

different sampling strategies (i.e., different test spacings) on the expected error of average 

deflections of homogenous road segments, when compared with comprehensive test spacings. 

The comprehensive test spacings were defined as the typical 0.1-mi (0.016-km) spacing 

commonly used by transportation departments for project-level FWD testing. The theoretical 

statistical study was then compared to field data obtained from State transportation departments.

Supplemental Data to Support Optimum Test Spacing Analysis

Supplemental data were required to investigate optimum FWD test spacings for network-level 

deflection data collection. FWD data from three State transportation departments were obtained 

and used to test results obtained from the theoretical statistical study.

LTPP Data to Support Optimum Test Frequency Analysis

Selected sections from the GPS and SPS studies were monitored for temperature and moisture 

at higher-than-normal intervals for distress, deflection, and longitudinal profile (IRI). These 

sections were part of the SMP database and were classified as either flexible or rigid pavements. 
28

Table 6 shows the classification of these SMP sections and the availability of FWD data from 

these sections.

Table 6. FWD data availability for SMP sites.

Pavement 

Type

Experiment 

Type

Number of SMP 

Sections with 

FWD Data

Number

of Years

(Average)

Flexible

SPS-1 10 13.7

SPS-5 1 16.6

SPS-8 2 14.1

SPS-9N 1 14.0

SPS-9O 1 9.3

GPS-1 26 8.8

GPS-2 5 8.9

Total 46

Rigid

SPS-2 4 13.6

GPS-3 8 17.7

GPS-4 6 21.0

Total 18

The SMP data sections were scrutinized in the same manner as was used for the GPS and SPS 

sections for data quality and reasonableness. The objective of incorporating the SMP sections 

was to provide data elements for the analysis of frequency of deflection measurements for 

network-level applications. Moreover, the data were used to evaluate and develop guidelines for 

the optimum time of day and season of year for FWD (or equivalent deflection testing device) 

data collection.

After initial inspection of data availability, it was found that monthly collection of data in most 

SMP sections occurred for about 2 years (or a maximum of 3 years). This volume of data 

reduced the chances for a robust assessment of the optimum frequency of FWD data collection 

for network-level applications. Therefore, it was decided to complement the dataset with 

additional LTPP sections from the dataset defined for the study of deflection-based techniques. 

The approach for using both datasets is further described in chapter 5 of this report.

LTPP Data to Support Time of Day and Day of Year Analysis

Different agency practices and provisions related to time-of-day and time-of-year data collection 

and analysis were reviewed. For example, the UK highway agency has a requirement for 

network-level deflectograph data collection from March 15 to June 15 and from September 15 to 

November 30. This requirement is primarily based on the climate in the United Kingdom. For 

the United States, different climate zones will most likely have different periods during which 

data collection will be most favorable to capture useful network-level deflection data. The subset 

of the LTPP database used to evaluate the deflection techniques was also used to analyze FWD 

data for different climatic zones that were taken during different months to determine favorable 

data collection periods for different regions.
29

CHAPTER 4—EVALUATION OF APPLICABLE LOAD DEFLECTION TECHNIQUES

Deflection data analysis provides qualitative and quantitative assessment of the structural 

integrity and bearing capacity of a pavement. Pavements with poor structural quality are more 

likely to develop distresses prematurely. It is commonly expected that the rate of deterioration 

increases as the structural condition worsens. Identifying pavements in poor structural condition 

is important to prevent early and rapid development of load-related distresses. This is the main 

motivation for the approach presented in this chapter.

Based on these premises, a probabilistic approach was developed to determine the likelihood of 

premature failure using load deflection techniques. Premature failure is defined by the presence 

of excessive distress (i.e., levels of distress higher than design threshold) occurring prior to the 

end of the design life of the pavement section.

Deflection data are commonly used at project-level analysis, mostly through back-calculation of 

layer moduli for overlay design purposes. Limited use has been observed at network-level 

analysis, in part due to difficulties in establishing thresholds to guide the structural evaluation. 

On such occasions, deflection data are used to create a rating system which yields a qualitative 

assessment of the structural condition. This assessment is used to determine prospective M&R 

treatments or remaining service life of the pavement. The rating criteria are often based on 

experience and common trends observed in the network.

The probabilistic approach proposed in this research can be used to establish thresholds for 

deflection data based on performance measures and assist with the creation of the network-level 

structural decision matrix. The following list includes benefits of using a deflection-based 

probabilistic model sensitive to structural pavement performance:

• It provides a direct link to pavement performance by estimating the likelihood of the 

development of load-related distresses in early stages of the pavement’s service life. The 

intent is not to have a regression predictive model based on deflection data, but rather a 

simplified procedure to identify critical sections with a high likelihood of developing 

structural distresses prematurely.

• Rating criteria can be created in the same manner equivalent to the functional decision 

matrix. Different tiers of structural quality can be defined based on deflection thresholds 

and the likelihood of acceptable performance. The structural decision matrix can then 

follow rating criteria similar to the functional decision matrix which facilitates the 

implementation in existing PMS algorithms.

• The probabilistic models can be locally calibrated to meet the network characteristics 

(e.g., typical surface distresses observed, interval between M&R projects, and the 

threshold of acceptable limits for distresses).

• The probabilistic models can be recalibrated as new survey data are collected.
30

ANALYSIS APPROACH

Binary Logistic Model

Logistic regression is useful to predict the outcome of an event based on a set of predictor 

variables. Logistic models are best used when the dependent variable is dichotomous (i.e., 

variables that assume binary values, such as acceptable and not acceptable). It is a powerful 

analysis tool to model complex problems where the number of variables affecting the outcome 

is large.

(24)

Formulation and Calibration

The logistic regression model general equation is provided in figure 21. In this case, P is the 

probability that an event will occur, and b is the exponent parameter in logistic distribution, 

which is a linear function of the predictor variables, as given in general form by the equation in 

figure 22. The event is defined as the performance of the pavement section, “acceptable” for 

sections outlasting the design life and “not acceptable” for sections exhibiting premature failure. 

The predictor variables, also known as explanatory variables, are selected to best explain the 

behavior of the event. In this research, the predictor variables were load deflections and site 

characteristics, such as climate, traffic, and pavement structure. A typical logistic model 

probability function of a predictor variable X is shown in figure 23.

( ) 1

1 b P evente− = +

Figure 21. Equation. General formulation of the logistic model.

0 11 2 2 n n b a ab ab ab =+ + ++ 

Figure 22. Equation. General linear formulation for the exponent term of the 

logistic model.
31

Figure 23. Graph. Typical logistic model probability function of a predictor variable X.

Predictor variables can be continuous (e.g., traffic volume) or discrete (e.g., pavement subgrade 

type assigned to coarse- or fine-grained soil). The dichotomous event is modeled as binary 

numbers—1 for acceptable and 0 for not acceptable. The model coefficients are computed using 

optimization algorithms. The most widely used is the maximum likelihood estimate. In this 

algorithm, the coefficients of the predictor variables are obtained to maximize the probability of 

the event occurring. The maximum likelihood estimate is well suited for problems in which the 

event occurs in the majority of the cases. This is the case in pavement performance where the 

majority of the pavements are expected to perform well.

There is no limitation to the number of predictor variables used. In fact, it is part of the process 

to eliminate variables with no significant relevance to the probabilistic function. This 

characteristic greatly helps the analysis—there is no need to refine the selection of variables,

and all possible candidates can be considered. The selection of significant variables is achieved 

through a stepwise regression. At first, all predictor variable candidates are used in the 

calibration process. The predictor coefficients are calculated using the optimization algorithm,

and the significance of each predictor to the probability function is computed. One by one 

according to step, the predictors with the least significance to the problem are eliminated.(25)

The process is concluded when all remaining variables have significance levels higher 

than 95 percent or the maximum number of iterations is reached. This approach is called 

“backward elimination.”

Conventional statistics cannot be used to measure the goodness-of-fit of binary logistic models. 

Instead, the receiver operating characteristics (ROC) curve is used to evaluate the accuracy of the 

model. ROC curves have been used in signal detection theory to depict the tradeoff between hit 

rates and false alarm rates of classifiers, and they are also used in medical decisionmaking.

(26)
32

Recently, ROC curves have also been used in data mining research. One important characteristic 

is that ROC analysis allows the selection of possibly optimal models and allows researchers to 

discard suboptimal ones independently from the class distribution of the predictor.

ROC curves are useful for organizing predictors and visualizing their performance. The 

ROC curve is drawn using the true positive rate (TPR) and false positive rate (FPR). TPR is 

determined by the number of true positive predictions normalized by total number of positive 

observed values. Conversely, FPR defines how many incorrect positive results occur among all 

negative samples available during the test.

The ROC space is defined by FPR and TPR as the x- and y-axes, respectively, which depict the 

relative trade-offs between true positive and false positive. TPR is often described as the 

sensitivity of the model, while (1 ‒ FPR) is often seen as the true negative rate (TNR) or 

specificity. Therefore, the ROC curve is also referred to as the sensitivity versus

(1 ‒ specificity) curve.

Each case consisting of a prediction and observed values represents one point in the ROC space. 

Given the discrete nature of the problem (i.e., the predicted probability is associated with a 

discrete definition of pavement performance, acceptable or not), algorithms are used to create the 

ROC curve.

(26)

An example of an ROC curve is shown in figure 24. Several points in the ROC curve are 

important to note. The best possible prediction would yield a point in the upper left corner or 

coordinate (0,1) of the ROC space, representing 100 percent sensitivity (no false negatives) and 

100 percent specificity (no false positives). The (0,1) point is also called a perfect classification. 

A completely random guess would give a point along a diagonal line, also referred to as line 

of no discrimination, which consists of points (0,0) and (1,1). Points above the diagonal line 

indicate good classification results. In comparative terms, one point in ROC space is better than 

another if it is to the northwest (TPR is higher, FPR is lower, or both) of the first.

Figure 24. Graph. Example of an ROC curve.
33

The area under the ROC curve defines the goodness-of-fit of the predictions. In an analogy with 

measures of linear optimization techniques, the area under the ROC curve can be viewed as the 

R2 value. By definition, the area under the ROC curve cannot be lower than 0.5, which 

corresponds to the reference line in figure 24. The highest value is determined by the boundary 

of the graph, which represents the perfect classification when the area under the ROC curve 

equals 1.

In addition to the goodness-of-fit, the ROC curve is used to define the cutoff value of the model. 

This is an important parameter that defines how the results from the probability density function 

can be interpreted in a binary system (i.e., the threshold used to separate probabilities that are 

referred to as acceptable and not acceptable). The cutoff is defined as the probability value that 

corresponds to the point in the ROC curve closest to the perfect classification point (0,1). When 

the cutoff is used to convert the predicted probabilities into binary outcomes, the model yields 

the highest level of accuracy (i.e., highest TPR and TNR).

Stochastic Approach to Evaluate Load Deflection Techniques to Network-Level 

Applications

The objective of a pavement design is to provide a structure that will exhibit adequate 

performance throughout its design life. In this case, performance is defined as the level of 

distresses that can affect the ride quality of the pavement or its structural adequacy. Therefore, a 

pavement has acceptable performance if distress levels do not exceed the threshold during a 

period of time (e.g., fatigue cracking does not exceed 25 percent of the total area in 15 years of 

service). Since the logistic model describes the likelihood of an event being acceptable or not as 

a function of a predictor variable, it can be used to model probability of acceptable performance 

with measurements of deflections or parameters (techniques) computed from them.

The goal of the stochastic approach proposed is to use the probability density function to obtain 

information about the pavement structural condition required to achieve the desired performance 

during a period of time. This new knowledge can then be used to define strategic treatments 

(maintenance or rehabilitation) to be used in the PMS optimization process.

A typical logistic model probability function is shown in figure 25. It describes the likelihood of 

the pavement section to exhibit acceptable performance in a particular distress as a function of a 

given deflection parameter, named “predictor variable X.” In this example, the cutoff value was 

determined from the ROC curve and plotted in the figure.

In the proposed stochastic approach, the probability density function is used to determine the 

thresholds that define the structural condition. By definition, the cutoff value in a logistic model 

determines how to convert the continuous probability prediction as a dichotomous outcome 

(i.e., predicted probabilities above the threshold are defined as acceptable while others are 

defined as not acceptable). In addition to the cutoff threshold, other values can be used to further 

detail the structural condition. As an example, figure 25 describes a second threshold created at 

the 0.4 probability level and used to define sections with fair structural condition from poor ones.

(Note that this definition is arbitrary and can be adjusted to better fit an agency’s rehabilitation 

practices or network characteristics.)
34

Figure 25. Graph. Example of logistic model probability function of a predictor variable X

used to create a structural decision matrix.

Once thresholds and their respective deflection parameters are identified, a structural decision 

matrix (also referred to as a structural rehabilitation matrix) can be generated. Table 7 shows 

an example of a structural decision matrix obtained from the probability density function in 

figure 25.

Table 7. Example of structural decision matrix.

Structural 

Condition

Deflection 

Parameter

Good < 200

Fair 200–350

Poor > 350

The advantages of the stochastic process to evaluate the structural condition of the pavement for 

network-level analysis are as follows:

• The structural condition is related to the performance through a probability 

density function.

• The probability density function is based on qualitative performance measure—

acceptable and not acceptable.

• The stochastic model is site-specific (i.e., additional variables may be incorporated that 

reflect site characteristics, such as traffic and pavement structure).
35

• Different structural decision matrices can be defined based on different types of distress. 

Therefore, the final evaluation can be made based on the most critical or the most 

typical distress.

• The calculations are simple and do not require an interactive process. Therefore, it can be 

automated and incorporated in virtually any PMS in which deflection data are available.

• The logistic models can be calibrated locally to enhance its goodness-of-fit and accuracy 

of predictions.

• Deflection data obtained from project level analysis or quality control after construction 

can be used in this process.

ANALYSIS STEPS

The evaluation of applicable deflection techniques was based on the quality and accuracy of the 

corresponding logistic model developed. A selection process was established to evaluate each 

model within each distress group and pavement type (e.g., roughness in flexible pavements). 

The evaluation criteria considered the accuracy of the logistic model, the consistency with 

engineering principles, and errors in the predictions (error types I and II). The entire analysis 

process can be summarized in the following steps:

Data preparation:

1. Compile performance measurements, deflections, pavement structure, climate, and traffic 

for each eligible site in the LTPP database.

2. Compute deflection techniques as referenced in table 1.

3. Rate the performance over time as acceptable or not acceptable according to 

load-related distresses.

4. Prepare a subset of the data for model validation.

Evaluation of selected techniques based on observed performance:

1. Conduct a preliminary screen to sort out the best deflection techniques as potential 

candidates for logistic model development.

2. Develop and calibrate a logistic model using the LTPP analysis database. There should be 

one model developed for each load-related distress using each screened deflection technique.

3. Compute descriptive statistics of each model.

Verification of deflection techniques:

1. Compare stochastic analyses of performance, inferred by the deflection technique under 

study, with measured pavement performance.
36

2. Adjust the logistic model based on previous comparisons.

3. Conduct sensitivity analysis of model parameters.

Validation analysis:

1. Analyze the models using an LTPP set-aside dataset for validation (part of the database not 

used to develop the models).

2. Perform a theoretical analysis through mechanistic simulations.

Selection of deflection technique:

1. Recommend logistic models based on deflection parameters for different pavement types and 

critical distresses.

The following sections describe the steps in the analysis process in greater detail. An example is 

provided in each step to illustrate the process.

Data Preparation

The data selected for this study were prepared following the steps and processes described in 

chapter 3 of this report. The data type and respective LTPP table sources were described in 

table 3. Basic statistics on the final data set used are presented in table 8 and table 9 for flexible 

pavements and table 10 and table 11 for rigid pavements.

Microsoft Excel® spreadsheets were used to compute all of the deflection parameters identified 

in the literature review as potential candidates for evaluating the structural condition of 

pavements (see table 1). In the case of closed-form mechanistic parameters (i.e., subgrade Hogg 

and Elmod moduli), macros were used to solve the equations.

The dichotomous performance variable was determined based on expected service life of flexible 

and rigid pavements—arbitrarily defined as 15 years for flexible pavements and 20 years for 

rigid pavements. The average year in service when the first deflection measurement was taken 

was 2 years for both pavement types. The LTPP sections compiled for this study exhibited an 

average service life of 11.3 years (flexible) and 13.8 years (rigid) at the last performance 

measurement. As a requirement of the logistic model assumption for acceptable performance, all 

pavement sections had to be evaluated at the end of the chosen expected service life. Therefore,

extrapolations of the performance curves were computed to achieve this requirement—3.7 years 

for flexible pavements and 6.2 years for rigid pavements. Typical load-related distresses in 

flexible and rigid pavements are given in table 12.
37

Table 8. Input continuous data summary for flexible pavement sections.

Input Data Average

Standard 

Deviation Minimum Maximum Median

Service life used 1.5 1.4 0.0 10.5 1.0

Annual precipitation 

(mm) 843.9 442.2 73.2 2,153.3 876.9

Annual minimum

temperature (°C) 6.4 5.9 -7.0 20.8 6.7

Annual maximum

temperature (°C) 19.6 6.2 3.8 31.3 20.3

Annual mean 

temperature (°C) 13.0 6.0 -1.6 25.6 13.3

AADTT 723.8 728.7 7.3 3,955.0 454.7

Total thickness 

(inches) 22.1 9.4 6.3 85.5 20.3

AC thickness 

(inches) 7.3 3.5 0.9 23.2 7.1

Class 5 (volume) 146.8 141.7 2 1,770.0 106.3

Class 9 (volume) 401.7 554.6 1 2,838.0 175.9

1 inch = 25.4 mm

1 °F = 1.8(°C) + 32

Table 9. Input discrete data summary for flexible pavement sections

Input Data

Possible Attributes 

and Corresponding 

Binary Values

Percentage of 

Sections in the 

Database

Subgrade type Fine-grained soil (1) 32.6 percent

Coarse-grained soil (0) 67.4 percent

Pavement type Bound base layer (1) 42.3 percent

Unbound base layer (0) 57.7 percent
38

Table 10. Input continuous data summary for rigid pavement sections.

Input Data Average

Standard 

Deviation Minimum Maximum Median

Service life used 2.2 1.5 0.0 9.7 2.2

Annual precipitation 

(mm) 848.0 372.1 128.9 1,856.4 894.7

Annual minimum

temperature (°C) 5.9 4.8 -2.2 21.0 5.1

Annual maximum

temperature (°C) 18.7 5.1 9.9 30.9 17.8

Annual mean 

temperature (°C) 12.3 4.8 3.8 25.8 10.9

AADTT 1267.2 1039.5 99.3 5,157.0 891.6

Total thickness 

(inches) 19.6 9.1 9.2 61.3 16.4

AC thickness 

(inches) 10.0 2.5 6.4 20.4 9.4

Class 5 (volume) 238.0 232.2 14 998 178.3

Class 9 (volume) 705.3 752.6 13 866 415.3

1 inch = 25.4 mm

1 °F = 1.8(°C) + 32

Table 11. Input discrete data summary for rigid pavement sections.

Input Data

Possible Attributes 

and Corresponding 

Binary Values

Percentage of 

Sections in the 

Database

Subgrade type Fine grain soil (1) 42.1 percent

Coarse grain soil (0) 57.9 percent

Pavement type Bound base layer (1) 55.3 percent

Unbound base layer (0) 44.7 percent

Table 12. Structural distresses in flexible and rigid pavements.

Flexible Pavements Rigid Pavements

• Fatigue cracking

• Rutting

• Roughness

• Transverse cracking

• Joint faulting

• Roughness

Extrapolations were computed on a section-by-section basis by fitting nonlinear regression 

models to the historical data. Figure 26 provides an example of nonlinear extrapolation used to 

adjust the performance data.
39

1 inch = 25.4 mm

1 mi = 1.61 km

Figure 26. Graph. Example of performance extrapolation based on historical data.

The threshold for an acceptable performance was defined based on the Mechanistic-Empirical 

Pavement Design Guide (MEPDG) limit values for an acceptable design and are described in 

table 13.

(27) The acceptable level for each distress could also be defined based on the network 

characteristics and the agency’s practice for defining rehabilitation and maintenance timing, 

which would provide the agency with greater flexibility to adjust the technique based on its 

network characteristics and preferred M&R timing.

Table 13. Distress threshold for flexible and rigid pavments.

Flexible Pavements Rigid Pavements

Distress Threshold Distress Threshold

Roughness 172 Roughness 172

Rutting (inches) 0.5 Joint faulting (inches) 0.12

Fatigue cracking 

(percent of total area) 25

Transverse cracking 

(percent of slabs) 15

One section would be classified as exhibiting acceptable performance for a given distress if the 

deterioration was lower than or equal to the threshold at 15 years for flexible pavements and 

20 years for rigid pavements.

The final step in data preparation was the selection of a subset of data for model validation. The 

selection was based on a stratified sampling technique. The technique consisted of selecting 

12 percent of the original dataset in a random process designed to pick sections distributed in a

variety of site characteristics that would result in a representation equivalent to the original 
40

dataset. Climate conditions, traffic volume, pavement type (in terms of base layer type), and 

subgrade type were used.

The climate condition was defined based on the freeze index and average rainfall for each site. 

Sites with an average annual rainfall greater than 39 inches (1,000 mm) were classified as 

wet, otherwise dry. Sites with a freeze index greater than 140 °F (60 °C) were classified as

freeze; sites with a freeze index less than 140 °F (60 °C) were classified as no freeze. This 

classification is part of the LTPP experiment definition. The classification of traffic was defined 

based on two characteristics: volume and commercial vehicle distribution. These characteristics 

are easy to evaluate and are most influential on pavement performance predictions estimated 

with the MEPDG. The combination of criteria generated two groups of sites, one identified as 

low traffic and the other as high traffic. Table 14 describes the characteristics of both groups 

used in this study.

Table 14. Traffic characteristics used for sampling.

AADTT

Low Traffic High Traffic

340–950 75–2,750

Vehicle class 5 

(percent in volume) 25–75 5–20

Vehicle class 9 

(percent in volume) 10–50 40–85

In total, 51 deflection parameters were computed based on the literature review findings. The 

first deflection survey available after construction/rehabilitation was used to compute these 

parameters. The latest performance measurement available was used. This process was repeated 

for all load-related distresses in both pavement types evaluated.

Evaluation of Selected Techniques Based on Observed Performance

The evaluation of selected deflection techniques was based on the logistic model approach and 

the notion that the best deflection techniques yield the most accurate models. Since there were 

many deflection parameters to be evaluated, a first screening was conducted to eliminate poor 

correlations. A simple linear Pearson regression was used to test the level of correlation between 

measured performance and the deflection parameter. Although this correlation is not expected to 

be good, Pearson’s R2 and the significance level were used to identify good candidates for the 

full binary logistic analysis. The screenings were conducted for both flexible and rigid 

pavements and all load-related distress types. Tables with the results from the screening process 

are presented in appendix B.

As a general rule, the deflection techniques that resulted in high Pearson’s R2 values and a 

significance level inferior to 0.05 were selected. In this case, the significance level is the 

probability that the null hypothesis is accepted, meaning that no correlation exists between 

the deflection parameters and the performance measure. Some deflection techniques were 

computed based on maximum deflection adjusted for temperature using the process described 

by Lukanen et al.(6)
41

After the screening was completed, the selected deflection parameters were used one at a time to 

develop logistic models for each load-related distress described in table 12. The statistical 

package IBM SPSS Statistics® was used to develop the logistic models. The process of 

developing the model follows a backward elimination approach. All variables described in 

table 8 through table 11 for flexible and rigid pavements, respectively, were used in the first 

step, along with the deflection parameter and the independent performance variable (acceptable 

or not acceptable).

The model’s exponent, b, (see figure 21) was calibrated to minimize the false positives and false 

negatives in the probability analysis. The significance of each variable was computed, and the 

less significant variable was removed from the calculation in the next step, eliminating the 

variable with the least relationship with performance. This process continued until all remaining 

variables had significance levels higher than 95 percent or the maximum number of iterations 

was achieved. With each step, the number of variables decreased and the overall level of 

significance decreased, indicating an improvement in the model’s capability of predicting the 

likelihood of acceptable performance.

The significance terminology may seem confusing, but the significance level represents the 

probability of the null hypothesis, which is defined as the nonexistence of any relationship 

between the variable in question and the predicted likelihood of acceptable performance. 

Therefore, high values of significance mean a high probability that the variable has a weak or no 

relationship as a performance predictor.

This process was repeated for all deflection variables, resulting in one model for each variable. 

After this first step was completed, each model was evaluated to eliminate confounding variables 

and unreasonable trends. Confounding variables are dependent variables that are related to each 

other to some extent. Volume of class 5 and 9 trucks, which according to typical vehicle class 

distributions are inversely proportional to each other, are a good example of confounding 

variables. The various site-specific temperature values selected as part of the inputs are also 

related to each other. During the review of each model, only one variable of each group was 

allowed to remain in the model. The one with the highest significance level was chosen.

Variables that resulted in unreasonable trends were also eliminated. An example of this situation 

was a model in which pavement thickness had an inverse trend with performance—thicker 

pavements would yield lower probability of acceptable performance, which is a contradiction to 

expected behavior. After confounding variables and variables resulting in unreasonable trends 

were eliminated, the model with the best accuracy was selected.

Table 15 provides the results for the logistic model based on roughness performance of flexible 

pavements. The primary model evaluation consists of best deflection models after the first 

screening was conducted and detailed analysis of each model’s variables was completed to 

remove confounding variables and unreasonable trends.
42

Table 15. Statistics of calibrated models based on roughness performance of flexible 

pavements.

Deflection Parameter

Primary Model Evaluation

I2 CI4 CI5 D2 D3 Hogg

Area ROC 0.733 0.720 0.731 0.720 0.727 0.694

Hosmer-Lemeshow 

significance test 0.397 0.137 0.339 0.351 0.592 0.198

Calibration—

correct cases (percent) 68.4 62.8 67.9 64.6 67.3 63.9

Validation—

correct cases (percent) 74.2 61.3 69.4 66.1 71.0 74.2

Error type I

(false acceptable) (percent) 6.6 4.7 5.7 5.9 6.5 7.0

Error type II

(false not acceptable) (percent) 25.0 32.5 26.4 29.4 26.2 29.1

TPR

(acceptable) (percent) 69.3 60.0 67.5 63.8 67.8 64.2

TNR (not acceptable) (percent) 64.4 75.0 69.2 68.3 65.4 62.5

The following observations can be made when analyzing table 15:

• The area under the ROC curve represents the accuracy of the model.

• The removal of confounding variables and unreasonable trends from the preliminary 

analysis of the I2 model had a small effect on the model’s accuracy. This is often 

expected because these variables usually exhibit poor significance to the predictability of 

the performance variable.

• The Hosmer-Lemeshow test is another way to evaluate the significance of the model. 

This test is commonly used to evaluate binary logistic models when the conventional 

Pearson’s R2 is not possible.

• The error type I (false acceptable) is the worst error type in the problem at hand. It occurs 

when the model predicts that the pavement section has a good structural condition when, 

in fact, the structural condition is the contrary. From an agency’s perspective, this would 

be the worst outcome from the model prediction.

• The TPR (true acceptable) and the TNR (true not acceptable) are good at 64 percent.

Sensitivity of Model to Deflection Parameter

In addition to evaluating basic statistics of each model, it was necessary to evaluate the 

sensitivity of models’ outcome to the deflection parameter. The main objective of this evaluation 

was to observe if there was any bias in the models’ predictions towards acceptable or not

acceptable performance. 
43

Figure 27 shows the sensitivity curve of the I2 model based on roughness performance. In this 

case, the cutoff is set at 0.812, which corresponds to I2 equal to 0.1092 1/mil (0.0043 1/ )

(or D2 equals to 9.13 mil (232 )), which is a reasonable value for a well designed pavement 

structure. (Recall that the deflection for D2 measured at 8 inches (203.2 mm) from the center 

of the load.) Therefore, figure 27 indicates that flexible pavements with D2 deflections below 

9.13 mil (232 ) have a higher than 80 percent chance of exhibiting acceptable roughness 

performance for the next 12 years and can therefore be classified as good structural condition. 

In contrast, figure 28 shows the sensitivity curve of the Hogg model based on roughness. The 

cutoff value of 0.802 yields a Hogg value of 65,000 psi (447,850 kPa), which is high and 

unreasonable for subgrade moduli. In this case, the Hogg model is biased toward probabilities 

under the cutoff value and, consequently, toward low probabilities of acceptable performance.

11/ = 25.4 1/mil

Figure 27. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

I2 for flexible pavements.

μm

μm

μm

μm
44

1 psi = 6.89 kPa

Figure 28. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

Hogg for flexible pavements.

This type of sensitivity analysis was performed to all models developed and proved to be 

essential to rule out models that provided very good statistics at first but were biased. The 

sensitivity analyzes of other logistic models are provide in appendix C.

Validation Analysis

The validation analysis was performed on a subset of the database that was set aside prior to 

model calibration. In total, 12 percent of the sections available for calibration were removed 

from the database. Since the LTPP database covers a wide range of pavement sections, traffic 

levels, and environmental conditions, a stratified random sampling technique was employed to 

retrieve the sections. The following characteristics were used in the stratified sampling approach:

• LTPP climate regions: Wet-freeze (WF), wet-no freeze (WNF), dry-freeze (DF), and 

dry-no freeze (DNF).

• Traffic: Low versus high (as described in table 12).

• Base layer type: Unbound versus bound (only for flexible pavement).

• Subgrade type: Fine-grained versus coarse-grained soil.

The stratified random sampling technique consists of grouping all sections in all possible 

combinations of the characteristics defined for the selection. After the groups are formed, the 

target percentage of samples is randomly selected proportionally to the size of each group and its 

participation in the entire dataset. For example, if one group consisting of sections with WF, low 

traffic, unbound base type, and fine subgrade has 43 sections, the sampling of this group would 
45

yield 5 sections randomly selected. There were 32 possible combinations of all characteristics 

mentioned. An algorithm was written to group the sections with equal characteristics and 

randomly select the target number of sections.

The validation was performed in all steps of the model evaluation. Table 14 provides the results 

for the structural logistic model based on roughness for flexible pavements. In this case, the 

validation dataset consisted of 61 sections, which is a proportional representation of all sections 

available in the database for model calibration. The results indicate that good accuracy was also 

observed in the validation dataset, which suggests that the final model is capable of identifying 

the structural condition of the pavement based on expected roughness performance. The 

validation results for all models developed in this study are provided in appendix B along with 

the statistics of the calibrated equation.

Table 16. Example of validation results for the structural logistic model based on 

roughness for flexible pavements.

Deflection Parameter

Primary Model Evaluation

Final 

Model

I2 CI4 CI5 D2 D3 Hogg I2

Validation—

correct cases (percent) 74.2 61.3 69.4 66.1 71.0 74.2 69.4

Selection of Deflection Technique

The logistic model based on deflection parameter I2 had the best accuracy. Table 17 shows 

the final model variables with respective p-values (i.e., significance of the variable to the 

performance variable) and the corresponding cutoff value that resulted in the highest accuracy. 

Table 17. Variables in the I2 final model (based on roughness).

Variables (bi) ai p-Value

I2 239.849 0.000005706

Current life -0.189 0.01174

Class 9 volume -0.0006781 0.0001037

Constant 0.8375 0.01071

Cutoff 0.812

Note: Variables bi and ai are defined in the equation in figure 22.

Figure 29 provides the equation used to compute the deflection parameter.

Figure 29. Equation. Calculation of I2.

THEORETICAL VALIDATION

Deflections are normally used to back-calculate the elastic moduli of the pavement layers. In an 

inverse process, the mechanistic validation consisted of simulating different pavement structures 

and material properties using simple multilayer elastic theory. Computed responses (deflections, 

I2 = 1

D2
46

stresses, and strains) were used to compute the deflection parameters and estimate damage and 

performance through mechanistic-empirical models. The structural logistic models were used 

with the computed deflection parameters as inputs. The probabilities of good structural condition 

were then compared with the estimated performance.

The software KENPAVE, developed by Huang, was used to model typical flexible and rigid 

pavement structures.(28) The mechanistic responses were then used to predict performance using 

the MEPDG.(27) This section describes the theoretical validation and provides examples of each 

step in the process. The complete validation for flexible and rigid pavement models is provided

in greater detail in appendix D.

Mechanistic-Empirical Analysis

Flexible Pavements

Several pavement structures were simulated using the KENLAYER computer program that is 

part of the KENPAVE software. The intention was to evaluate different asphalt concrete and 

base layer thicknesses at different stiffnesses and different subgrade moduli. A factorial study 

was designed and is presented in table 18.

Table 18. Summary of the mechanistic analysis inputs for flexible pavements.

HMA Thickness 

(inches)

HMA Modulus 

(psi)

Base Thickness 

(inches)

Base Modulus 

(psi)

Subgrade 

Modulus (psi)

3, 7, 11 250,000, 500,000,

750,000, 1,000,000,

1,250,000, 1,500,000,

1,750,000, 2,000,000,

2,250,000, 2,500,000,

2,750,000, 3,000,000

8, 12, 16 10,000,

20,000,

30,000, 40,000

5,000, 10,000,

20,000

1 inch = 25.4 mm

1 psi = 6.89 kPa

The combination of all parameters in the factorial experiment resulted in 1,296 sections. It 

was necessary to find a common variable for comparing the mechanistic responses among 

different combinations of the input parameters. The choice was the SN used in the 1993 

AASHTO Guide for Design of Pavement Structures.

(8) The equations for computing SN are 

provided in appendix D.

The deflection parameters of the best logistic models developed were computed for the structures 

simulated in the factorial experiment. Figure 30 shows the trends between deflection parameter 

I2 and SN. For simplicity, the data were grouped by subgrade modulus. I2 was chosen for the 

final structural logistic model based on roughness performance. Plots for deflection parameters 

used in the structural logistic models based on rutting and fatigue cracking are provided in

appendix D.
47

11/ = 25.4 1/mil

1 psi = 6.89 kPa 

Figure 30. Graph. Deflection parameter I2 as a function of SN for a flexible pavement with 

HMA modulus of 500,000 psi (3,445,000 kPa).

Rigid Pavements

Several pavement structures were simulated using KENSLAB, which is part of the KENPAVE 

software.(28) The intention was to evaluate different JPCP slab thicknesses and subgrade moduli 

and the consequences to the outcome of the structural logistic models. The pavement structure 

was simulated as an elastic slab on a dense liquid foundation. A factorial study was designed and 

is presented in table 19.

Table 19. Summary of the mechanistic analysis inputs for rigid pavements.

PCC Thickness 

(inches)

PCC Modulus 

(psi)

Subgrade Modulus 

(psi)

8, 9, 10, 11, 12 4,000,000 5,000, 10,000, 20,000

1 inch = 25.4 mm

1 psi = 6.89 kPa

The deflection parameters of the best logistic models developed were computed for the structures 

simulated in the factorial experiment. Only the FWD test at the center of the slab was evaluated. 

The objective was to verify if trends would agree with expected outcomes from the models. At 

first, the deflection parameters were plotted against the slab thickness (i.e., considered as 

reference for the strength of the pavement section).

Figure 31 shows the trends between deflection parameter I1 and slab thickness for three subgrade 

moduli. I1 was chosen for the final structural logistic model based on roughness performance. 

μm
48

The results indicate that I1 increases as slab thickness increases, as expected. Plots for deflection 

parameters used in the structural logistic models based on faulting and slab cracking are provided 

in appendix D.

11/ = 25.4 1/mil

1 inch = 25.4 mm

1 psi = 6.89 kPa

Figure 31. Graph. Sensitivity of deflection parameter I1 to slab thickness.

Comparison with MEPDG Predicted Performance

The MEPDG performance prediction models were used to compare predicted distress 

performance at the end of the design life with the estimated structural condition obtained from 

the logistic structural model. This task was accomplished by applying the MEPDG models using 

the mechanistic responses calculated by KENPAVE.

Flexible Pavements

Two models were considered for flexible pavements—rutting and fatigue cracking. At first, the 

roughness model was also included in the scope. However, this particular model requires 

additional site factors that often dominate the analysis. Therefore, a comparison between the 

outcome of the structural logistic model based on roughness and predicted roughness 

performance was not included in this exercise. The calculations were performed in Microsoft 

Excel® and not within the MEPDG software due to computational time required to run all 

scenarios. Since the objective is the comparison and trend evaluation, this assumption had no 

impact on the outcome or conclusions.

μm
49

Figure 32 shows an example of the sensitivity of I1 structural logistic model probability based on 

fatigue cracking to MEPDG predicted fatigue cracking performance for flexible pavements. It 

can be seen that the trends agree with expectations; high probabilities of good structural 

condition are associated with low levels of fatigue cracking. As the probability decreases, the 

predicted area of fatigue cracking increases.

1 psi = 6.89 kPa

Figure 32. Graph. Sensitivity of I1 structural logistic model probability based on fatigue 

cracking performance to MEPDG predicted fatigue cracking for flexible pavements.

The complete comparison between the outcome of the structural logistic models and MEPDG 

predicted performance are described in appendix D, which also includes the predictive model 

equations for fatigue cracking that were implemented in Microsoft Excel®.

Rigid Pavements

In the case of rigid pavements, the MEPDG was used to generate the performance predictions. 

There were 15 scenarios to run, and the rigid pavement analysis was performed much faster in 

the MEPDG than the flexible pavement analysis.

Figure 33 shows the sensitivity of the I1 structural logistic model probability based on roughness 

to MEPDG predicted roughness performance for rigid pavements. The trends agree with 

expectations—high probabilities of good structural condition are associated with low values of 

IRI. As the probability decreases, the predicted IRI increases. This plot confirms that the 

structural logistic model is capable of providing an assessment of structural condition that is tied 

to an expectation of performance. The complete comparison between the outcome of the 

structural logistic models and MEPDG predicted performance is described in appendix D.
50

1 inch = 25.4 mm

1 mi = 1.61 km

1 psi = 6.89 kPa

Figure 33. Graph. Sensitivity of I1 structural logistic model probability based on roughness

performance to MEPDG predicted roughness for rigid pavements.

IMPORTANCE OF LOCAL CALIBRATION

The models developed in this research were calibrated using data from several States and 

different local conditions. It is expected that the accuracy of the models can be improved by local 

calibration, which is hypothesized to minimize variability and to reduce sources of errors. Local 

calibration is achieved by selecting a sample dataset from the local network in which the models 

are to be applied and perform a local calibration of the logistic model.

Since data from a local network with comprehensive performance data for calibrating the models 

were not available, the LTPP database was used for this purpose. It was assumed that the models 

would improve accuracy if calibrated for an individual State (i.e., data from one State would 

have less variability and could be considered as part of a local network). Four States were 

used in this exercise—Texas, Minnesota, California, and Alabama. They were chosen 

based on the availability of data—the more data available, the higher the likelihood of a 

meaningful calibration.

This exercise was performed only for flexible pavements. States with a large number of rigid 

pavement sections were searched, but no State was found to have enough sections for this 

purpose. The structural logistic model based on fatigue cracking was chosen because it was the 

model with the least accuracy of all three models developed for flexible pavements.
51

The calibration process followed the same steps described in earlier sections of this chapter. 

Table 20 shows the statistics of the locally calibrated model for each of the four States. The 

statistics for the model calibrated with the entire dataset are also provided under the name of 

national calibration. It can be seen from the results that local calibration can significantly 

improve the accuracy of the model.

Table 20. Benefits of local calibration.

Statistics National Texas Minnesota California Alabama

Number of sections 467 57 21 33 17

Accuracy 0.72 0.73 0.76 0.92 0.90

Correct cases

(percent) 63 70 76 85 88

Error type I

(percent) 15.5 5.3 4.8 9.1 5.9

TPR (percent) 63 58 78 83 92

TNR (percent) 63 67 67 86 80

The national calibration resulted in a logistic fatigue cracking model with an equivalent R2 of 

0.66. The simulation of local calibration yielded models with R2 values ranging from 0.73 to 

0.92. The improvement in correct predictions increased from 63 to 88 percent, which was a good 

improvement considering the nature of the problem. Another indication of the benefits of local 

calibration was the improvement in TPR. As seen in table 18, TPR values increased from 63 to 

92 percent. These improvements are most likely attributed to the uniformity of the dataset in 

terms of site characteristics (materials, traffic, and climate) and similar design procedures.

The four examples of local calibration presented in this section show the potential improvements 

in accuracy and predictability that can be obtained if local data are used to calibrate the 

probabilistic models. Although these cases are just simple exercises retrieved from the LTPP 

database, it is clear that local calibration ultimately enhances the accuracy and quality of 

predictions, which significantly benefits analyses using PMS, especially for creation and 

allocation of M&R resources.

SUMMARY OF FINDINGS

The logistic model notation is described in figure 21 and figure 22. The general form of the 

probabilistic logistic model is given in the equation shown in figure 21, in which the exponent 

term is given by the general linear equation provided in figure 22. All logistic models developed 

in this study follow this notation.

During the course of this research, several models were developed and evaluated according to 

the principles and approach described in earlier sections in this chapter. Different structural 

logistic models were developed based on different distress performance measures using the 

national LTPP database. Detailed statistics of all models evaluated are provided in appendix B. 

The final models are presented in this section.
52

Flexible Pavements

Model Based on Roughness Performance

The model variables are described in table 21. The deflection parameter used is in figure 29, 

where D2 is the deflection 8 inches (203.2 mm) from the center of the load. The accuracy, 

measured by the area under the ROC curve, is 0.72, and the cutoff value is 0.812. Additional 

detailed statistics are provided in appendix B.

Table 21. Variables in the I2 final model for flexible pavements based on roughness 

performance.

Variables (bi) ai p-value

I2 239.849 0.000005706

Current life -0.189 0.01174

Class 9 volume -0.0006781 0.0001037

Constant 0.8375 0.01071

Cutoff 0.812

Roughness performance depends on the strength of the entire pavement structure. For example, 

it is expected that one robust pavement section tends to be smoother for longer periods of time 

than one weak section, assuming both have the same climate, traffic conditions, and subgrade. 

Therefore, the predominance of the deflection variable in the model is justified. Current life 

and traffic play a significant role in estimating the likelihood of premature failure due to 

roughness performance.

Model Based on Rutting Performance

The model variables are described in table 22, and the deflection parameter is in figure 34. The 

accuracy, measured by the area under the ROC curve, is 0.66, and the cutoff value is 0.792. 

Additional detailed statistics are provided in appendix B.

Table 22. Variables in the CI3 final model for flexible pavements based on rutting 

performance.

Variables (bi) ai p-value

CI3 -0.01146 0.00001594

Precipitation (mm) -0.0005259 0.04018

Class 9 volume -0.0007688 0.00005421

Constant 2.6586 1.0136*10^(-13)

Cutoff 0.792

Figure 34. Equation. Calculation of CI3.

Where D3 is the deflection 12 inches (304.8 mm) from the center of the load and D4 is the 

deflection 18 inches (457.2 mm) from the center of the load.

CI3 = D3 - D4
53

The rutting model is based on deflections located at the middle of the measured deflection basin.

The influence of the base and subbase is mostly noted on the deflection measured at this 

location. The strength of the underlying layers is critical in the development of rutting in the 

asphalt concrete layer and the sublayers, as well. One important aspect of the rutting 

phenomenon is the influence of the subgrade. It is understood that the subgrade contributes to 

the overall magnitude of rutting and the rate of development over time. The influence of the 

subgrade is not completely captured by the deflections used in this model. During the model 

development the type of subgrade (fine or coarse) was included as a variable, but it was excluded 

by the calibration process. However, the influence of precipitation was observed, which directly 

affects the subgrade strength more than any other granular layer in the pavement structure. 

Further improvements to this model at local calibration level should include the subgrade type 

and subgrade modulus if possible.

Model Based on Fatigue Cracking Performance

The model variables are described in table 23, and the deflection parameter is in figure 35. The 

accuracy, measured by the area under the ROC curve, is 0.72, and the cutoff value is 0.605. 

Additional detailed statistics are provided in appendix B.

Table 23. Variables in the I1 final model for flexible pavements based on fatigue cracking 

performance.

Variables (bi) ai p-value

I1 154.764 0.0006015

AADTT -0.0005073 0.0007847

Pavement type 0.3774 0.07598

Constant -0.2202 0.4422

Cutoff 0.605

Figure 35. Equation. Calculation of I1.

Where D1 is the deflection at the center of the load.

Fatigue cracking performance is influenced by the stiffness of the asphalt concrete layer, the 

number of load repetitions, and the type/strength of underlying layers. Stiff asphalt concrete 

layers are more susceptible to cracking because the binder hardens and becomes brittle, which 

reduces its flexural strength. The overall stiffness of the pavement can be captured in part by the 

maximum deflection, represented in this model as I1. The mechanism for crack initiation and 

propagation, regardless of the location where it starts (bottom or surface), depends on the 

growing damage due to load repetitions. The truck volume in the model addresses this issue to 

some extent. Finally, the type of pavement (unbound or bound base layer) is related to the 

stiffness of the underlying layers. Pavements with a bound base layer are less likely to develop 

fatigue cracking than pavements with an unbound base layer.

I1 = 

1

D1
54

Rigid Pavements

Two sets of models were developed for rigid pavements: one based on FWD testing at a

9,000-lb (4,086-kg) load and one at a 12,000-lb (5,448-kg) load. These tests are identified in the 

LTPP database as drops 2 and 3, respectively.

Model Based on Roughness Performance (9,000 lb (4,086 kg))

The model variables are described in table 24. The deflection parameter is shown in figure 36. 

The accuracy, measured by the area under the ROC curve, is 0.65, and the cutoff value is 0.665. 

Additional detailed statistics are provided in appendix B.

Table 24. Variables in the CI5 final model for rigid pavements based on 

roughness performance (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

CI5 -0.078 0.00406

Class 9 volume -0.0003877 0.115

Constant 2.057 0.00002168

Cutoff 0.665

Figure 36. Equation. Calculation of C15.

Where D5 is the deflection 24 inches (609.6 mm) from the center of the load and D6 is the 

deflection 36 inches (914.4 mm) from the center of the load. Both deflections are obtained from 

tests at the center of the slab. Additional models based on FWD tests at different locations in the 

slab were investigated (i.e., tests at joint approach, corner edge, and mid-edge). Since they are 

unusual locations for typical FWD surveys conducted by State transportation departments (with 

the exception of the joint test), they are provided only in appendix B.

Roughness in rigid pavements is mainly related to faulting. Faulting is a distress that is directly 

related to the stiffness of the support layer and the quality of the dowel bars. The deflection 

parameter CI5 captures the influence of the underlying layer stiffness. The traffic load repetition 

is represented by the volume of class 9 trucks, which are the most damaging commercial vehicles 

to the pavement performance.

Model Based on Roughness Performance (12,000 lb (5,448 kg))

The model variables are described in table 25. The deflection parameter is shown in figure 37. 

The accuracy, measured by the area under the ROC curve, is 0.66, and the cutoff value is 0.695. 

Additional detailed statistics are provided in appendix B.

CI5 = D5 - D6
55

Table 25. Variables in the CI4 final model for rigid pavements based on 

roughness performance (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

CI4 -0.117 0.007378

Class 9 volume -0.0004607 0.06459

Constant 2.148 0.0000447

Cutoff 0.695

Figure 37. Equation. Calculation of CI4.

Where D4 is the deflection 18 inches (457.2 mm) from the center of the load and D5 is the 

deflection 24 inches (609.6 mm) from the center of the load. Both deflections are obtained from 

tests at the center of the slab. Additional models based on FWD tests at different locations in 

the slab were investigated and are provided in appendix B. This model is similar to the one 

developed based on the 9,000-lb (4,086-kg) FWD load. The deflection parameter is D5 in this 

case, which is also related to the stiffness of the underlying layers.

Model Based on Faulting at Joints Performance (9,000 lb (4,086 kg))

The model variables are described in table 26. The accuracy, measured by the area under the 

ROC curve, is 0.64, and the cutoff value is 0.635. Additional detailed statistics are provided in 

appendix B.

Table 26. Variables in the D6 final model for rigid pavements based on faulting 

at joints performance (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D6 -0.009225 0.138

Subgrade type -0.495 0.2003

Constant 1.499 0.005818

Cutoff 0.635

Where D6 is the deflection 36 inches (914.4 mm) from the center of the load. The deflection is 

obtained from tests at the center of the slab. Additional models based on FWD tests at different 

locations in the slab were investigated and are provided in appendix B.

Faulting is a distress that is directly affected by the condition of the subgrade or the underlying 

base layer. The variables that were selected during the calibration process reflect the importance 

of the subgrade on the faulting performance of the pavement. The further the measured 

deflection is from the center of the applied load, the greater the contribution of the underlying 

layers to its magnitude. The deflection parameter D6 can be related to the instant stiffness of the 

supporting layers. In addition, the subgrade type (fine or coarse) was also selected as one of the 

variables, which confirms the importance of the subgrade on faulting performance.

CI4 = D4 - D5
56

Model Based on Faulting at Joints Performance (12,000 lb (5,448 kg))

The model variables are described in table 27. The accuracy, measured by the area under the 

ROC curve, is 0.63, and the cutoff value is 0.651. Additional detailed statistics are provided in

appendix B.

Table 27. Variables in the D6 final model for rigid pavements based on faulting at joints 

performance (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D6 -0.008789 0.06896

Subgrade type -0.579 0.139

Constant 1.734 0.002499

Cutoff 0.651

Where D6 is the deflection 36 inches (914.4 mm) from the center of the load. The deflection is 

obtained from tests at the center of the slab. Additional models based on FWD tests at different 

locations in the slab were investigated and are provided in appendix B.

Model Based on Transverse Slab Cracking Performance (9,000 lb (4,086 kg))

The model variables are described in table 28. The deflection parameter used is shown in 

figure 37. The accuracy, measured by the area under the ROC curve, is 0.77, and the cutoff value 

is 0.7. Additional detailed statistics are provided in appendix B.

Table 28. Variables in the CI4 final model for rigid pavements based on transverse slab 

cracking performance (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

CI4 -0.254 0.0003759

Class 9 volume -0.001012 0.001084

Constant 3.630 0.0000003134

Cutoff 0.7

For this model, D4 is the deflection 18 inches (457.2 mm) from the center of the load, and D5 is 

the deflection 24 inches (609.6 mm) from the center of the load. Both deflections are obtained 

from tests at the center of the slab. Additional models based on FWD tests at different locations 

in the slab were investigated and are provided in appendix B.

Slab cracking develops when the slab support is no longer adequate or loading is too excessive 

for the designed concrete slab. As any crack mechanism, it also develops over traffic load 

repetition. The final model developed based on transverse slab cracking incorporates both 

characteristics. The deflection parameter is obtained from the midsection of the deflection basin 

which can be associated with the instant stiffness of the underlying support layers of the concrete 

slab. The load repetition is characterized by the volume of class 9 trucks.
57

Model Based on Transverse Slab Cracking Performance (12,000 lb (5,448 kg))

The model variables are described in table 29. The deflection parameter is shown in figure 37. 

The accuracy, measured by the area under the ROC curve, is 0.66, and the cutoff value is 0.695. 

Additional detailed statistics are provided in appendix B.

Table 29. Variables in the CI4 final model for rigid pavements based on transverse slab 

cracking performance (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

CI4 -0.231 0.00007858

Class 9 volume -0.001029 0.001282

Constant 3.9796 0.0000001201

Cutoff 0.71

In this model, D4 is the deflection 18 inches (457.2 mm) from the center of the load,and D5 is the 

deflection 24 inches (609.6 mm) from the center of the load. Both deflections are obtained from 

tests at the center of the slab. Additional models based on FWD tests at different locations in the 

slab were investigated and are provided in appendix B.

GUIDELINES FOR SELECTING BEST-FITTING TECHNIQUES

The process for selecting the best-fitting technique is simple. A complete example is described in 

the previous sections of this chapter. A summary of the steps is provided as guidelines for 

selecting the best-fitting deflection techniques.

The process for selecting the best model is as follows:

1. Data Preparation

Data availability is important. Logistic regression models are obtained from the statistical 

analysis of several independent variables that may potentially have an impact on pavement

performance. At first, no variable should be eliminated without it properly being assessed. 

Typical groups of variables include deflection, structure, traffic, climate, and performance. It is 

important that any available variable in these categories is used, but dependent variables that are 

related to each other to some extent should be avoided.

Deflections obtained from FWD testing are used to compute deflection parameters to be used 

as independent variables in the logistic models. A detailed literature review of most used and 

more successful applications was done as part of this research.

In this study, thickness and material type were used as structure variables. In addition, 

two dichotomous variables based on the structure characteristics were used—one related to the 

subgrade type (coarse- or fine-grained) and other related to the base type (bound or unbound). 

Traffic was limited to the total volume of trucks and the volume of the two most predominant 

classes in the FHWA truck classification, classes 5 and 9. Two main variables for climate were 

used—precipitation and temperature. For simplification, annual averages were used for both.
58

The main characteristic of a logistic model is the prediction of a probability of an event occurring 

given a set of independent variables. The assumption is that the rate of deterioration increases as 

the structural condition worsens, and the probability of a pavement failing prematurely can be 

calculated based on a combination of a deflection parameter and site characteristics. Therefore,

performance must be transformed in a dichotomous variable representing the occurrence of this 

event (acceptable performance after a number of years in service). The service life can be chosen 

to reflect the expected performance in the network.

2. Logistic Model Calibration

The calibration and evaluation of selected deflection techniques is based on the logistic model 

approach and the notion that the best deflection techniques yield the most accurate models. Each 

deflection parameter available can be used to develop a logistic model for each performance 

measure in the dataset. A statistical package can be used to expedite the process, although a 

spreadsheet can be used to program the optimization algorithm. In this study, PASW StatisticsTM 

(formerly known as SPSS) was used to develop the logistic models with an approach called 

backward elimination. The general formulation of the logistic model is shown in figure 21

and figure 22.

The model’s exponent, b, is calibrated to minimize the false positives and false negatives in the 

probability analysis. The significance of each variable is computed, and the least significant 

variable is removed from the calculation. This process continues until no improvements in 

accuracy can be made or the maximum number of iterations is achieved.

3. Verification of Accuracy

Logistic model accuracy is best evaluated through the analysis of the ROC curve. An ROC 

analysis allows researchers to select possible optimal models and discard suboptimal ones 

independently from the class distribution of the predictor.

The ROC curve is drawn using only the TPR and FPR. TPR is determined by the number of true 

positive predictions, normalized by total number of positive observed values. Conversely, FPR 

defines how many incorrect positive results occur among all negative samples available during 

the test.

The ROC space is defined by FPR and TPR as x- and y-axes, respectively, which depicts the 

relative tradeoffs between true positive and false positive. TPR is often described as the 

sensitivity of the model, while (1 ‒ FPR) is often seen as TNR or specificity. Therefore, the ROC 

curve is also referred to as the sensitivity versus (1 ‒ specificity) curve. Each case consisting of a 

prediction and observed values represents one point in the ROC space. Details about the ROC 

curve were provided earlier in this chapter and are shown in figure 24.

The area under the ROC curve defines the goodness-of-fit of the predictions. In an analogy with 

measures of linear optimization techniques, the area under the ROC curve can be viewed as the 

R2 value. In addition to the goodness-of-fit, the ROC curve is used to define the cutoff value of 

the model. This is an important parameter that defines how the results from the probability 

density function can be interpreted in a binary system (i.e., the threshold used to separate 

probabilities that are referred to acceptable and not acceptable). The cutoff is defined as the 
59

probability value that corresponds to the point in the ROC curve closest to the perfect 

classification point (0,1). When the cutoff is used to convert the predicted probabilities into 

binary outcomes, the model yields the highest level of accuracy (i.e., highest TPR and TNR).

4. Sensitivity Analysis

The last step in the analysis process is the sensitivity of the logistic models to its variables. It is 

important that the model produces as accurate results as possible, as well as reasonable 

probabilities with reasonable values of the deflection parameter. Plots of predicted probability 

versus the deflection parameter can provide valuable information about the reasonableness of the 

model for a given set of site characteristic variables (e.g., high truck volume, unbound base, and 

cold climate). If results from the sensitivity plots are unreasonable, a new model must be 

calibrated to eliminate unrealistic outcomes.

61

CHAPTER 5—PROCEDURES FOR OPTIMUM DEFLECTION TEST SPACINGS AND 

FREQUENCY FOR PMS APPLICATIONS

One important aspect of optimum deflection test spacing and frequency is the measurement 

accuracy. The accuracy is mainly a function of the combined effects of different sources of 

variability, such as number of measurements, equipment variability, and spatial variability, 

which is often associated with the inherent section variability.

(29) In addition to measurement 

accuracy, optimum deflection test spacing and frequency for PMS applications is a function of 

the following considerations:

• Priority and level of sophistication of the structural prediction models in the PMS.

• PMS system inventory mileage.

• Equipment availability.

• Personnel availability and flexibility.

• Traffic levels.

• Available budget to conduct testing.

Structural models in pavement management systems range from the very simple to relatively 

complex. The simplest models utilize deflections or deflection basin parameters to characterize 

subgrade and pavement structural properties. For example, the outer deflections can be used to 

estimate subgrade stiffness, while the inner deflections are indicative of the degree of support 

provided by the pavement layers above the subgrade. The more complex structural models utilize 

pavement layer moduli (derived from deflections) and pavement layer thicknesses and material 

types to calculate pavement response which is then used to predict failure, much like projectlevel pavement design analysis. Any PMS system using the latter more complex approach would 

undoubtedly need more deflection information than the former more simplistic approach.

PMS inventory mileage is another consideration in deflection spacing. Texas maintains 

approximately 89,000 centerline mi (143,290 centerline km) of pavement, while Alaska 

maintains approximately 5,000 centerline mi (8,050 centerline km). Certainly, it would be easier 

to collect deflection data on the majority system for a State with fewer miles, and the deflection 

spacing could be closer.

Most States and local agencies only have a handful of FWDs, and these are mainly used to 

collect project-level deflection data for scoping M&R work and for research purposes. PMS 

deflection data collection are, in most cases, prioritized below project-level work, so the 

equipment availability for network level data collection is often limited.

Data collection for PMS requires equipment operators to be in the field for long periods of time, 

often weeks at a stretch, as it is not efficient for the operator to mobilize back and forth from the 

home base to the job site. Multiple operators are required, and the agency must be flexible in its 

overtime policies as it is more efficient to work a 10- or 12-h day in the summer as opposed to 
62

the traditional 8-h day, 40-h work week. Personnel turnover is an issue as well. Many operators 

are motivated by the high-tech aspects of operating the FWD. They tend to be highly capable and 

multitalented and, as such, are often quickly promoted through the agency, leaving a void to fill. 

FWD operator turnover within the agency is often higher than other positions, so the issue of 

training new operators must be addressed.

Traffic levels are a significant factor when determining optimum (i.e., “minimum possible”) test 

spacing. Higher traffic facilities require expensive lane closures. Moderate traffic requires at 

least a sign truck and a crash attenuator mounted on a large vehicle, typically a flatbed single unit 

truck. These operations require three personnel, one for each vehicle. Ironically, the lowest 

traffic facilities are typically ranked lowest in priority in the PMS data collection effort but 

afford the opportunity to collect the most data.

Given the above, the annual agency budget ultimately controls the quantity of deflection data 

that can be collected in any given year. Objective recommendations and guidelines are provided 

in this report to determine optimum test spacings, but in the end, the optimum spacings for any 

agency, network, or portion of the network will be dictated by data collection priorities (project 

versus network), total mileage to be tested, equipment and personnel availability, traffic levels, 

and the portion of the annual budget available for network-level testing.

ANALYSIS OF TEST SPACINGS FOR FWD DATA COLLECTION

The objective of this analysis was to develop an approach to determine the optimum spacing 

between FWD tests for use in network applications. The approach is based on an evaluation of 

the probability of introducing errors as a function of different test spacings and pavement section

lengths. Different spacings were evaluated in a probabilistic procedure, resulting in a set of 

expected error curves for various reliability levels that can be used in the future for determining 

the optimum test spacing. The error represents the expected difference between the sample of the 

data and the idealized true value of the population, which, in this case, is represented by the 

average deflection value of a homogeneous road segment. Monte Carlo simulations were used to 

model the error function. They are particularly useful in this type of problem in which variables 

are stochastically distributed and analytical solutions are difficult to obtain. The effectiveness of 

this approach was verified using data from various road segments in five states. The expected 

outcome of this study is a procedure that can be easily implemented in a pavement management 

system during the planning stages of the survey campaigns by simply defining an acceptable 

magnitude of error and a reliability level.

Modeling the Error Using a Monte Carlo Simulation

The main purpose of this task was to evaluate the sources of variability of FWD testing 

associated with different sampling strategies and their impact on the average deflection values 

measured in a road segment. This analysis also provides an opportunity to compare a desirable 

level of accuracy with the costs associated with the associated sampling strategy (i.e., level of 

expected error versus number of data points in the sample).
63

An assumption has to be made about the pavement segment for which the sampling strategy is 

being defined. The segment must be homogenous in the following characteristics:

• Road functional class.

• Pavement structure.

• Traffic (volume, vehicle class, and load distributions).

• Surface condition of pavement.

The characteristics are likely to provide a pavement segment with a deflection profile without 

significant variations in deflection magnitudes. These conditions are necessary for any sampling 

strategy to be effective and produce meaningful results.

The basic approach involves the use of a Monte Carlo simulation to assess the effects of each 

source of variability. The Monte Carlo simulation is an iterative method for evaluating a 

deterministic model using sets of random numbers as inputs. This method is useful when the 

model is complex, nonlinear, or involves more than just a few uncertain parameters. By 

simulating the probability distributions for each source of variability, it is possible to evaluate the 

overall error of average FWD measurements when different sampling procedures are selected at 

network-level. Figure 38 represents the process to evaluate different sampling alternatives.

Figure 38. Illustration. Monte Carlo simulation.

Precision

Number of repeated measures

Inherent section variability

Spatial correlation

Test spacing

Variability of deflection measurements

Monte Carlo Simulation

Deflection variability 

associated with time 

interval between surveys
64

To begin a Monte Carlo simulation, operators should select random deflection data that were 

generated for a 10-mi- (16.1-km)-long section at an assumed 0.1-mi (0.161-km) interval between 

test points. In each scenario, different means and standard deviations were simulated. The chosen 

values for means and standard deviations were selected based on observations of data in the 

LTPP database and State transportation department data available for this research. The interval 

of 0.1 mi (0.161 km) was chosen because it represents the typical spacing used at FWD surveys 

for project-level designs. The average deflection of this randomly generated profile was used as 

the true deflection value for the section (i.e., the errors associated with sampling strategies were 

determined in relation to this value).

First, the entire data in each randomly generated deflection profile were divided in groups of 

increasing spacing by skipping up to 19 deflection points, which corresponds to a 0.2- to 2-mi

(0.322- to 3.22-km) spacing. These subgroups represented different sampling strategies defined 

by the spacing between deflection points. All possible combinations of data points that yield the 

target spacing were generated. For instance, the first spacing was achieved by skipping one 

deflection point. In this case, two combinations were possible, one starting with the first data 

point and skipping the second and the other by skipping the first and starting with second one. 

For each consequent spacing, the number of combinations was increased by one. This is 

exemplified in figure 39 for spacings of 0.2 and 0.3 mi (0.322 and 0.483 km).

1 mi = 1.61 km

Figure 39. Illustration. Deflection measurement pairings based on 

0.1-, 0.2-, and 0.3-mi (0.161-, 0.322-, and 0.483-kg) spacings.

After each subgroup was defined, the mean for each spacing combination was calculated and 

compared to the mean of the entire dataset created at a 0.1-mi (0.161-km) spacing. (Recall that 

the mean of the 0.1-mi (0.161-km) spacing data was considered to be the true mean.) The errors 

associated with each spacing were calculated as a percentage of the true mean. This process was 

repeated for each random simulation in the Monte Carlo process. A total of 5,000 simulations 

1 2 3 4 5 6 7 8 9 10 11 12

0.1-mile increments

1 2 3 4 5 6 7 8 9 10 11 12

0.2-mile increments

1 2 3 4 5 6 7 8 9 10 11 12

0.3-mile increments
65

were run, and the results were used to create a distribution of average errors with spacing. The

error distribution as function of test spacing is plotted in figure 40. This graph indicates that as 

the spacing between test points increases, the error increases in relation to the reference value 

(i.e., true mean). The error is interpreted as the accuracy of the average deflection of the 

homogeneous segment associated with a selected sampling strategy (spacing) when compared 

to the true mean given by a FWD survey at a 0.1-mi (0.161-km) spacing.

In addition to modeling the expected average error, the results from the Monte Carlo simulation 

can be also used to model a probabilistic component to the calculation of expected error. 

Therefore, expected levels of reliability can be included in the analysis, which is an important 

characteristic in pavement design and evaluation today (e.g., the MEPDG).(27) The standard 

deviation of the error was computed for each spacing combination. Normal distribution of the 

error was assumed, and the expected error at different spacings and different reliability levels

could be calculated. The average expected error is shown in figure 41 for various spacings and 

different probability levels for sections that are 10 mi (16.1 km) long.

1 mi = 1.61 km

Figure 40. Graph. Expected average error as function of spacing for 

10-mi-(16.1-km)-long sections.
66

1 mi = 1.61 km

Figure 41. Graph. Expected average errors for 10-mi- (16.1-km)-long section at different 

spacings and probability levels.

An example of how the process works is illustrated in figure 42. For a given spacing, s, the 

probability distribution can be computed based on the average error and standard deviation 

obtained from the Monte Carlo simulation. In the figure, 90 ε is the error calculated for a 

90 percent probability at s. This means that P(ε < ε 90 ) = 0.9 . If 90 ε is an acceptable error, 

choosing s implies that there is a 90 percent probability that the error associated with this 

sampling strategy is less than 90 ε .

Figure 42. Graph. Normal distribution.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 5 10 15 20

Probability

Error

μɛ ɛ 90
67

A concern was raised about the influence of the section length on the expected error, since the 

error in samples is a function of the number of test points in the sample. The hypothesis was that 

for the same spacing, errors would increase for shorter sections and decrease for longer sections. 

For this reason, a set of 5,000 simulations were run for sections that were 2, 3, 5, 10, 15, 20, and 

25 mi (3.22, 4.83, 8.05, 16.1, 24.15, 32.2, and 40.25 km) long with deflections randomly 

generated every 0.1 mi (0.161 km). The average error was plotted against spacing for each length 

(see figure 43). Looking at the graph, it is evident that the length of the section influences the 

magnitude of the expected error. A power curve of the form y = a × x

b was fit to all curves. 

Comparing the intercept, a, and the exponent, b, in each curve suggested that these values could 

be modeled as power functions of the section length themselves. These two functions are shown 

in figure 44.

1 mi = 1.61 km

Figure 43. Graph. Average error curves for different section lengths.

1 mi = 1.61 km

Figure 44. Graph. Values of a and b from the seven average error curves.
68

The results from figure 43 and figure 44 suggest that the expected error can be calculated for a 

particular section depending on its length and the chosen sampling strategy (spacing) according 

to the equation in figure 45.

0.031 0.523 0.6687 2 0.1494 ( 0.998) L με Ls R − − ⋅ = ⋅⋅ =

Figure 45. Equation. Average expected error due to sampling.

Where:

= Expected average error (percent).

L = Length (miles).

s = Spacing (miles).

The same process was repeated for the standard deviation of the expected error, which is shown 

in figure 46. The two functions for the intercept, a, and exponent, b, are shown in figure 47. The 

standard deviation of the expected error can be calculated for a particular section depending on 

its length and the chosen sampling strategy (spacing) according to figure 48.

1 mi = 1.61 km

Figure 46. Graph. Standard deviation of average error curves for different section lengths.

με
69

1 mi = 1.61 km

Figure 47. Graph. Values of c and d from the seven standard deviation curves.

0.044 0.519 0.4218 2 0.08 ( 0.996) L σ ε Ls R − − ⋅ =⋅ ⋅ =

Figure 48. Equation. Standard deviation of the expected error due to sampling.

Where:

= Standard deviation of the expected error (percent).

L = Length (miles).

s = Spacing (miles).

The effectiveness of these two equations is demonstrated in figure 49 and figure 50. Both figures 

show a good fit between the predicted error and standard deviation of error versus computed 

values from the Monte Carlo simulation.

σε
70

1 mi = 1.61 km

Figure 49. Graph. Observed average error (data points) plotted with the computed average 

error (lines).

1 mi = 1.61 km

Figure 50. Graph. Observed standard deviation (data points) plotted with the computed 

average error (lines).

The final step in the development of these equations involved the influence of the coefficient of 

variation (COV) on the average error. For this purpose, simulations were run for various means 

and standard deviations. The results are shown in figure 51. The numbers in the legend 

correspond to the mean, standard deviation, and COV. For the same COV, the average error 

remains the same regardless of the mean and standard deviation. Also, it is important to point out 

that an increase in COV increases the average error significantly.
71

1 mi = 1.61 km

Figure 51. Graph. Calculated errors for a 10-mi- (16.1-km)-long section with different 

means and standard deviations of errors.

In order to consider the effect of COV, a shift factor was determined to incorporate COV into the 

average error equation. The equation for the COV shift factor is shown in figure 52.

fCOV = 5.342 ⋅COV

Figure 52. Equation. Calculation of COV shift factor.

Although the shift factor was calculated and is available, COV will not likely be known prior to 

surveying the road with an FWD. Therefore, for practical applications, it is recommended that 

the average error should be calculated for a COV of 33 percent. This value was obtained from 

the FWD measurements used in this study and could be representative of the variability observed 

in field FWD data. This value was also used in this research for verifying the reliability approach 

laid out in this section. The verification of this approach is described in the following section.

Being able to predict the expected error and its standard deviation enables the development of 

error curves for different section lengths and reliability levels without running any more Monte 

Carlo simulations. Table 30 can be used to calculate the expected error in the average deflection 

as a result of a selected sampling strategy (spacing) for a given section length and 90 percent 

reliability. Additional tables were developed using this approach for a variety of section lengths 

and different reliability levels and are presented in appendix E.
72

Table 30. Errors in percentage for 90 percent reliability based on various section lengths,

sample spacings, and COV of 33 percent.

Probability

Length 

(mi)

Spacing (mi)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

90 percent

1 14.18 17.94 21.24 24.22 26.98 29.57 32.02 34.35 36.59

2 10.10 12.71 14.98 17.03 18.93 20.70 22.37 23.96 25.48

3 8.28 10.38 12.21 13.86 15.38 16.80 18.13 19.41 20.62

4 7.19 9.00 10.56 11.97 13.27 14.48 15.63 16.71 17.75

5 6.44 8.05 9.44 10.69 11.84 12.91 13.92 14.88 15.80

6 5.89 7.35 8.61 9.74 10.78 11.75 12.67 13.54 14.36

7 5.46 6.80 7.97 9.01 9.97 10.86 11.70 12.49 13.25

8 5.11 6.36 7.45 8.42 9.31 10.14 10.92 11.66 12.36

9 4.82 6.00 7.02 7.93 8.76 9.54 10.27 10.96 11.62

10 4.58 5.69 6.65 7.51 8.30 9.03 9.72 10.38 11.00

1 mi = 1.61 km

Comparison to Available Data

Deflection data from various roads in three States (New Mexico, Oregon, and Kansas) were 

obtained and analyzed. FWD data from New Mexico and Kansas were spaced at 0.1 mi 

(0.161 km) per test point, while Oregon was spaced at 0.05 mi (0.08 km). Overall statistics 

are presented in table 31. The roads were further separated into smaller sections based on the 

asphalt concrete layer thickness and base thickness (not available for every road) for creating 

homogenous sections. An overview of the deflection data for each state is given in figure 53. 

More detailed information is presented in appendix E.

Table 31. Deflection data for New Mexico, Oregon, and Kansas.

Statistics

New 

Mexico Oregon Kansas

Maximum (mil) 11.34 22.48 18.20

Minimum (mil) 4.33 4.31 4.27

Average (mil) 7.12 11.30 10.68

Standard 

deviation (mil) 2.51 3.90 3.09

COV 0.352 0.345 0.289

1 mil = 25.4

First, similar to the theoretical approach, the entire section data were divided in groups of 

increasing spacing by skipping up to 19 deflection points when enough data were available. The 

average error for each spacing was then computed for all sections. Next, the mean was compared 

to the mean of the entire section, which was assumed to be the true mean. Figure 54 shows the 

average error of means at different spacings averaged for all the sections in New Mexico. It can 

be noted that as the spacing increased, the difference to the true mean increased, as well, similar 

to the randomly generated deflections. The same trend follows for the other States.

μm
73

1 = 0.039 mil

Figure 53. Graph. Maximum and minimum section means and weighted mean deflection 

for all sections in each State.

1 mi = 1.61 km

Figure 54. Graph. Average error for each spacing.

The verification of the theoretical approach with field measured data was done by comparing the 

expected average error, computed using the equation in figure 45 and the COV shift factor 

equation in figure 52, with calculated values from the field distribution. Figure 55 through 

figure 57 show the measured error for a specific sampling strategy (spacing) and the expected 

error computed by the equations developed in the theoretical approach considering a reliability 

level of 50 percent (i.e., without including the standard deviation). As a consequence, it is 

expected that at least 50 percent of the sections would have errors less than or equal to the 

calculated error. It can be seen from all three figures that the theoretical approach provides a 

reasonable estimate of the error expected when one particular sampling strategy is selected. 

μm
74

Figure 55. Graph. Comparison between measured error and predicted error for all 

New Mexico sections at 0.2-mi (0.322-km) spacing.

Figure 56. Graph. Comparison between measured error and predicted error for all 

New Mexico sections at 0.5-mi (0.805-km) spacing.
75

Figure 57. Graph. Comparison between measured error and predicted error for all 

New Mexico sections at 1-mi (1.61-km) spacing.

ANALYSIS OF FREQUENCY FOR FWD DATA COLLECTION

The recommended frequency of FWD data collection on pavements is dependent on the overall 

“rate of change” of structural conditions over time. Since pavement deflection measurements, 

particularly the deflection at the center of the load plate, are a direct measurement of the overall 

structural condition of a pavement, the LTPP database was evaluated to determine how quickly 

deflections change over the range of testing dates and pavement thicknesses contained in the 

database. Flexible pavements were evaluated separately from rigid pavements with 

recommendations given for each.

Flexible Pavements

The objective of this analysis was to determine the rate of change of the center deflections over 

time for a variety of asphalt pavement thicknesses, traffic levels, subgrade types, and climatic 

conditions. The rate of change is used to determine how often deflection measurements should 

be taken on a network-level basis. Center deflections were used because they represent the total 

response of all the layers in the pavement structure.

The LTPP database contains 2,873 days of FWD tests taken for 59 State codes, 297 SHRP sites, 

and 8 construction cycles. Each record in the database contains the average of the deflections 

collected on a particular day over the entire SHRP test section along the outer wheel path. The 

records also contain the average air and mid-depth AC temperatures for the day of test. The 

deflection data were reviewed for statistical outliers, such as deflections measured on frozen 

pavements which were removed. In addition, those sites with too few or insufficient data 

collection cycles were omitted from the analysis. 
76

The analytical process consisted of the following steps:

1. Sort the order of the records by the total number of test days on a particular test section, as 

well as the standard deviations of center deflections (D1).

2. Normalize the deflections to a 9,000-lbf (40,050 N) load for each SHRP section.

3. Determine the degree of temperature sensitivity due to the AC layer for each SHRP section 

by regressing D1 versus mid-depth AC temperatures.

4. Remove the influence of temperature from the D1 measurements by adjusting them to a 

reference temperature of 68 °F (20 °C).

5. Regress D1 versus time to determine the slope (change in D1 over time).

6. Determine relationship between the slope and AC thickness, traffic levels, subgrade type, and 

climatic conditions (WF, DF, WNF, and DNF).

This process is demonstrated in figure 58 for one particular SHRP section. In this case, the State 

code is 50 and the SHRP ID number is 501002, which is US-7 near New Haven, VT. This 

section is composed of 8.5 inches (215.9 mm) of AC over 26 inches (660.4 mm) of unbound 

base or subbase materials, a fine-grained subgrade, and a WF climatic designation. There were 

60 days of FWD data collection available for analysis on this section, starting in September 1989 

and ending in October 2003. The traffic classification for this section was high, with an AADTT 

of 300 and 28 percent trucks of the class 9 variety. The deflection versus temperature 

characteristics for log (D1) are shown in the figure 58.

1 = 0.039 mil

1 °F = 1.8 °C + 32

Figure 58. Graph. Plot of log (D1) versus temperature for SHRP section 501002.

μm
77

The slope of the regression line is 0.0114 and is used in the following equation in figure 59 to 

adjust each deflection to the standard temperature of 68 °F (20 °C):

Figure 59. Equation. Deflection adjustment by temperature.

Where D1adj is the center deflection adjusted to 68 °F (20 °C), D1meas is the center deflection 

adjusted to 9,000 lb (4,086 kg), load b is the slope of the regression equation, T is the average 

mid-depth temperature, and Tref is the reference temperature of 68 °F (20 °C).

Figure 60 shows the center deflections plotted against test date for SHRP section 501002 before 

and after the temperature corrections were applied.

1 = 0.039 mil

1 lb = 0.454 kg

Figure 60. Graph. Center deflection measurements versus test date—adjusted and 

unadjusted.

Note that in figure 60, a long-term trend of increasing deflections can be detected. There are 

some seasonal variations, but these are minor in relation to the overall trend.

By fitting a linear regression line to the temperature adjusted data, as seen in figure 61, the rate 

of change of structural condition on the section can be determined. Note that the change is 

essentially linear. The slope of the regression line, 0.0164, represents the increase in microns per 

day for the center deflection. This can be converted to a yearly rate by multiplying it by 365, 

which equals roughly 0.234 mil (6 ) per year.

D1adj = 10log(D1meas) - b(T - Tref)

μm

μm
78

1 = 0.039 mil

Figure 61. Graph. Temperature-adjusted center deflections versus test date for 

SHRP section 501002.

A similar analysis was done for the remaining selected sections. Some sections displayed 

decreasing deflections over time, so the scalar value of the slope was used for the analysis. A 

summary of slope values is provided in table 32. The average slopes were grouped by traffic 

level, subgrade type, AC thickness, and climate classification in table 33 through table 36.

μm
79

Table 32. Annual change in D1 by SHRP test section.

State 

Code SHRP_ID

Construction 

Number

Annual Deflection 

Change (microns)

Number of 

Test Dates

48 3739 1 24.68 13

1 1019 1 21.28 4

20 1010 1 20.99 9

31 1030 2 18.50 10

27 6251 2 15.18 9

30 509 2 14.16 4

90 6405 1 12.67 17

49 1001 1 10.94 21

1 4155 1 9.85 4

83 1801 1 8.58 20

4 1024 3 8.15 13

27 1018z 4 8.03 10

20 1005 1 7.72 11

48 1060 1 6.98 32

33 1001 1 6.72 33

16 1010 1 6.32 28

50 1002 1 5.98 57

34 502 2 4.88 11

48 1119 2 4.64 5

56 1007 1 4.56 25

30 8129 1 4.31 33

23 1026 2 4.10 14

28 1802 1 3.76 21

2 1008 1 2.90 4

28 1016 1 2.21 18

2 1004 2 1.95 4

1 6019 3 1.84 4

1 4125 1 1.63 4

23 1026 1 1.51 18

24 507 2 1.44 9

34 507 2 1.43 13

87 1622 1 1.22 24

13 1031 1 1.18 4

13 1031 3 1.18 26

34 509 2 1.18 12

2 6010 1 1.12 4

34 506 2 1.07 12

13 1005 2 1.02 28

8 1053 1 0.96 39

24 1634 1 0.96 28

27 6251 1 0.83 30

37 1028 1 0.79 31
80

34 505 2 0.78 10

1 509 2 0.71 6

40 4165 1 0.68 29

34 504 2 0.56 12

2 1002 1 0.51 5

1 6012 1 0.50 4

27 1028 1 0.42 25

9 1803 1 0.30 12

35 1112 1 0.29 39

1 4127 2 0.24 4

34 508 2 0.23 12

34 503 2 0.10 14

1 = 0.039 mil

Table 33. Rate of deflection change by traffic level.

Traffic 

Classification

Average Annual Rate of 

Change in Center Deflection

(microns)

High 3.8

Low 4.5

1 = 0.039 mil

Table 34. Rate of deflection change by subgrade type.

Subgrade 

Type

Average Annual Rate of 

Change in Center Deflection

(microns)

Fine 4.2

Coarse 4.4

1 = 0.039 mil

Table 35. Rate of deflection change by AC thickness.

AC Thickness

(mm)

Average Annual Rate of 

Change in Center Deflection

(microns)

≤ 50 7.8

51–100 4.3

101–250 4.5

> 250 2.8

1 mm = 0.039 inches

1 = 0.039 mil

μm

μm

μm

μm
81

Table 36. Rate of deflection change by climate classification.

Climate

Average Annual Rate of 

Change in Center Deflection

(microns)

DF 5.8

DNF 6.4

WF 2.8

WNF 3.1

1 = 0.039 mil

From table 32 through table 36, the following can be concluded:

• The annual rate of change of pavement deflections shows little correlation with 

traffic levels.

• The annual rate of change of pavement deflections shows little correlation with 

subgrade type.

• The annual rate of change of pavement deflections does show some correlation to AC 

thickness—lower thicknesses produce higher rates of change, as expected.

• Dry climates seem to produce larger annual changes in pavement deflections, which is 

counter-intuitive.

• Once temperature influences are removed, the rate of change of deflection measurements 

is relatively small for most pavement sections contained in the LTPP database.(1)

Based on the analysis of these pavement sections, a test frequency of 5 years between tests is 

recommended for flexible pavements.

Rigid Pavements

The rigid pavement sections that were evaluated also exhibited temperature dependency and 

were adjusted to a standard temperature of 68 °F (20 °C). This dependency is most likely due to 

slab curling under higher temperatures. Subsequent to normalizing the deflections to 9,000 lb

(4,086 kg) and then removing the temperature effects, the annual change in D1 was less overall 

than that observed on the flexible pavement sections. It appears that the frequency of network 

level testing of rigid pavements can be less than flexible sections, perhaps up to 10 years 

between tests.

μm

83

CHAPTER 6—GUIDELINES FOR CONSIDERATION OF TIME OF DAY AND 

SEASON OF YEAR FOR OPTIMAL FWD DATA COLLECTION FOR PMS 

APPLICATIONS

SUMMARY OF APPROACHES FROM LITERATURE REVIEW

Since little has been published until recently about including deflection data in PMS applications, 

it stands to reason that even less has been published on the subjects of time of day and season of 

year when FWD testing should take place.

However, in July 2009, the Michigan Department of Transportation (MDOT) mentioned the 

potential of utilizing FWD load deflection testing at the network level.

(30) According to the 

report, MDOT intended to prescribe 500-ft (152.5-m) testing intervals, or about 10 test points per 

mile of pavement. MDOT also mentioned spring and late summer/early fall; however, no 

particular time of day to conduct deflection tests was mentioned.

Other agencies by and large either do not utilize load deflection tests at the network level, or the 

few that already use deflection testing generally allow their engineers to fix the proper test point 

intervals and/or the time of year to test, depending on the application and climatic region. For 

example, AkDOT also utilizes 500-ft (152.5-m) test intervals; however, it does not yet use 

deflection testing on their entire roadway network and is currently adding FWD test results as 

time allows (only the Parks Highway has been completed to date). The viable testing season is 

vastly shortened in Alaska due many months of frost penetration as well as the occasional yearround permafrost presence.

The vast majority of deflection testing—whether at the network or project level—is generally 

carried out during normal daytime work hours. Similarly, with seasonal testing, it is generally 

believed that the gathering of deflection data should occur when these data can be gathered as 

climatic conditions allow (and the pavement temperature is above freezing). This is to allow 

agencies to carry out network-level testing as far as possible at their own convenience because 

what is convenient as far as timing goes will most likely produce good deflection data for use in 

the stochastic relationships developed for this project.

While there are exceptions to the above statements, particularly when concrete pavements are 

tested, the general rule from the literature and practice alike is to test whenever possible during 

the day or year and not restrict when an agency can test for PMS applications. At some point 

in the future, it is also likely that the RWD will become a feasible and reasonably low-cost 

alternative to the FWD; but this is not currently the case, so this eventuality is not considered in 

this report.

It is also important to consider the issue of protection and maintenance of traffic (P&MT). For 

most medium to high traffic roads, FWD testing must be fit around the periods of high traffic 

flow, which often happens in the morning (6 to 9 a.m.) and afternoon periods (3 to 5 p.m.).
84

RESULTS OF LTPP DATA ANALYSIS

The LTPP database was reviewed in detail to ascertain whether limitations should be imposed, or 

suggested, to either the time of day or season of year when network-level FWD testing should 

(or should not) take place. At the outset, it was assumed that any significant limitations of this 

nature would tend to discourage the use of simplified techniques for both gathering and 

analyzing load deflection data, since roadway networks are, by definition, very extensive 

compared to individual projects.

DEFLECTION ADJUSTMENT PROCEDURES

The main reasons for adjusting the measured pavement deflections (at a given load level) is 

pavement temperature for flexible pavements or temperature gradients for PCC pavements.

For flexible pavements, in general, the use of an adjusted deflection level due to pavement 

temperature was not observed. Figure 62 shows the accuracy of the fatigue cracking model 

developed in chapter 4 for flexible pavements. The figure shows the ROC curve for two 

deflections, one adjusted by temperature and the other not adjusted. The fatigue cracking model 

indicates no improvement whatsoever by adjusting D1 due to pavement surface temperature 

variation. A similar analysis is provided in figure 63 for rutting. The statistics of these 

regressions are shown in table 37 and table 38.

Figure 62. Graph. Specificity of fatigue cracking models for flexible pavements.
85

Figure 63. Graph. Specificity of rutting models for flexible pavements.

Table 37. Statistics for flexible pavement fatigue cracking models: D1 versus D1 adjusted.

Model Significance

Area Under 

ROC Curve

Correct Cases—

Modeling (percent)

D1 0.53 0.64 59.0

D1adj 0.73 0.64 61.7

Table 38. Statistics for flexible pavement rutting models: D1 versus D1 adjusted.

Model Significance

Area Under 

ROC Curve

Correct Cases—

Modeling (percent)

D1 0.40 0.67 68.3

D1adj 0.12 0.62 59.5

While the fatigue cracking model showed virtually no change in either the area under the ROC 

curve or the correct cases predicted by the model, no improvement was noted. For the rutting

model, on the other hand, adjusting D1 made the model inferior to the unadjusted model.

In the case of the roughness model, deflection parameters involving D1 were not among those 

that showed the most promise overall. Therefore, the question of adjusting D1 or not is mute.

It was concluded that an adjustment to D1 due to asphalt temperature variations is neither helpful 

nor worth the time and effort to carry out this extra step for applications at the network level. 

Such an adjustment would also cause agencies to have to gather even more data—in this case, air 

and pavement surface temperature plus the previous day’s high and low temperatures at a 

minimum. To keep the network-level PMS application of adding simplified deflection analysis 

techniques to routine pavement management data would be counterproductive and is ill advised.

Since concrete surfaces are not subject to the same visco-elasticity that asphalt surfaces are, a 

temperature correction for concrete surfaces was not investigated.
86

Recommendation: Do not adjust deflection measurements—not even D1—due to temperature 

variations in any visco-elastic surface course layer.

RECOMMENDATIONS FOR TIME OF DAY FOR DEFLECTION MEASUREMENTS 

AT NETWORK LEVEL

As mentioned in the previous section, “Results of LTPP Data Analysis,” no limits for agencies 

are recommended for the time of day for FWD load deflection testing except normal daytime 

working hours. The main reason for this is to encourage agencies from doing network-level 

deflection testing by restricting the time of day when measurements should be conducted. A 

secondary but equally important reason is that the time of day generally does not appreciably

affect the accuracy of the simple models used by the logistic model, as recommended in this 

report. Networks are very large compared to individual projects, and since at least a statistically 

significant sampling of each uniform or standard pavement management section should be 

sampled, it would indeed be discouraging for an agency to also have to further limit their FWD 

testing window due to the large number of lane miles involved to cover an entire network.

Exceptions to this rule may apply to jointed PCC pavements when large temperature gradients

within the slab are present. Another possible exception is very high volume urban freeways when 

traffic control will be an issue. In such cases, only late evening through early morning testing is 

feasible and should be carried out in lieu of doing nothing. Finally, running FWD load deflection

tests while the underlying unbound layers may be frozen, or during the spring thaw in many of 

the northerly regions, should also be avoided for network-level FWD testing.

Exactly when concrete pavements have excessive temperature gradients and thus curling or 

warping due to these gradients is largely a function of local weather patterns, temperature 

differentials between day and night air temperatures (e.g., in desert regions), and when there is 

little or no cloud cover during the daytime, in which case, there is probably not a significant 

temperature gradient. If highly variable daily temperature swings occur on a 24-h basis, it is 

generally recommended to only test during morning hours before the sun has excessively heated 

the concrete slabs at the top (thus causing slab warping).

Recommendation: Limit the agency’s time window for testing flexible pavements to normal 

daytime working hours. Oftentimes, jointed concrete pavements are an exception to this rule, 

depending on climatic zone and/or temperature gradients in the slab, etc. Urban freeways are also 

a potential exception for safety reasons. Finally, do not test when the unbound materials are 

frozen beneath the pavement or during spring thaw.
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RECOMMENDATIONS FOR SEASON OF YEAR FOR MEASUREMENTS AT 

NETWORK LEVEL

An analysis and review of the FWD data in the LTPP database reveals that testing at virtually 

any (completely) thawed time of year is acceptable for network-level deflection testing. An 

example of the LTPP data analysis is shown in table 39.

Table 39. Statistics for flexible pavement IRI as a function of season.

Statistics All Data Spring Summer Fall Winter

Accuracy of model 0.73 0.65 0.78 0.77 0.80

Correct prediction 

rate (percent) 68 56 68 69 77

Error type I (false 

positive) (percent) 6.6 5.3 2.5 5.1 7.5

TPR (percent) 69 54 63 68 81

TNR (percent) 64 68 88 71 67

Note: Error type I predicts acceptable performance incorrectly, TPR predicts correctly acceptable

performance, and TNR predicts correctly not acceptable performance.

In this example and almost all other seasonal examples, there is little important difference 

between the overall goodness-of-fit and the corresponding values where the data are broken 

down by season. In table 39, the apparent improvement for some statistical categories during 

winter testing is due to the fact that only two of the four climatic regions are represented—DNF

and WNF. Error type I (false positive), the most serious of the two potential error types, is 

evidently improved by using summer season data only, which is the time of year that is most 

likely suitable for field testing and scheduling for most agencies.

For network data collection purposes, deflection testing during the spring thaw period for the 

DF and WF zones should be avoided because these data tend to cause bias results toward 

rehabilitation of those pavements that were tested during spring thaw.

Recommendation: Do not limit an agency’s seasonal time window for network-level deflection 

testing except during spring thaw conditions.

APPLICATIONS AND LIMITATIONS

The real issues indicted in the foregoing sections are that depending on location and 

environmental circumstances, the overall recommendations as to when to conduct FWD test 

surveys at the network-level may differ significantly. Obviously, limitations will inhibit any 

potential network testing program to the degree these limitations impose testing restrictions not 

generally encountered otherwise by agencies that manage roadway networks.

In areas such as Florida and coastal California, winter restrictions are more of an oxymoron than 

a real test scheduling hindrance, so winter testing can and should take place. Conversely, in 

Alaska, the testing season is greatly shortened for equally obvious reasons.
88

Finally, the deciding factor for mainline highways, especially urban freeways, may be traffic 

control. Accordingly, sometimes testing with the FWD will have to take place during nighttime 

closure hours—if it can take place at all.

Regard the above suggestions and recommendations as being general in nature, not specific for 

every region of the United States and Canada that was covered by the extensive LTPP 

monitoring and testing program, which was started by SHRP in the late 1980s.
89

CHAPTER 7—PRACTICAL EXAMPLE

INTRODUCTION

This chapter provides a practical example of how to apply the methodology resulting from this 

research to evaluate FWD load deflection data in network-level applications. At first, three large 

datasets were considered: the Illinois Tollway, the Maryland State Highway Administration

(MDSHA), and Parks Highway in Alaska.

The majority of the Illinois Tollway system consists of composite pavements. Since no reliable 

model was found during this research for composite pavements due to the shortage of data, the 

analysis of the Illinois Tollway dataset was jeopardized. The effort to retrieve only sections for 

rigid and flexible pavements was significant and not efficient.

The Parks Highway in Alaska has a simple and straightforward dataset. The pavements were 

already managed using a statewide PMS. FWD data were available for use with the appropriate 

flexible pavement models. The State’s treatment decision matrix was based on roughness. 

However, there were significant limitations on the variety of available treatments. The Parks 

Highway, which is located between Anchorage and Fairbanks, AK, uses few alternative 

treatments, most of which consist of mill and fill or a thin overlay. The impact of introducing a 

decision matrix based on structural condition would have been minimal, since no alternative was 

available for preventive treatment in part due to the light traffic using the facility.

MDSHA has a pavement management system that is based on ride quality (i.e., IRI). It 

utilizes PMS software for network analysis, budget optimization, and pre- and post-processing. 

Deflection data are available at the project level. There are a variety of treatment options 

covering preventive M&R.

This chapter illustrates how to apply simplified deflection techniques for structural analysis 

in network-level applications. The example uses the available dataset retrieved from 

MDSHA’s PMS.

REVIEW OF RECOMMENDED APPLICATION

The objective of a pavement design is to provide a structure that will exhibit adequate structural 

performance throughout its design life. It is expected that the structural condition affects the rate 

the pavement deteriorates over time. By definition, a given pavement structure has acceptable 

performance if distress levels do not exceed their threshold values during a period of time 

(e.g., fatigue cracking not to exceed 25 percent of the total area within the first 15 years 

of service).

Logistic models describe the probability of an event being acceptable or unacceptable as a 

function of a predictor variable. Therefore, they can be used to establish a link between 

performance and structural condition by modeling the probability of acceptable performance 

using measurements of deflections or parameters (techniques) computed from deflection basins.
90

The goal of the proposed stochastic approach is to use the probability density function from the 

logistic model to obtain insightful information about the pavement structural condition required 

to achieve the desired performance during a desirable (design) period of time. This new PMSbased knowledge can then be used to define strategic treatments (maintenance or rehabilitation) 

to be used in the PMS optimization process.

A typical logistic model probability function is described in chapter 4 of this report (see 

figure 25). It describes the likelihood of the pavement section exhibiting acceptable performance 

of a particular distress as a function of a given deflection parameter, named “predictor variable 

X.” In this example, the cutoff value was determined from the ROC curve and plotted.

In the stochastic approach, the probability density function is used to determine the thresholds 

that define structural condition. By definition, the cutoff value in a logistic model determines 

how to convert the continuous probability prediction as a dichotomous outcome (i.e., predicted 

probabilities above the threshold are defined as acceptable, while others are defined as 

unacceptable). In addition to the cutoff threshold, other values can be used to define further 

details about the structural condition. For example, figure 25 describes a second threshold 

created at the 0.4 probability level, and it is used to separate sections with fair structural 

condition from poor ones. (Note that this definition is arbitrary and can be adjusted to better fit 

an agency’s rehabilitation practices or network characteristics.)

Once thresholds and their respective deflection parameters are identified, a structural decision 

matrix (also referred to as a structural rehabilitation matrix) can be generated. Table 7 shows an 

example of structural decision matrix obtained from the probability density function in figure 25.

MDSHA EXAMPLE

MDSHA is responsible for managing approximately 17,000 lane-mi (27,370 lane-km) of 

roadways (about 11,000 directional-mi (17,710 directional-km) or some 22,000 centerline-mi

(35,420 centerline-km)). The budget for the Pavement System Preservation Program is between 

$150 million and $190 million per year, and it covers the maintenance and improvement of 

MDSHA’s pavement network. The network is divided into three regions: Mountain, Central, and 

Coastal. Among these, there are seven engineering districts, three rural districts, and four urban 

districts. The Pavement Management Division is responsible for the network-level data 

collection, analysis, and budget optimization through the PMS. The outcome of the budget 

optimization is typically the selection of sections for M&R. The Pavement and Geotechnical 

Division is responsible for project-level data collection, pavement design, and analysis after 

candidate projects are identified for M&R. These projects are assigned to the respective districts,

and the districts are responsible for construction bids, quality control, and acceptance.

Flexible pavements correspond to 61 percent of MDSHA’s network, rigid pavements correspond 

to 2 percent of the network, and the remaining 37 percent are composite pavements.

Overview on MDSHA PMS

The MDSHA PMS is constructed on an Oracle® database platform, and it is supported by 

the RoadcareTM software. RoadcareTM is responsible for data management, inputs, analysis, 

and outputs.

(31)
91

The performance of MDSHA’s pavement network is monitored annually. Each year, pavement 

ride quality, rutting, and friction conditions are recorded in the outside lane of both directions of 

travel for the majority of mainline roadways in Maryland. A video record of the pavement 

surface and right-of-way is also captured every year. This information (with the exception of 

friction data) is collected at highway speeds using an Automatic Road Analyzer testing device. 

Friction condition is tested with the pavement friction tester. MDSHA collects IRI, cracking, and 

friction data on about 95 percent of the entire pavement network.

Data are collected at 0.1-mi (0.161-km) intervals. After data collection, quality control is 

performed, and data are processed and entered into the MDSHA’s PMS, along with traffic data 

and structure (mainly changes in structure due to annual M&R). The PMS uses homogenous 

segments based on region, traffic level, pavement type, M&R treatments, and pavement 

condition. The identification of homogeneous segments is the first step in the analysis process 

and precludes all budget optimizations. MDSHA uses the FHWA classification based on IRI to 

identify the pavement condition qualitatively, as described in table 40.

Table 40. MDSHA pavement classification based on IRI values.

Pavement 

Classification

IRI Values 

(inches/mi)

Very good < 60

Good 60–94

Fair 95–170

Mediocre 171–220

Poor > 220

1 inch = 25.4 mm

1 mi = 1.61 km

MDSHA uses two preventive and four corrective treatment options for its flexible, concrete, and 

composite pavements. These treatments are currently assigned based on the age, pavement 

condition, and history of previously applied treatments. The 2-year maintenance and 4-year 

preventive maintenance strategies are labeled M2 and M4, respectively. The corrective 

treatments are classified as T5, T8, T12, and T15 based on the expected service life of the 

treatment—5, 8, 12, and 15 years, respectively.

Expected service life is assigned for every treatment. This is a crucial step in the development of 

the treatment decision matrix. It defines the years before any treatment can be applied to a 

specific road section after the M&R has been carried out. In addition, it also defines the years 

before the same treatment can be applied on the same section. The last caveat is important to 

prevent the optimization algorithm to be locked in just one treatment over long analysis periods.

The last step in the development of the decision matrix is the assignment of expected 

improvement in ride quality (i.e., IRI). MDSHA refers to this as “proposed consequences.”

The expected improvement in IRI is considered in the year immediately after the treatment is 

applied. LTPP’s Results of Long-Term Pavement Performance SPS-3 Analysis: Preventive 

Maintenance of Flexible Pavements study, along with the analysis of historical data in the 

MDSHA PMS, provides guidance for defining the proposed consequences.(32)
92

The complete treatment decision matrix is depicted in table 41. The range for the decrease in IRI 

after treatment reflects the variation expected in ride quality improvement as a function of 

pavement surface condition prior to treatment. Pavements in worse condition than others are 

likely to have a higher percentage improvement in IRI.

Costs are associated with each treatment reported in table 41. These costs are calculated based on 

road class, pavement type, distress level (IRI), and the region/district the section is located. The 

budget optimization takes these costs into consideration and uses the expected decrease in IRI 

values as benefit. The expected span between treatments is used to estimate service life and to 

program future M&R measures.

Table 41. MDSHA PMS treatment decision matrix.

Treatment 

Type

Treatment 

Code

Typical 

Treatment

Expected Span Between 

Treatments (years)

Decrease in 

IRI After 

Treatment 

Preventive Corrective (percent)

Preventive

M2 Fog seal 2 2 2 Crack sealing

M4 Slurry seal 2 4 5 Microsurfacing

Preventive/

corrective T5 In-place recycling 4 5 8–14 Thin overlay

Corrective

T8

Thin overlay

5 8 16–23

Mill/level and 

recycled 

Asphalt pavement 

overlay

T12

Thin overlay

6 10 17–27

Mill/level and 

recycled

Asphalt pavement 

overlay

T15 Mill/level and 

asphalt overlay 7 12 33–55

Sample of MDSHA Network

The MDHSHA PMS does not currently use deflection data for performance analysis or budget 

optimization. Network-level deflection surveys were not available. The alternative was to select 

sections that have been identified as targets for rehabilitation projects but where construction has 

not begun. In these cases, a complete project-level survey is conducted with FWD deflection 

testing performed at 0.1-mi (0.161-km) intervals.

In total, 50 sections were selected for this example where sufficient data were available, and the 

average length was 1.8 mi (2.90 km). The total lane-miles only corresponded to around 1 percent 

of the entire network. Additionally, 10 different districts were represented, and only flexible 
93

pavements were considered. Detailed descriptions of each site are provided in appendix F, 

including location, road class, thickness, traffic, and deflections. A summary of the sample 

statistics is provided in table 42 and table 43.

Table 42. Summary statistics of MDSHA sections used in the example.

Statistics Average

Standard 

Deviation Minimum Maximum

AC thickness 

(inches) 7.6 3.96 1.0 18.5

Total thickness 

(inches) 15.8 3.83 10.0 25.5

AADTT

(number of vehicles) 1,322.4 1,562.51 12.5 6,373.5

Volume of class 5

(number of vehicles) 439 423 7 1,748

Volume of class 9

(number of vehicles) 425 700 1 2,520

1 inch = 25.4 mm

Table 43. Summary statistics of MDSHA sections used in the example 

(percent distribution of sections).

Road Class

Distribution 

(percent)

Rural interstate 10

Urban interstate 6

Rural principal 8

Urban principal 6

Rural collector 72

Incorporation of Structural Analysis on MDSHA PMS

For this example, a new subset of the PMS database was created containing only sections 

identified in the sample. Since the sample size was only 1 percent of the total lane-miles in the 

State, the PMS simulation was carried out on 1 percent of the annual cost allocation for MDSHA 

pavement M&R program. In 2010, this value was $177 million. Therefore, the budget scenario 

for this example was assumed to be $1.7 million per year.

The analysis period was defined as 25 years, which is a typical period of time for an MDSHA 

optimization and budget study. 2007 was set as the initial year for this analysis, the earliest in 

which deflection data were available.
94

The analysis process consisted of performing the typical functional evaluation and budget 

optimization process, considering the functional decision matrix already in use and based 

on IRI performance alone. After the selection of treatments was generated, the structural analysis

was incorporated as an extra data element. The following steps were taken as part of the 

incorporation of structural analysis on MDSHA PMS as an example to this project:

1. Prepare the dataset.

2. Define the analysis period and budget constraints.

3. Perform the functional analysis and budget optimization.

4. Compute the structural condition of each section based on the logistic model.

5. Compare the solutions created from the functional analysis with the structural condition.

6. Adjust the prescribed treatments to reflect the structural needs.

7. Rerun the budget optimization to reflect the changes in the prescribed treatments.

8. Evaluate the impact on expected pavement condition and estimated service life due to 

structural analysis.

Two logistic models were used; one was based on roughness performance and one was based on 

rutting. These two models are shown in table 21 and figure 30 for roughness and table 22 and

figure 34 for rutting. Table 44 describes the structural decision matrix adopted for this example. 

Each section was evaluated, and the structural condition was assessed based on the model 

constants shown in table 45.

Table 44. Structural decision matrix based on roughness and rutting performance.

Structural 

Condition

Probability of Acceptable 

Performance

Roughness Rutting

Good > 0.812 > 0.792

Fair 0.812–0.406 0.792–0.396

Poor < 0.406 < 0.396

The next step is the comparison between the usual solution generated by the functional 

analysis only and the need for structural improvement. To simplify this comparison, table 45

was created to help identify where there was disagreement between the solution proposed based 

on functional analysis and the structural need of the pavement. For purposes of this example, 

table 45 was created based on engineering best judgment and adaptation to MDSHA current 

treatment options.
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Table 45. Adjustment of MDSHA treatment option based on structural analysis.

Treatment Type

MDSHA 

Treatment 

Option

Modified Treatment 

Option

Good Fair Poor

Preventive M2 M2 M4 T5

M4 M4 T5 T5

Preventive/corrective T5 M4 T5 T8

Corrective

T8 T5 T8 T8

T12 T8 T12 T12

T15 T8 T15 T15

Results of the Analysis Without Structural Component

The results of the analysis without a structural component were provided at the end of step 3

mentioned above. The majority of sections were identified as in need of some type of treatment 

within the 25-year analysis period. Figure 64 illustrates the distribution of sections by prescribed 

treatment. Only the first treatment for each section in the analysis period was considered. The 

average year for the first treatment was 2011 (4 years after the initial year).

In total, 32 percent of the sections were prescribed preventive treatment, 36 percent were 

prescribed corrective treatment, and 32 percent did not require any treatment. Improvements on 

the network sample were calculated in terms of improvement in service life and ride quality 

(i.e., a decrease in IRI). The expected increase in interval between treatments averaged 2.4 years. 

Additionally, the IRI values were expected to decrease by 6.9 percent between the first and 

second predicted intervention times.

Figure 64. Graph. Distribution of prescribed treatment for the first intervention.

Results of the Simulation With Structural Component

The decision of when to apply a treatment in a pavement section is part of the budget 

optimization process. In this analysis with a structural component, it was assumed for simplicity 

that the year the alternative is recommended remained as defined by the previous functional 

analysis (based on IRI) alone. In other words, the structural analysis did not define or modify 
96

when M&R is planned. Therefore, the new analysis could be carried out without the need to 

modify the PMS algorithm.

Two logistic structural models were used in this example: roughness and rutting. The models 

were used to compute the probabilities of acceptable performance based on FWD load deflection

parameters. Table 44 was used to qualitatively assess pavement structural condition. Based on 

this assessment and in conjunction with the prescribed treatment already defined based on the 

previous functional analysis, table 45 was used to adjust the treatments to incorporate the 

expected structural needs of each candidate pavement section.

After the conclusion of the analysis, improvements to the network were recomputed to reflect 

the new selection of treatments. Table 46 combines the results from the optimization with a 

structural analysis component and the previous results from the optimization without a structural 

analysis (labeled MDSHA).

The incorporation of the new structural analysis changed the outcome of prescribed treatments in 

about 60 percent of the sections. The majority of changes happened to sections that initially did 

not have any prescribed treatment. In these cases, the majority received preventive treatments. 

The percentage of corrective cases remained the same when the structural analysis was 

associated with roughness performance. In the cases association with rutting performance, there 

was a drop in corrective cases. These results agree with the expected outcome. Pavements in 

MDSHA’s network are more likely to fail due to roughness. Rutting is not a major problem in 

most of the State’s highways. The structural analysis reflected this particular characteristic of 

MDSHA’s network.

The new allocation of treatments obtained from the structural analysis provided greater 

improvement in ride quality. On average, about 10 percent improvement in IRI was expected 

when the optimization was done with a structural analysis for roughness, compared with 

6.9 percent when it was only a functional optimization and 7.4 percent for when it was with 

structural analysis for rutting.

The interval between treatments also increased. The previous functional analysis had an expected 

increase of 2.1 years in the period between treatments. The incorporation of a structural analysis 

in the optimization results expanded this period by some 60 percent to a total of 3.4 years 

(structural analysis based on roughness) and by 33.7 percent to a total of 2.9 years (structural 

analysis based on rutting).
97

Table 46. Results from the PMS optimization considering the structural analysis.

Results MDSHA

Optimization with 

Structural Analysis

Roughness Rutting

Preventive cases (percent) 32.0 64.0 78.0

Corrective cases (percent) 36.0 36.0 14.0

Solutions modified by structural 

analysis (percent) N/A 60.0 68.0

Improvement in IRI (percent) 6.9 10.0 7.4

Expected average increase in interval 

between treatments (years) 2.1 3.4 2.9

Improvement in expected average 

increase in interval between treatments, 

compared to MDSHA (percent) N/A 60.6 33.7

N/A = not available.

Cost Implications

The incorporation of structural analysis on the PMS optimization had an impact on the budget. 

Since the objective was not to perform a comprehensive budget analysis, some assumptions were 

made to simplify the process shown in this example.

There was no change in year allocated for treatments. Optimization prior to the structural 

analysis provided the year for any given treatment. In other words, the analysis considering the 

structural condition did not change the year associated with the first prescribed treatment in the 

analysis period.

The cost of treating sections without an assigned year was evenly spread across the 25-year 

analysis period. This reflects directly on sections that did not have any treatment assigned by the 

functional analysis, most likely due to budget constraints and cost/benefit analysis. However, 

during the structural analysis, some of these sections needed structural improvement. Without an 

assigned year, the extra cost of maintaining these sections was evenly distributed over the 

analysis period.

The cost analysis only reflected the first treatment prescribed to the section during the 

analysis period. Preventive treatments are common practice at MDSHA. Its PMS reflects this 

characteristic by incorporating preventive treatments to extend the service life of the pavement. 

Subsequent maintenance alternatives (M2 and M4 in table 41) were often predicted throughout 

the analysis period. The costs of subsequent maintenance efforts were not incorporated in this 

example’s cost analysis. The monetary values were not correct by any rate during the analysis 

period. Figure 65 provides an overview of cost allocation for the first treatment throughout the 

analysis period.
98

Figure 65. Graph. Cost distribution over the analysis period.

Table 47 provides a summary of differences observed in the budget. The total cost of all first 

interventions was $5.9 million for the optimization without structural analysis. The incorporation 

of structural analysis increased the budget by 59 percent to a total of $9.4 million (roughness 

model) and by 10.6 percent to a total of $6.5 million (rutting model). While these numbers may 

seem surprising, there is a considerable amount of new mileage being treated. Only 53.6 mi 

(86.3 kg) from the original 88.7 mi (142.8 kg) in the sample network were prescribed treatment 

when the current MDSHA PMS was used. Some treatment was prescribed to all sections when 

the structural model based on roughness was incorporated and to 79.5 mi (127.9 km) if the model 

was based on rutting.

Table 47. Impact on costs from the PMS optimization considering the structural analysis.

Results MDSHA

Optimization with 

Structural Analysis

Roughness Rutting

Total cost ($ in millions) 5.9 9.4 6.5

Cost difference (percent) 69.5 59.4 10.6

Mileage treated 53.6 88.7 79.5

Cost/mile ($ in thousands) 110.4 106.3 82.3

The benefit of including the structural component in the PMS can be observed when cost

per mile is compared between all three alternatives (see table 47). The cost/mile for the 

MDSHA PMS was $110,000/1 mi (1.61 km). After incorporating the structural component, 

the cost/mile reduced by 4 percent to $106,000/1 mi (1.61 km) (roughness model) and 

25 percent to $82,000/1 mi (1.61 km) (rutting model). The association of these numbers with 

the improvements in service life and ride quality and the overall impact of including the 

structural analysis in the PMS is encouraging.
99

CONCLUSIONS

The incorporation of structural analysis provided a new dimension in the prediction of 

performance and prescribed treatments to mitigate ride quality and structural deterioration of the 

pavement network. The process is simple and can be easily incorporated in existing PMS. An 

algorithm can be written to include the structural analysis as part of the optimization routine, or it 

can be done externally, like in the example based on the sample from MDSHA PMS.

Two structural models were tested. In this particular example, the scenario in which the 

structural model was based on roughness was the critical example. Roughness is the most 

common performance indicator driving the need for M&R in MDSHA’s network.

The incorporation of the new structural analysis changed the outcome of prescribed treatments 

on about 60 percent of the sections. Sections that initially did not have any prescribed treatment

received preventive treatments. Preventive maintenance is key to an effective level of service in 

any pavement network. The identification of segments where early structural failure is likely to 

happen helps mitigate them through early preventive maintenance. As a consequence, more 

M&R can be done with the same budget level and the backlog of pavement repairs can be 

reduced.

The new allocation of treatments obtained from the structural analysis provided greater 

improvement in ride quality. On average, about 10 percent improvement in IRI was expected 

when the optimization was done with a structural analysis for roughness, compared with 

6.9 percent when it was only a functional optimization.

The interval between treatments also increased. The previous functional analysis had an expected 

increase of 2.1 years in the period between treatments. The incorporation of a structural analysis 

in the optimization results expanded this period by some 60 percent to a total of 3.4 years 

(structural analysis based on roughness) and by 33.7 percent to a total of 2.9 years (structural 

analysis based on rutting).

There was a clear impact on budget allocation, which could be better adjusted if the optimization 

process was repeated with the new treatments. However, even without a new optimization, the 

benefits outlast the costs. There was a nominal increase in cost of 50 percent, considering the 

critical scenario. At the same time, there was a significant change in the improvements expected 

from the new M&R scenario based on the structural analysis. A 44 percent increase in expected 

ride quality performance and a 60 percent increase are expected in interval between treatments. 

Overall, the consideration of structural condition in the network-level analysis improved 

performance, minimized maintenance, and reduced the M&R costs per mile.

101

CHAPTER 8—CONCLUSIONS AND RECOMMENDATIONS

The primary objectives of this study were to identify/develop, verify, and recommend simplified 

deflection-based analytical techniques suitable for rapid automated screening of pavement 

structural capacity for inclusion in a network-level analysis, such as PMS. The LTPP database 

was the primary source of information for this study.

(1) The results can be readily implemented in 

national, State, and local municipality systems alike.

An additional objective was to provide recommendations for data collection procedures that will 

maximize testing productivity and minimize risk while still providing adequate information for 

use in a typical PMS. Test point spacings and frequency of data collection were the two primary 

parameters of interest.

A handful of successful techniques for use in network-level PMS applications were identified 

through the literature search. A few highway agencies have been using deflections as part of their 

network condition assessment. Among these, Texas, Virginia, and South African approaches 

were selected for further investigation. Several techniques commonly used at the project-level 

were investigated, as well. Combining all sources available, a list of potential applicable 

techniques was created. These deflection techniques formed the basis for the analyses carried 

out in this project.

SIMPLIFIED TECHNIQUES FOR EVALUATION AND INTERPRETATION OF 

PAVEMENT DEFLECTIONS FOR NETWORK-LEVEL ANALYSIS

Deflection data analysis provides qualitative and quantitative assessment of the structural 

integrity and bearing capacity of a pavement. Pavements with poor structural quality are more 

likely to develop distresses prematurely. It is commonly expected that the rate of deterioration 

increases as the structural condition worsens. Identifying pavements with poor structural 

condition is important to prevent early and rapid development of load-related distresses.

Based on the above premises, a probabilistic approach was developed to determine the likelihood 

of premature failure using simplified and easy-to-apply load deflection techniques. Premature 

failure was defined by the presence of excessive distress occurring prior to the end of the design

life of the pavement section (i.e., levels of distress higher than a design threshold). This was 

achieved by adopting binary logistic models that utilized deflection techniques derived from the 

FWD deflection basin coupled with various site-specific parameters.

The probability density function was used to determine the threshold levels that define structural 

condition. This was accomplished by determining the cutoff value in the logistic model, which 

determines how to convert a continuous probability prediction to a dichotomous outcome (i.e.,

predicted probabilities above the threshold were defined as acceptable while others were defined 

as not acceptable). This process was shown to be simple and straightforward. A structural 

decision matrix can be generated and incorporated as an integral part of an agency’s PMS 

optimization tools.
102

Several models were created based on pavement type and critical performance measures. For 

flexible pavements, the models created were based on roughness, rutting, and fatigue cracking. 

For rigid pavements, the models were based on roughness, faulting, and transverse slab cracking.

The advantages of the stochastic approach to evaluate the structural condition of the pavement 

for network-level analysis can be summarized as follows:

• It provides a direct link to pavement performance by estimating the likelihood of the 

development of load-related distresses in the early stages of the pavement’s service life. 

The intent was not to have a regression-based predictive model based on deflection data, 

but rather a simplified procedure to identify critical sections with a high (stochastic) 

likelihood of developing structural distresses prematurely.

• The probability density function is based on qualitative performance measures—

acceptable and not acceptable.

• Rating criteria can be created in the same a manner equivalent to the functional decision

matrix. Different tiers of structural quality can be defined based on deflection thresholds 

and the likelihood of acceptable performance. The structural decision matrix can then 

follow rating criteria similar to the functional decision matrix, which facilitates the 

implementation in existing PMS algorithms.

• The stochastic model is site-specific (i.e., additional variables may be incorporated that 

reflect site characteristics such as traffic, pavement structure, and climatic conditions).

• Different structural decision matrices can be defined based on different types of 

distresses. Therefore, the final evaluation can be made based on the most critical or most 

typical distress(es) observed in the network.

• The calculations are simple and do not require an interactive, labor-intense process. 

Therefore, it can be automated and incorporated in virtually any PMS in which deflection 

data are available.

• Deflection data obtained from project-level analyses or quality control after construction 

can also be used as an agency’s initial input data.

• The probabilistic models can be locally calibrated to reflect an agency’s own network 

characteristics (e.g., typical surface distresses observed, the interval between M&R 

projects, and the threshold of acceptable limits for distresses). In addition, the models can 

be recalibrated every time a new FWD testing campaign is completed and new load 

deflection data become available.

The importance of local calibration is underscored. Four examples were provided, which showed 

the potential improvements in accuracy and predictability that can be obtained if local data are 

used to calibrate the probabilistic models. The examples were simple exercises retrieved based 

on subsets of the LTPP database. Nevertheless, it was clear that local calibration could ultimately 
103

enhance the accuracy and quality of predictions, which would significantly benefit analyses at 

the network level, especially for the creation and allocation of M&R resources.

OPTIMUM DEFLECTION TEST SPACINGS AND FREQUENCY FOR PMS 

APPLICATIONS

Test Spacing

The approach was based on an evaluation of errors as a function of different test spacings in a 

variety of section lengths. The error represents the expected difference between the data sample 

and the idealized true value of the population, which is represented in this case by the average 

deflection value of a homogeneous road segment. It was assumed that the true value of the 

population was the average deflection of a homogenous segment where the spacing between 

deflection points was at the project-level (i.e., 0.1 mi (0.161 km)). Monte Carlo simulations were 

used to model the error function.

In addition to modeling the predicted (average) error, the results from the Monte Carlo 

simulation were also used to model a probabilistic component to the calculation of the expected 

error. This component was easily related to the length of the section and the expected error for a 

given reliability level. The reliability component is an important characteristic of this approach, 

as it fits well with current design practices such as the MEPDG.

(27) Tables were created that 

relate reliability level and section length with expected error, which can be used to define the 

optimum test spacings for a given section in a network-level analysis.

Ultimately, it is an agency’s budget that controls the quantity of deflection data that can be 

collected in any given year. Objective recommendations and guidelines were provided in this 

report to determine optimum test spacings given the level of accuracy and reliability desired.

Frequency

The recommended frequency of FWD data collection on pavements is dependent on the overall 

“rate of change” of structural conditions over time. The analysis of the deflections available in 

the LTPP database provided the following conclusions for flexible pavements:

• The annual rate of change of pavement deflections showed little correlation with 

traffic levels.

• The annual rate of change of pavement deflections showed little correlation to 

subgrade type.

• The annual rate of change of pavement deflections showed some correlation to AC 

thickness—lower thicknesses produced higher rates of change, as expected.

• Dry climates seemed to produce larger annual changes in pavement deflections, which 

is counterintuitive.
104

• Once temperature influences were removed, the rate of change of deflection 

measurements was relatively small for most pavement sections contained in the 

LTPP database.

Based on the analysis of these pavement sections, 5 years between FWD testing is recommended 

at the network-level for flexible pavements.

A similar analysis was conducted for rigid pavements. As expected, the variations in deflections 

measured at the center of the slab were significantly smaller than observed for flexible 

pavements. The recommendation is for a frequency of 10 years maximum between networklevel testing.

Time of Day and Season of Year

The vast majority of deflection testing—whether at the network or project level—is carried out 

during normal daytime (or nighttime in high trafficked areas) work hours. In fact, any agency 

that may want to limit network-level testing to anything more or less than their normal working 

hours is unlikely to end up using deflection testing in their PMS at all. Similarly, with seasonal 

testing, it is generally believed that gathering deflection data should occur when climatic 

conditions allow it (i.e., pavement temperature is above freezing), except during spring thaw 

conditions, which are important to avoid since they are not representative of the rest of the year.

It is also important to consider the issue of P&MT. In reality, for most medium to high traffic 

roads, FWD testing must be carried out to avoid periods of high traffic flow, which often occurs 

during the morning rush hour (6 to 9 a.m.) and afternoon rush hour (3 to 5 p.m.).

Regarding the adjustment of deflections based on temperature, it is recommended that no 

adjustment is needed if the deflection data are going to be used at the network level.

Depending on the location and environmental circumstances, the overall recommendations as to 

when to conduct FWD test surveys at the network level may differ significantly. Obviously, 

limitations will inhibit any potential network testing program to the degree these limitations 

impose testing restrictions not generally encountered otherwise by agencies that manage 

roadway networks.

EXAMPLE OF INCORPORATING STRUCTURAL ANALYSIS ON PMS

The incorporation of structural analysis provided a new dimension in the prediction of pavement 

performance and prescribed treatments to mitigate ride quality and structural deterioration of the 

overall pavement network. This process is relatively simple and can be easily incorporated in 

existing PMS. Algorithms can be written to include the structural analysis as part of the 

optimization routine. It was also shown that this process can be effectively done externally.

The incorporation of the new structural analysis changed the outcome of prescribed treatments 

on about 60 percent of the sections. Sections that initially did not have any prescribed treatment 

received preventive treatments. Preventive maintenance is key to an effective level of service in 

any pavement network. The identification of segments where early structural failure is likely to 

happen helps mitigate them through early preventive maintenance. As a consequence, more 
105

M&R can be done with the same budget level, and the backlog of pavement repairs can 

be reduced.

The new allocation of treatments obtained from the structural analysis provided greater 

improvement in ride quality. On average, about 10 percent improvement in IRI was expected 

when the optimization was done with a structural analysis for roughness compared to 

6.9 percent when it was only a functional optimization.

The interval between treatments also increased. The previous functional analysis had an expected 

increase of 2.1 years in the period between treatments. The incorporation of a structural analysis 

in the optimization results expanded this period by 60 percent to a total of 3.4 years (structural 

analysis based on roughness) and by 33.7 percent to a total of 2.9 years (structural analysis based 

on rutting).

The incorporation of structural analysis in the example presented in this report had a clear impact 

on pavement preventive M&R program budget allocation, with a nominal increase in M&R cost 

of 50 percent, considering the critical scenario. However, there was a reduction in cost per mile 

of about 4 percent, indicating that more could be done with the same allocated budget. At the 

same time, there was a significant change in the improvements expected from the new M&R

scenario based on the structural analysis—a 44 percent increase in expected ride quality and a 

60 percent increase in the interval between treatments.

Overall, the consideration of structural condition in the network-level analysis improved 

performance, minimized maintenance, and reduced M&R costs per mile. The pay-off in lowered 

agency costs of pavement M&R easily surpasses the cost of adding FWD load deflection testing 

to the agency.

APPENDIX A

Table 48. Useful practices for FWD use in network-level analyses.

Agency and 

Publication

Use of 

Deflection 

Data in PMS

FWD Test 

Point Spacing

FWD Test 

Frequency

FWD Sensor 

Positions

Limiting 

Specifics on 

PMS Use

Applicability of 

Current 

Analysis 

Approach in 

Streamlined

and Simple 

PMS

Would 

Unmodified Result 

be Useful Relating 

Observed Rate of 

Deterioration to 

Deflection?

Possibility 

of this 

Approach 

Combined 

with Others Summary

Caltrans;

Caltrans Test 

Method No. 356(3)

No N/A N/A N/A N/A Yes No Probably Uses center deflection only plus 

existing AC or AC + PCC layer 

thickness. Since it only applies 

to the DNF regions of 

California, the criteria would 

need shifting, and the time of 

year or day of testing would 

have to be better defined. 

Although it is generally used for 

rehabilitation design, it could be 

tiered into three or more 

categories (e.g., immediate 

project-level design, cosmetic 

or pavement preservation 

improvements, and no rehab 

or cosmetic improvements at 

this time).

FHWA;

Review of the LTPP 

Backcalculation 

Results(4)

No N/A N/A N/A N/A Yes No No If the subgrade modulus or 

indicator is regressed against 

various performance indicators, 

the Hogg model can be 

regressed at the same time. 

Furthermore, the entire LTPP 

database contains all available 

Hogg model subgrade stiffness 

values. While it is possible that 

surface course stiffness can also 

be derived using a related 

approach reported to FHWA, 

this is probably not worth the 

effort (subject to review by other 

team members).

107
NCHRP

;

“Assessing 

Pavement Layer 

Condition Using 

Deflection Data”(5)

No; 

feasibility 

study only

Probably not 

studied

Probably not 

studied

SHRP 

positions, 

generally

No limits 

pavement 

types were 

studied 

using LTPP 

database

Yes Yes Probably This project used easy-to-obtain 

deflection basin parameters and 

related these parameters to 

observed pavement distresses. 

As far as performance indicators 

are concerned, this study fits 

well into the current study. More 

information on the specifics 

should be obtained from the 

final report.

Swedish Road and 

Transport;

Strategic Highway 

Research Program 

and Traffic Safety 

on Two 

Continents(33)

No; 

feasibility 

study only

N/A N/A N/A N/A No No No The method uses a kind of 

forward-calculation using 

modulus matrices similar to how 

the MODULUS program works. 

It was only proposed for a single 

province in Sweden, and it is not 

practical or easy to understand 

for a typical transportation 

department. Mechanistic 

concepts are employed, which 

are unlikely to be met with 

widespread success in the 

United States or Canada. AC 

pavements only.

South Carolina 

Department of 

Transportation;

Feasibility of 

Including Structural 

Adequacy Index as 

Indicator of Overall 

Pavement Quality in 

the SCDOT Pavement 

Management 

System34)

No N/A N/A N/A N/A No No No Conclusions were that FWD 

data may be useful for flexible 

pavements only; recommended 

pilot study for this purpose. Not 

useful for the present study.

108
FHWA

;

Temperature 

Predictions and 

Adjustment Factors 

for Asphalt 

Pavement (FHWA-

RD-98-085)(6)

No N/A N/A N/A N/A Yes No Yes The adjustment for asphalt 

pavements for temperature-at-

depth and center deflection 

adjustments for pavement 

temperature may be used to 

assist in the present study.

FHWA; 

Backcalculation of 

Layer Moduli of 

LTPP General 

Pavement Study 

(GPS) Sites, 

FHWA-RD-97-

086(35)

No N/A N/A N/A N/A No No No Not useful for present study 

(back-calculation only).

Kansas Department 

of Transportation;

“ Network-Level 

Pavement 

Deflection Testing 

and Structural 

Evaluation”(7)

No; study 

only based on 

3 years of 

data from one 

district

Minimum of three tests per 

mile; five tests

is preferred.

One-third of 

network per 

year; however, 

one-fifth of 

network may 

be adequate

Unknown; 

probably 

unimportant

AC only Yes YesProbablyData were used from one Kansas 

district on AC surfaces only 

(non-interstate). For the 

technology and information 

available at the time, it used a

similar approach to the current 

study. The study was based on

the 1993 AASHTO Guide for 

Design of Pavement Structures. 

FWD, especially center 

deflection, added considerably 

to predictive capability of 

method used.(8) Based on the 

concept of PSE; PSE is twice as 

important as a pavement 

performance predictor than any 

other observable parameter.

Bayesian statistical approaches

were recommended; however, 

Kansas didnot implement it on 

a statewide basis thereafter.

109
Taiwan

;

“Evaluating the 

Structural Strength 

of Flexible 

Pavements in 

Taiwan Using the 

Falling Weight 

Deflectometer”(21)

No N/A N/A N/A N/A Yes No Probably as 

it uses 

deflection-

based 

parameters 

to a 

structural 

index

The report elaborates on using a 

combination of deflection-based 

parameters into a structural 

index. The index was 

empirically developed and 

relates to poor or good pavement 

condition assessed by 

experienced engineers and 

surveys. The method employed 

is not clearly described, but it 

involves binary assessment (0 

and 1) of pavement conditions. 

This assessment is then related 

to the structural index through a 

linear equation. The binary 

analysis is similar in concept to 

what the research team is 

proposing using the probabilistic 

model.

Independent study 

in the United 

Kingdom; “Assessing 

Variability of In 

Situ Pavement 

Material Stiffness 

Moduli”

(36)

No N/A N/A N/A N/A N/A N/A N/A The report discusses variability,

and conclusions are made 

regarding spacing of FWD 

testing.

Independent study 

in Minnesota;

Spatial Variability 

of Falling Weight 

Deflectometer Data: 

A Geostatistical 

Analysis(29)

No N/A N/A N/A N/A Yes No Probably This report discusses variability 

in FWD measurements using the 

geostatistical concept. Geostatistics are used when a 

continuous measure is sampled 

at discrete points in space, like 

deflections. They use a 

variogram to assess the variance 

of measurements and infer the 

optimum spacing that will 

results in maximum coverage of 

pavement sections with different 

structural behavior. This 

approach is similar to what the 

research team is proposing for phase II.

110
Netherlands

;

Application of FWD

Measurements at the 

Network Level(37)

No N/A N/A N/A N/A Possibly No Probably The report describes 

development of a structural 

adequacy indicator based on 

SCI600 in non

-trafficked area, 

and structural distress indicator

based on SCI600 in trafficked and 

non-trafficked area and 

cracking.

United Kingdom;

Use of Deflections 

at Network Level in

England for 

Programming and 

Other Purposes(13)

Yes N/A; used 

deflectograph, 

complemented 

by FWD

3–5 years N/A Flexible 

pavements 

only

No N/A N/A Used TRRL equations to 

calculate residual life and 

strengthening requirements 

based on deflection. The 

conclusion was that deflection 

does not increase with time and,

in some cases, decreases due to 

increases in pavement materials 

stiffness. This approach was 

used in United Kingdom until 

2000.

Department of Main 

Roads, Queensland, 

Australia;

Reliability of 

Optimal Intervals 

for Pavement 

Strength Data 

Collection at the 

Network Level(38)

No;

feasibility 

study only

200–1,000 m, 

1,000 m 

selected

N/A Unknown; 

probably 

unimportant

Flexible 

pavements 

only, wet 

and non-

reactive soil

No No NoBudget estimates were developed for different FWD 

spacings. SNs were calculated 

from deflections. The 

information obtained is not 

useful in the present project.

Department of Main 

Roads, Queensland, 

Australia 

A Probability-Based 

Analysis for 

Identifying 

Pavement 

Deflection Test 

Intervals for Road 

Data Collection(39)

No;

feasibility 

study only

200–1,000 m, 

1,000 m 

selected

N/A Unknown; 

probably 

unimportant

Flexible 

pavements 

only, wet 

and non-

reactive soil

Possibly No Probably Kolmogorov-Smirnov 

probability wasused based on 

goodness-of-fit test to identify 

optimal interval for pavement 

deflection data collection. Based 

on limited amount of data on a 

specific pavement type (surface 

treated pavement with granular 

base) and subgrade. Not 

applicable to present project.

111
Hong Kong

;

“Pavement 

Management—

Development of a 

Pilot PMS”

(40)

Pilot project 50 m N/A N/A N/A No No No Only the abstract was available, 

and it provided little useful 

information.

Europe;

The Way Forward 

for Pavement 

Performance 

Indicators Across 

Europe, Final 

Report —COST 

Action 354 

Performance 

Indicators for Road 

Pavements(41)

N/A. 

European 

project that 

collected data 

from different 

countries/ 

agencies

N/A N/A N/A N/A Possibly No Yes The proposed approach uses 

residual life or SCI300 for 

calculation of bearing capacity 

performance index. There are no 

details how remaining life is 

calculated and that part is 

probably not useful for current 

project. The use of parameters 

of deflection basin (like SCI300) 

can be considered in present 

project.

Europe;

Use of Falling 

Weight 

Deflectometers in 

Pavement 

Evaluation(42)

Yes 200–500 m3–5 years 0, 300, 600, 

900,1,200, and

1,500 mm for 

d0

> 1.0 mm; 

0, 300, 600, 

900, 1,500,

and 2,100 mm 

for d0

< 0.50 

mm

Not 

specified

Possibly No Yes The proposed approach uses 

central deflection or SCI 

(eventually SN calculated from 

deflections) at the first two 

levels. At the third level, it 

proposes the use of back-

calculation, which is not feasible 

for the present project.

Australia;

Comparison of

Project-Level and 

Network-Level 

Pavement Strength 

Assessment(43)

Yes, some 

members of 

Austroads

N/A N/A 0, 900, and

1,500 mm

Flexible and 

semi-rigid 

pavements

Possibly No Yes Uses adjusted SN (SNP) as an

indicator for pavement bearing 

capacity. SNP is calculated 

based on d0, 

d900, and d1500.

United Kingdom;

Structural 

Assessment of the 

English Strategic 

Road Network—

Latest 

Developments(16)

Yes,but 

rolling deflectometer 

only.

N/A N/A N/A N/A No No No The report discusses future use 

of traffic speed deflectometer 

instead of deflectometer or 

FWD at the network level. A 

modified BELLS equation was 

used for pavement temperature 

estimate based on air 

temperatures. Not useful for 

present project.

112
AkDOT

;

Modeling Flexible 

Pavement Response 

and Performance(9)

Yes 0.1 mi After repaving SHRP 

positions 

No limits Possibly, for 

"standardized" 

pavement 

structures

No Yes Deflections are converted to 

layer moduli, which are then 

used to obtain stress/strain 

values under a standard ESAL. 

Transfer functions relate 

stress/strain to cracking in 

bound layers and permanent 

deformation in unbound layers.

TxDOT; 

Incorporating a 

Structural Strength 

Index into the Texas 

Pavement 

Evaluation 

System(10)

Yes, but 

optional by 

district

0.5 mi Recommended 

one per year

1 ft Flexible 

pavements 

less than 5.5 

inches AC 

thickness

Yes Yes Yes SSI varies from zero (weak) to 

100 (strong). Based on 

normalized basin parameters 

such as outer deflections, SCI, 

and center deflection under a 

9,000 lb (4,086 kg) load. Can 

characterize subgrades and 

pavement structure 

independently in terms of 

relative stiffness. The system is 

based on statistical evaluation of 

deflections statewide.

TxDOT;

“Development of 

Structural Condition 

Index to Support 

Pavement 

Maintenance and 

Rehabilitation 

Decisions at 

Network Level”

(17)

Yes 0.25 miN/A 1 ft Flexible 

pavements

Yes Yes Yes SNeffand Mr are calculated using 

deflection parameters and then 

compared to the structural 

number required (SNreq) using 

traffic data. Structural condition 

index (SCI) is the ratio of SNeff

and SNreq. Novel approach uses 

simplifications arrive at SNeff

directly from deflections. 

TxDOT;

Development of a 

New Methodology 

for Characterizing 

Pavement Structural 

Condition for 

Network-Level 

Applications(18)

Yes 0.25 miN/A 1 ft Flexible 

pavements

Yes Yes Yes SNeff and Mr are calculated using 

deflection parameters, then 

compared to SNreq using traffic 

data. SCI is the ratio of SNeff and 

SNreq. Novel approach uses 

simplifications to arrive at SNeff

directly from deflections. 

113
TxDOT

;

Network-Level 

Deflection Data 

Collection for Rigid 

Pavement(11)

Yes 0.5 miN/A 1 ft Rigid 

Pavements

N/AN/AN/A From an analytical standpoint, 

the report mostly provides

recommendations regarding 

field test procedures. It refers to 

an earlier document regarding 

maximum allowable deflections 

for rigid pavement network 

testing.(11)

VDOT;

Network-Level 

Pavement 

Evaluation of 

Virginia’s Interstate 

System Using the 

Falling Weight 

Deflectometer(12)

Yes 0.2 mi4–5 year cycle SHRP 

positions 

No Yes Yes Yes Flexible pavements were 

analyzed by calculating the 

subgrade resilient modulus, the 

effective pavement modulus, 

and the effective SN. Rigid and 

composite pavements were 

analyzed by calculating the area 

under the deflection basin and 

the static modulus of subgrade 

reaction.

United States;

Modern Pavement 

Management(44)

No; propose 

method only

Unspecified Unspecified Uses center 

def only

Flexible 

pavements

Yes Yes Yes Uses traffic loading info to 

establish a maximum tolerable

Benkelman beam deflection. 

Not useful for purposes at-hand.

South Africa;

“Benchmarking the 

Structural Condition 

of Flexible 

Pavements with 

Deflection Bowl 

Parameters”(14)

Yes 0.2 kmN/A 300 mm 

typical

Flexible 

only

Yes Yes Yes Pavement is divided into three 

zones based on depth. The 

report uses basin parameters to 

characterize base, mid-depth,

and subgrade properties as 

sound, warning, or severe.

N/A = Not available.

1 mi = 1.61 km

1 inch = 25.4 mm

1 ft = 0.305 m

1 lb = 0.454 kg

114
115

APPENDIX B

PRE-SCREENING OF DEFLECTION PARAMETERS FOR FLEXIBLE PAVEMENTS

Table 49. Pre-screening of deflection variables for roughness-based logistic model for 

flexible pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further Analysis

(Y/N)

CI6 ( ) -0.178370162 4.29226E-06 Y

D4 ( ) -0.167037282 1.70543E-05 Y

D3 ( ) -0.164112365 2.40023E-05 Y

D5 ( ) -0.16348482 2.58087E-05 Y

I3 (1/ ) 0.157423073 5.13086E-05 Y

I4 (1/ ) 0.156412322 5.73986E-05 Y

CI5 ( ) -0.155825464 6.12415E-05 Y

D2 ( ) -0.1543182 7.22556E-05 Y

I2 (1/ ) 0.153150944 8.20426E-05 Y

S7_adj ( ) -0.145537369 0.000183728 Y

I1 (1/ ) 0.145204065 0.000190161 Y

Hogg (MPa) 0.144599721 0.000202367 Y

D6 ( ) -0.141494246 0.000277534 Y

I5 (1/ ) 0.141103268 0.000288662 Y

CI4 ( ) -0.140740184 0.000299369 Y

D1 ( ) -0.13426463 0.000564927 Y

S7 ( ) -0.128831936 0.000942315 Y

CI3 ( ) -0.116143945 0.002890483 Y

S6 ( ) -0.115692158 0.003002481 Y

TA7 -0.11326404 0.00367494 Y

F6 -0.112768646 0.003827883 Y

RA7 -0.1106046 0.004565907 Y

S5 ( ) -0.103761014 0.007821201 Y

CI2 ( ) -0.096945272 0.012986893 Y

I6 (1/ ) 0.095691166 0.014212626 Y

S4 ( ) -0.094183161 0.015820468 Y

RA2 0.091226217 0.0194418 Y

TA3 0.089415962 0.021998853 Y

RA3 0.086226561 0.027217802 Y

F5 -0.082867329 0.033834195 Y

D7 ( ) -0.07998036 0.040572597 Y

S3 ( ) -0.07923162 0.04249503 Y

TA6 -0.078396572 0.044729169 Y

TA2 0.078323562 0.04492912 Y

RA6 -0.073234091 0.060841102 N

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
116

CI1 ( ) -0.066884912 0.086944662 N

S2 ( ) -0.066884912 0.086944662 N

RoC 0.063457987 0.104406829 N

F4 -0.056337502 0.149489485 N

ELMOD E_sg 

(MPa) 0.052969563 0.175402664 N

F3 -0.046275974 0.236564727 N

F1_adj -0.040754908 0.297283156 N

TA5 -0.040536443 0.299882421 N

RA5 -0.035445108 0.364728857 N

D0_adj ( ) -0.032754064 0.402290133 N

RA1 0.029409516 0.452064746 N

TA1 0.025467297 0.514954392 N

S6_adj ( ) -0.021204611 0.587730186 N

S4_adj ( ) 0.019039547 0.626425273 N

D8 ( ) 0.018874369 0.629421864 N

S3_adj ( ) 0.018313619 0.639639986 N

D9 ( ) 0.017910311 0.647031718 N

TA4 -0.017904864 0.64713179 N

I7 (1/ ) 0.015566382 0.690661398 N

TA1_adj 0.014938567 0.702531384 N

RA4 -0.01483872 0.704425947 N

F2 0.014184956 0.716875694 N

S5_adj ( ) 0.007559144 0.846769384 N

SNeff_adj 0.007200049 0.853964888 N

SNeff 0.00667353 0.864536983 N

CI1_adj ( ) 0.005064275 0.896991944 N

S2_adj ( ) 0.005064275 0.896991944 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
117

Table 50. Pre-screening of deflection variables for rutting-based logistic model for flexible 

pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further Analysis

(Y/N)

S7_adj ( ) -0.167153505 5.79988E-05 Y

S4 ( ) -0.159500041 0.000125945 Y

S5 ( ) -0.158999373 0.00013234 Y

D1 ( ) -0.158966299 0.000132772 Y

S7 ( ) -0.157046194 0.000160318 Y

S6 ( ) -0.155896287 0.000179293 Y

S3 ( ) -0.154475825 0.000205643 Y

CI2 ( ) -0.154290947 0.000209328 Y

CI1 ( ) -0.152277305 0.000253673 Y

S2 ( ) -0.152277305 0.000253673 Y

CI3 ( ) -0.151222309 0.000280276 Y

D2 ( ) -0.150224418 0.000307818 Y

D0_adj ( ) -0.146393262 0.000438791 Y

S6_adj ( ) -0.142390152 0.000629805 Y

D3 ( ) -0.138246877 0.000906671 Y

I2 (1/ ) 0.13559866 0.001138587 Y

I1 (1/ ) 0.134151486 0.001287334 Y

Hogg (MPa) 0.134129037 0.001289776 Y

I3 (1/ ) 0.131225181 0.001644168 Y

CI4 ( ) -0.128016379 0.002138211 Y

S5_adj ( ) -0.119820535 0.004075148 Y

I4 (1/ ) 0.118144701 0.004628285 Y

CI1_adj ( ) -0.114405717 0.006113999 Y

S2_adj ( ) -0.114405717 0.006113999 Y

F1_adj -0.112114422 0.007223881 Y

TA5 -0.110044615 0.008378028 Y

RA5 -0.10896261 0.009044589 Y

D4 ( ) -0.108718381 0.009201425 Y

I5 (1/ ) 0.107963358 0.009701696 Y

F4 -0.107833906 0.009789857 Y

TA4 -0.10680269 0.010517957 Y

F3 -0.106526151 0.010721206 Y

RA4 -0.106305726 0.0108857 Y

TA2 0.102916715 0.013711708 Y

S4_adj ( ) -0.102089477 0.014492741 Y

RA2 0.101108758 0.015469154 Y

S3_adj ( ) -0.099499097 0.017197161 Y

RA6 -0.095460674 0.022294469 Y

RoC 0.094785846 0.023263186 Y

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
118

TA6 -0.093565581 0.025107621 Y

CI5 ( ) -0.09292169 0.026130799 Y

I6 (1/ ) 0.091444486 0.028614837 Y

D5 ( ) -0.090683049 0.029972663 Y

RA1 0.08641406 0.038651129 Y

TA1 0.086062505 0.039452319 Y

I7 (1/ ) 0.078829119 0.059324557 N

F5 -0.077055931 0.065294931 N

F2 -0.076739951 0.066409057 N

CI6 ( ) -0.075871511 0.069551778 N

D6 ( ) -0.073512315 0.078708057 N

SNeff 0.061135443 0.143851844 N

SNeff_adj 0.061050224 0.144412359 N

D7 -0.058430659 0.162468174 N

TA3 0.040223503 0.336485173 N

Elmod (MPa) 0.039244059 0.348392765 N

RA7 -0.037469644 0.370636181 N

TA7 -0.034111786 0.415071049 N

F6 -0.029939226 0.474446453 N

TA1_adj 0.020053403 0.631919684 N

RA3 0.004643708 0.911682772 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

μm

μm

μm

μm

μm

μm

μm

μm
119

Table 51. Pre-screening of deflection variables for fatigue cracking-based logistic model for 

flexible pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further Analysis

(Y/N)

D5 ( ) -0.157433136 0.000613975 Y

D6 ( ) -0.154864767 0.00075498 Y

D4 ( ) -0.154460852 0.000779708 Y

CI6 ( ) -0.153654425 0.000831333 Y

I4 (1/ ) 0.151051867 0.001020282 Y

I2 (1/ ) 0.149858715 0.001119523 Y

I1 (1/ ) 0.146532512 0.001445036 Y

Hogg (MPa) 0.145504691 0.001561978 Y

I3 (1/ ) 0.145381074 0.001576613 Y

I5 (1/ ) 0.139867364 0.002372627 Y

D3 ( ) -0.129861295 0.004805684 Y

D7 ( ) -0.12775584 0.005542626 Y

I6 (1/ ) 0.125224224 0.00656233 Y

CI5 ( ) -0.123675232 0.007266266 Y

D2 ( ) -0.120957194 0.008666145 Y

I7 (1/ ) 0.11905933 0.009781293 Y

D1_adj ( ) -0.115409302 0.012289432 Y

CI4 ( ) -0.115305763 0.012368194 Y

D1 ( ) -0.109334164 0.017734818 Y

S7 ( ) -0.098533789 0.03270609 Y

S6 ( ) -0.087200407 0.058888422 Y

RoC 0.082914884 0.072517007 Y

S5 ( ) -0.077466286 0.093448944 Y

CI2 ( ) -0.07365144 0.110792825 Y

S3 ( ) -0.06978492 0.130861177 Y

S4 ( ) -0.068774378 0.13654375 Y

CI1 ( ) -0.066345399 0.15097771 Y

S2 ( ) -0.066345399 0.15097771 Y

CI3 ( ) -0.057965846 0.209704568 Y

F5 -0.034265062 0.458639839 Y

RA2 0.033275762 0.471722237 Y

TA2 0.030577618 0.508422251 N

RA5 -0.025808734 0.576760343 N

RA6 -0.025702294 0.578333557 N

TA5 -0.024710043 0.593095202 N

TA6 -0.024306983 0.599140244 N

TA7 0.021979308 0.634581271 N

RA7 0.020701959 0.654398118 N

Elmod (MPa) 0.020351098 0.659884951 N

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
120

F3 -0.019932256 0.666458795 N

F2 -0.016123413 0.727360242 N

RA3 -0.015665734 0.734804513 N

SNeff 0.014228486 0.758340753 N

F6 -0.01094936 0.812849595 N

TA3 -0.008833073 0.848533217 N

RA1 0.008637656 0.85184507 N

TA1 0.007210874 0.876100985 N

RA4 -0.006796251 0.88317262 N

TA4 -0.002443006 0.957873617 N

F4 -0.002248203 0.961229969 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

μm

μm
121

PRE-SCREENING OF DEFLECTION PARAMETERS FOR RIGID PAVEMENTS

Table 52. Pre-screening of deflection variables for drop 2 roughness-based logistic model 

for rigid pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further Analysis

(Y/N)

CI6 ( ) 0.290964248 0.00023977 Y

D3 ( ) 0.248633096 0.00181135 Y

D2 ( ) 0.246794947 0.001963281 Y

D4 ( ) 0.245888742 0.002042366 Y

D5 ( ) 0.2456318 0.00206531 Y

D6 ( ) 0.240971679 0.002524188 Y

D1 ( ) 0.229180614 0.004124758 Y

S7 ( ) 0.226764149 0.004548299 Y

CI5 ( ) 0.220848663 0.005754184 Y

D7 ( ) 0.189099045 0.018447614 Y

CI4 ( ) 0.185710522 0.020693802 Y

I2 (1/ ) -0.17606761 0.028420732 Y

I1 (1/ ) -0.175443457 0.028996223 Y

I3 (1/ ) -0.174607503 0.029782537 Y

I4 (1/ ) -0.169595685 0.034887189 Y

I5 (1/ ) -0.163303473 0.04232556 Y

I6 (1/ ) -0.158141519 0.049380227 Y

CI3 ( ) 0.150567999 0.061475724 N

S6 ( ) 0.149266308 0.063781117 N

F2 -0.133454769 0.097830619 N

RA4 -0.129301034 0.108825846 N

I7 (1/ ) -0.122839154 0.127826608 N

CI2 ( ) 0.104097936 0.197390008 N

S5 ( ) 0.101999146 0.206626384 N

TA4 -0.099066256 0.220047952 N

F3 -0.095856024 0.235435942 N

TA1 0.08585525 0.288145047 N

TA7 0.080398249 0.319999581 N

RA7 0.076080697 0.34675897 N

F6 0.073356961 0.364344917 N

RA1 0.06976884 0.388337761 N

S4 ( ) 0.065926936 0.415056855 N

RA5 -0.063757985 0.430604574 N

RA3 -0.040641468 0.615601402 N

TA5 -0.039568813 0.624960894 N

TA2 0.033292173 0.680894243 N

CI1 ( ) -0.022171058 0.784217743 N

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
122

S2 ( ) -0.022171058 0.784217743 N

RA6 -0.021692424 0.788765571 N

TA3 -0.013100384 0.871475017 N

TA6 -0.011709822 0.885018028 N

F5 0.010944526 0.892485894 N

RA2 0.008716199 0.914281698 N

F4 -0.006492686 0.936094241 N

S3 ( ) 0.005354119 0.947282974 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

μm

μm

μm

μm
123

Table 53. Pre-screening of deflection variables for drop 2 faulting at joints-based logistic 

model for rigid pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further Analysis

(Y/N)

RA4 0.214349291 0.011281936 Y

I2 (1/ ) 0.161565404 0.057416035 Y

I3 (1/ ) 0.160361554 0.059323912 Y

I1 (1/ ) 0.159170852 0.061261829 Y

D6 ( ) -0.156200068 0.066323697 Y

I4 (1/ ) 0.155593311 0.067398334 Y

D4 ( ) -0.153028941 0.072097672 Y

D7 ( ) -0.152695779 0.07272723 Y

D5 ( ) -0.151896626 0.074255495 Y

D2 ( ) -0.147777675 0.0825488 Y

D3 ( ) -0.147476565 0.083183089 Y

I5 (1/ ) 0.141306072 0.097062111 N

CI6 ( ) -0.139053803 0.102562136 N

F2 0.134250113 0.115110182 N

I6 (1/ ) 0.130758489 0.124957373 N

D1 ( ) -0.127324496 0.135263402 N

TA4 0.127273639 0.135420768 N

CI4 ( ) -0.126333254 0.138355905 N

TA5 0.114819951 0.178322227 N

CI5 ( ) -0.101339581 0.235209646 N

CI2 ( ) -0.093785547 0.27213776 N

I7 (1/ ) 0.092003504 0.281392403 N

S7 ( ) -0.090384211 0.289982989 N

TA6 0.086764329 0.309812411 N

RA3 0.081777812 0.338545115 N

CI1 ( ) 0.077138643 0.366746497 N

S2 ( ) 0.077138643 0.366746497 N

F6 -0.075823917 0.374994804 N

TA3 0.070939348 0.406620091 N

F5 -0.059745946 0.484765826 N

TA2 0.052545667 0.538994225 N

F3 0.051718498 0.545411074 N

S3 ( ) 0.048479555 0.5708925 N

RA7 -0.048003744 0.574682506 N

RA1 -0.047770038 0.576548354 N

TA7 -0.044011956 0.606932531 N

S6 ( ) -0.042862677 0.616363736 N

RA2 0.04167614 0.626166819 N

RA5 0.030637134 0.720321778 N

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
124

S4 ( ) 0.030282662 0.723425468 N

CI3 ( ) -0.019433974 0.820364969 N

S5 ( ) -0.010779953 0.899771713 N

F4 0.005368993 0.949982837 N

RA6 -0.00241349 0.977504457 N

TA1 -0.000615033 0.994266728 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

μm

μm

μm

μm

μm
125

Table 54. Pre-screening of deflection variables for drop 2 transverse cracking-based logistic 

model for rigid pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further 

Analysis (Y/N)

TA7 -0.319520892 0.000126034 Y

RA7 -0.309129475 0.000213244 Y

CI4 ( ) -0.306955021 0.000237474 Y

CI6 ( ) -0.290660239 0.000518252 Y

S7 ( ) -0.274478931 0.00107596 Y

TA4 0.256897328 0.002266946 Y

F6 -0.247093151 0.003362544 Y

CI5 ( ) -0.238760097 0.004646404 Y

D3 ( ) -0.226070126 0.007450775 Y

D2 ( ) -0.225810314 0.007521264 Y

S6 ( ) -0.223660568 0.00812757 Y

D1 ( ) -0.220186286 0.00919917 Y

TA5 0.220101063 0.009226954 Y

D4 ( ) -0.215542071 0.010825472 Y

TA3 0.208771514 0.013648107 Y

CI3 ( ) -0.205417654 0.015270576 Y

F5 -0.201190574 0.017552769 Y

D5 ( ) -0.200505623 0.017949136 Y

S5 -0.199383576 0.018615204 Y

RA3 0.194642561 0.021671013 Y

TA2 0.185174717 0.029081989 Y

D6 ( ) -0.184261972 0.029898859 Y

TA1 0.180364803 0.033609595 Y

RA4 0.17853298 0.035484122 Y

RA6 -0.166200723 0.050535274 N

F4 -0.156545559 0.065718058 N

I1 (1/ ) 0.156256774 0.066223983 N

S4 ( ) -0.150107761 0.07777058 N

I2 (1/ ) 0.147752122 0.082602476 N

RA2 0.146349322 0.085592375 N

I3 (1/ ) 0.145766991 0.086858681 N

RA1 0.144649399 0.089330809 N

CI2 ( ) -0.135085129 0.112847157 N

I4 (1/ ) 0.133642345 0.11677941 N

RA5 -0.117173684 0.16952878 N

I5 (1/ ) 0.113244047 0.184394515 N

D7 ( ) -0.099745631 0.242693723 N

I6 (1/ ) 0.090640262 0.288613104 N

S3 ( ) -0.086547813 0.311025894 N

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
126

CI1 ( ) -0.059860287 0.483928914 N

S2 -0.059860287 0.483928914 N

F2 -0.036991396 0.66550023 N

F3 -0.031803265 0.710143716 N

I7 (1/ ) 0.020959832 0.806527519 N

TA6 -0.013199013 0.877439786 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

μm

μm

μm

μm
127

Table 55. Pre-screening of deflection variables for drop 3 roughness-based logistic model 

for rigid pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further Analysis

(Y/N)

D4 ( ) -0.231018767 0.003712941 Y

D3 ( ) -0.229746336 0.003912289 Y

D6 ( ) -0.22855743 0.004107194 Y

D2 ( ) -0.227149579 0.004349247 Y

D5 ( ) -0.226131044 0.004532267 Y

CI4 ( ) -0.225944603 0.004566507 Y

D7 ( ) -0.220699984 0.005629836 Y

D1 ( ) -0.216701832 0.006583631 Y

CI6 ( ) -0.206045677 0.00986392 Y

S7 ( ) -0.182120356 0.022878806 Y

I1 (1/ ) 0.175994414 0.027972346 Y

CI5 ( ) -0.169157994 0.034769885 Y

I3 (1/ ) 0.16634895 0.037942875 Y

I2 (1/ ) 0.165665443 0.038750801 Y

I4 (1/ ) 0.161123224 0.044495586 Y

RA4 0.1563815 0.051234896 N

I5 (1/ ) 0.147310985 0.066484788 N

S6 ( ) -0.139239409 0.082994782 N

I6 (1/ ) 0.135039829 0.092803725 N

S5 ( ) -0.112764232 0.161043076 N

CI3 ( ) -0.103730919 0.197516944 N

I7 (1/ ) 0.099708982 0.215553836 N

F2 0.099122913 0.218277178 N

F3 0.098703882 0.220239284 N

TA4 0.080175763 0.319763512 N

CI2 ( ) -0.078646317 0.329111714 N

RA7 -0.0674084 0.403092486 N

S4 ( ) -0.064462533 0.424004346 N

TA7 -0.063736586 0.429252484 N

F5 -0.053849755 0.50435152 N

TA5 0.05261841 0.514162317 N

RA3 0.047573575 0.555358928 N

RA1 -0.04750079 0.555964775 N

F6 -0.041405776 0.607798199 N

TA3 0.033801743 0.675283394 N

TA6 0.028644655 0.722614238 N

S3 ( ) -0.027271501 0.735405113 N

F4 -0.020034283 0.803948281 N

RA6 -0.019587441 0.808235667 N

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
128

TA1 -0.017775778 0.825675524 N

RA2 -0.015148917 0.851112643 N

CI1 ( ) -0.00682074 0.932653462 N

S2 ( ) -0.00682074 0.932653462 N

TA2 0.006150142 0.939261428 N

RA5 -0.005108871 0.949530006 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

μm

μm

μm

μm
129

Table 56. Pre-screening of deflection variables for drop 3 faulting at joints-based logistic 

model for rigid pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further Analysis

(Y/N)

RA4 0.188987017 0.023294968 Y

I1 (1/ ) 0.161603177 0.052980999 Y

I2 (1/ ) 0.152590048 0.067875984 Y

I3 (1/ ) 0.152364798 0.068287933 Y

I4 (1/ ) 0.146249842 0.080270274 Y

D4 ( ) -0.1419625 0.089638018 Y

D6 ( ) -0.141573149 0.090530178 Y

D5 ( ) -0.140156854 0.093835239 Y

D2 ( ) -0.1386745 0.097396262 Y

D3 ( ) -0.138555983 0.097685525 Y

D7 ( ) -0.135651185 0.104989848 Y

I5 (1/ ) 0.132374263 0.113737442 N

TA4 0.130564787 0.11880547 N

CI6 ( ) -0.130322639 0.119496771 N

D1 ( ) -0.127358213 0.128214615 N

CI4 ( ) -0.124884514 0.135856987 N

TA5 0.123294493 0.140949989 N

I6 (1/ ) 0.116088695 0.165865195 N

CI5 ( ) -0.106009787 0.206015806 N

S7 ( ) -0.102867226 0.219857942 N

F6 -0.100247392 0.231892343 N

RA3 0.093745676 0.263734925 N

TA3 0.085112094 0.310446542 N

CI2 ( ) -0.08460367 0.313356211 N

I7 (1/ ) 0.080597394 0.336902843 N

F5 -0.080316235 0.338596553 N

F2 0.073339491 0.382346557 N

S6 ( ) -0.067625477 0.420614497 N

RA7 -0.065458196 0.435691782 N

TA2 0.062337517 0.457934103 N

TA7 -0.059877081 0.475905951 N

RA2 0.045153639 0.59099446 N

S5 ( ) -0.042101505 0.616344996 N

RA6 -0.039774591 0.635983013 N

CI3 ( ) -0.03486104 0.67827905 N

TA1 0.033612957 0.689191042 N

TA6 0.032097654 0.702525638 N

F3 0.03187355 0.704505571 N

CI1 ( ) 0.031789962 0.705244568 N

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
130

S2 ( ) 0.031789962 0.705244568 N

F4 -0.017149361 0.838342746 N

RA5 0.012474146 0.882034272 N

S4 ( ) -0.009344165 0.911493318 N

S3 ( ) 0.006621708 0.937216504 N

RA1 0.001026985 0.990252956 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

μm

μm

μm

μm

μm
131

Table 57. Pre-screening of deflection variables for drop 3 transverse cracking-based logistic 

model for rigid pavements.

Variable Pearson R2 Sig (2-tailed)

Selected 

Parameter for 

Further 

Analysis(Y/N)

TA7 -0.318133195 0.000127903 Y

CI4 ( ) -0.316043599 0.000142422 Y

RA7 -0.309706065 0.000196388 Y

CI6 ( ) -0.282610246 0.0007166 Y

TA4 0.277229365 0.00091297 Y

S7 -0.274594487 0.001026122 Y

F6 -0.254023959 0.002457351 Y

CI5 ( ) -0.230262146 0.006201163 Y

S6 -0.228549955 0.006606782 Y

TA5 0.225359967 0.00742585 Y

TA3 0.218493416 0.009500867 Y

F5 -0.217427811 0.009865044 Y

RA4 0.216846506 0.010068849 Y

D3 ( ) -0.214288228 0.011010506 Y

D2 ( ) -0.213766402 0.011211815 Y

D1 ( ) -0.213709696 0.011233885 Y

S5 -0.210347696 0.012612458 Y

D4 ( ) -0.205333449 0.01494342 Y

RA3 0.205106163 0.015057437 Y

CI3 ( ) -0.193490726 0.021987806 Y

TA2 0.190745922 0.0239787 Y

D5 ( ) -0.189155654 0.025201446 Y

TA1 0.181253285 0.032099053 Y

RA6 -0.172706742 0.041297304 Y

D6 ( ) -0.172617805 0.041403564 Y

F4 -0.163447125 0.053657567 N

I1 (1/ ) 0.162734621 0.054723516 N

S4 -0.160655304 0.05793456 N

RA2 0.146856149 0.083372035 N

I2 (1/ ) 0.143377562 0.091027987 N

I3 (1/ ) 0.141640515 0.095055002 N

RA1 0.13994456 0.09912168 N

I4 (1/ ) 0.13119929 0.122312382 N

CI2 ( ) -0.124717703 0.142053064 N

RA5 -0.118078917 0.164690301 N

I5 (1/ ) 0.108597401 0.201530737 N

S3 -0.105511781 0.21471442 N

D7 ( ) -0.086202733 0.311200346 N

I6 (1/ ) 0.084554097 0.320579338 N

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm

μm
132

CI1 ( ) -0.081171507 0.340388524 N

S2 -0.081171507 0.340388524 N

F2 -0.043488715 0.60991585 N

TA6 -0.021620604 0.799839718 N

F3 -0.02112466 0.804337849 N

I7 (1/ ) 0.014311662 0.866718386 N

Note: Variables without units are dimensionless.

1 = 0.039 mil

1 MPa = 145.03 psi

1 1/ = 25.4 1/mil

FLEXIBLE PAVEMENT STRUCTURAL ANALYSIS

Models Based on Roughness Performance

Table 58. Statistics of calibrated models based on roughness performance of flexible 

pavements—all models.

Deflection Parameter

Primary Model Evaluation

Final 

Model

I2 CI4 CI5 D2 D3 Hogg I2

Area ROC 0.733 0.720 0.731 0.720 0.727 0.694 0.716

Hosmer-Lemeshow 

significance test 0.397 0.137 0.339 0.351 0.592 0.198 0.995

Calibration—

correct cases (percent) 68.4 62.8 67.9 64.6 67.3 63.9 64.1

Validation—

correct cases (percent) 74.2 61.3 69.4 66.1 71.0 74.2 69.4

Error type I

(false acceptable)

(percent) 6.6 4.7 5.7 5.9 6.5 7.0 6.6

Error type II

(false not acceptable)

(percent) 25.0 32.5 26.4 29.4 26.2 29.1 29.3

TPR (acceptable)

(percent) 69.3 60.0 67.5 63.8 67.8 64.2 64.0

TNR (not acceptable)

(percent) 64.4 75.0 69.2 68.3 65.4 62.5 64.4

μm

μm

μm

μm
133

Models Based on Rutting Performance

Table 59. Statistics of calibrated models based on rutting performance of flexible 

pavements—all models.

Deflection 

Parameter

Primary Model Evaluation Final Model

CI3 CI2 S7 D1 RA6 Hogg CI3 Hogg D1

Area ROC 0.669 0.658 0.678 0.710 0.624 0.646 0.659 0.640 0.647

Hosmer-Lemeshow 

significance test 0.066 0.494 0.398 0.414 0.818 0.115 0.267 0.501 0.137

Calibration—correct 

cases (percent) 68.8 67.1 64.6 70.1 60.0 60.7 66.5 62.0 61.8

Validation—correct 

cases (percent) 69.4 67.7 64.5 66.1 59.7 61.3 66.1 61.3 46.8

Error type I (false 

acceptable) (percent) 9.2 8.8 8.1 9.2 8.1 8.6 8.6 8.8 6.2

Error type II (false 

not acceptable)

(percent) 22.0 24.1 27.3 20.8 31.9 30.6 24.8 29.2 32.0

TPR (acceptable)

(percent) 72.0 69.4 65.3 73.6 59.5 61.1 68.5 62.9 59.3

TNR (not 

acceptable) (percent) 57.0 58.7 62.0 57.0 62.0 59.5 59.5 58.7 71.1

Table 60. Variables in the CI3 final model (based on rutting).

Variables (bi) ai p-value

CI3 -0.01146 0.00001594

Precipitation (mm) -0.0005259 0.04018

Class 9 volume -0.0007688 0.00005421

Constant 2.6586 1.0136*10^(-13)

Cutoff 0.792

1 inch = 25.4 mm

Table 61. Variables in the Hogg final model (based on rutting).

Variables (bi) ai p-value

Hogg 0.008182 0.0008198

Class 9 volume -0.000633 0.001079

Total pavement thickness

(inches) -0.02071 0.05083

Total HMA thickness

(inches) 0.08315 0.01762

Constant 0.552 0.1433

Cutoff 0.777
134

Table 62. Variables in the D1 final model (based on rutting).

Variables (bi) ai p-value

D1 -0.002361 0.00011

Class 9 volume -0.0006459 0.00034

Constant 2.2818 4.2966*10^(-21)

Cutoff 0.812

Models Based on Fatigue Cracking Performance

Table 63. Statistics of calibrated models based on fatigue cracking performance of flexible 

pavements.

Deflection Parameter

Primary Model Evaluation Final Model

I1 D1 D4 CI6 I2 Hogg I1 Hogg

Area ROC 0.657 0.638 0.625 0.613 0.650 0.620 0.642 0.624

Hosmer-Lemeshow 

significance test 0.368 0.535 0.533 0.238 0.864 0.284 0.596 0.213

Calibration—correct 

cases (percent) 63.0 59.0 60.7 59.0 62.5 60.7 59.7 60.4

Validation—correct 

cases (percent) 65.0 60.0 60.0 55.0 60.0 52.5 70.0 55.0

Error type I (false 

acceptable) (percent) 15.5 12.6 16.9 15.5 16.4 13.8 12.9 16.9

Error type II (false not 

acceptable) (percent) 21.5 28.3 22.5 25.5 21.1 25.5 27.4 22.7

TPR (acceptable)

(percent) 63.1 51.4 61.4 56.2 63.9 56.2 53.0 61.0

TNR (not acceptable)

(percent) 62.9 69.7 59.6 62.9 60.7 66.9 69.1 59.6

Table 64. Variables in the I1 final model (based on fatigue cracking).

Variables (bi) ai p-value

I1 154.764 0.0006015

AADTT -0.0005073 0.0007847

Pavement type 0.3774 0.07598

Constant -0.2202 0.4422

Cutoff 0.605

Table 65. Variables in the Hogg final model (based on fatigue cracking).

Variables (bi) ai p-value

Hogg 0.005262 0.006867

AADTT -0.0004274 0.002824

Constant 0.03849 0.8837

Cutoff 0.581

The Hogg parameter is defined in table 3.
135

RIGID PAVEMENT STRUCTURAL ANALYSIS FOR 9,000 LB (4,086 KG) FWD LOAD

Models Based on Roughness Performance (9,000 lb (4,086 kg))

Table 66. Statistics of calibrated models based on roughness performance of rigid 

pavements (9,000 lb (4,086 kg)).

Deflection Parameter

Primary Model Evaluation Final Model

CI5 I1 D5 S7 D1 Hogg CI5 I1 LTEA

Area ROC 0.699 0.730 0.692 0.647 0.647 0.625 0.651 0.645 0.620

Hosmer-Lemeshow 

significance test 0.297 0.181 0.043 0.024 0.024 0.017 0.557 0.007 0.293

Calibration—correct 

cases (percent) 71.0 73.8 69.0 65.5 65.5 65.7 65.5 65.5 60.1

Validation—correct 

cases (percent) 42.9 42.9 42.9 42.9 42.9 42.9 28.6 42.9 50.0

Error type I (false 

acceptable) (percent) 10.3 9.0 11.0 10.3 10.3 14.3 14.5 15.2 13.3

Error type II (false not 

acceptable) (percent) 18.6 17.2 20.0 24.1 24.1 20.0 20.0 19.3 26.6

TPR (acceptable)

(percent) 71.9 74.0 69.8 63.5 63.5 69.6 69.8 70.8 60.0

TNR (not acceptable)

(percent) 69.4 73.5 67.3 69.4 69.4 58.3 57.1 55.1 60.4

Note: The deflection parameter is based on a survey at the middle of the slab and LTE calculated at the joint approach.

Table 67. Variables in the CI5 final model (based on roughness) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

CI5 -0.078 0.00406

Class 9 volume -0.0003877 0.115

Constant 2.057 0.00002168

Cutoff 0.665

Table 68. Variables in the I1 final model (based on roughness) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

I1 131.600 0.003928

Class 9 volume -0.0005649 0.03668

Constant -0.465 0.375

Cutoff 0.639

Table 69. Variables in the LTEA final model (based on roughness) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

LTEA 1.804 0.01261

Constant -0.429 0.363

Cutoff: 0.69
136

Figure 66. Equation. Calculation of LTEA.

Table 70. Statistics of calibrated models based on roughness performance of rigid 

pavements for alternative FWD test locations (9,000 lb (4,086 kg)).

Deflection Parameter

Final Model

D1 D1

FWD test location Edge corner slab Edge midslab

Area ROC 0.641 0.716

Hosmer-Lemeshow 

significance test 0.446 0.411

Calibration—correct cases

(percent) 67.6 75.177

Validation—correct cases

(percent) 42.9 57.143

Error type I (false acceptable) 

(percent) 15.9 12.766

Error type II (false not 

acceptable) (percent) 16.6 12.057

TPR (acceptable) (percent) 74.7 82.474

TNR (not acceptable) (percent) 54.0 59.091

Table 71. Variables in the D1 final model for FWD testing at edge corner slab 

(based on roughness) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D1 -0.010125 0.01368

Class 9 volume -0.0004173 0.08322

Constant 1.983 0.0001133

Cutoff 0.652

Table 72. Variables in the D1 final model for FWD testing at edge midslab

(based on roughness) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D1 -0.01349 0.00003341

Class 9 volume -0.0007071 0.01186

Constant 3.551 0.0000001944

Cutoff 0.675

LTEA= 

D3

D1
137

Models Based on Faulting at Joints Performance (9,000 lb (4,086 kg))

Table 73. Statistics of calibrated models based on faulting at joints of rigid pavements

(9,000 lb (4,086 kg)).

Deflection Parameter

Primary Model Evaluation Final Model

D6 I2 I1 D7 Hogg D6 LTEA

Area ROC 0.624 0.639 0.638 0.603 0.586 0.637 0.590

Hosmer-Lemeshow 

significance test 0.173 0.009 0.025 0.027 0.078 0.064 0.592

Calibration—correct 

cases (percent) 60.8 67.7 65.4 42.3 54.3 63.8 57.3

Validation—correct 

cases (percent) 80.0 100.0 100.0 40.0 50.0 100.0 50.0

Error Type I (False 

Acceptable) (percent) 10.8 16.2 15.4 0.8 11.0 16.2 9.9

Error Type II (false not 

acceptable) (percent) 28.5 16.2 19.2 56.9 34.6 20.0 32.8

TPR (acceptable)

(percent) 56.0 75.0 70.2 11.9 46.3 69.0 50.0

TNR (not acceptable)

(percent) 69.6 54.3 56.5 97.8 68.9 54.3 71.1

Note: The deflection parameter is based on a survey at the middle of the slab and LTE calculated at the joint 

approach.

Table 74. Variables in the D6 final model (based on faulting at joints) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D6 -0.009225 0.138

Subgrade type -0.495 0.2003

Constant 1.499 0.005818

Cutoff 0.635

Table 75. Variables in the LTEA final model (based on faulting at joints)

(9,000 lb (4,086 kg)).

Variables (bi) ai p-value

LTEA 0.796 0.2804

Subgrade type -0.5104 0.194

Constant 0.454 0.4401

Cutoff 0.659
138

Table 76. Statistics of calibrated models based on faulting at joints of rigid pavements

(9,000 lb (4,086 kg)).

Deflection Parameter

Final Model

D1 D1

FWD test location Edge corner slab Edge midslab

Area ROC 0.694 0.695

Hosmer-Lemeshow 

significance test 0.047 0.576

Calibration—correct cases

(percent) 64.9 62.6

Validation—correct cases

(percent) 40.0 66.7

Error type I (false acceptable)

(percent) 10.7 10.7

Error Type II (false not 

acceptable) (percent) 24.4 26.7

TPR (acceptable) (percent) 63.6 59.3

TNR (not acceptable)

(percent) 67.4 68.9

Table 77. Variables in the D1 final model for FWD testing at edge corner slab (based on 

faulting at joints) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D1 -0.003976 0.002237

Subgrade type -0.923 0.03008

Constant 2.315 0.000003115

Cutoff 0.687

Table 78. Variables in the D1 final model for FWD testing at edge midslab (based on 

faulting at joints) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D1 -0.00861 0.001208

Subgrade type -0.836 0.04503

Constant 2.583 0.00001405

Cutoff 0.695
139

Models Based on Transverse Cracking Performance (9,000 lb (4,086 kg))

Table 79. Statistics of calibrated models based on transverse cracking of rigid pavements

(9,000 lb (4,086 kg)).

Deflection Parameter

Primary Model Evaluation Final Model

CI4 D1 Hogg RA7 CI4 D1 LTEA

Area ROC 0.766 0.741 0.703 0.747 0.766 0.726 0.706

Hosmer-Lemeshow 

significance test 0.363 0.424 0.145 0.136 0.363 0.071 0.948

Calibration—correct 

cases (percent) 77.5 72.9 76.0 78.3 77.5 72.9 70.1

Validation—correct 

cases (percent) 100.0 83.3 80.0 83.3 100.0 83.3 40.0

Error Type I (false 

acceptable) (percent) 10.1 8.5 11.2 11.6 10.1 10.1 8.7

Error Type II (false not 

acceptable) (percent) 12.4 18.6 12.8 10.1 12.4 17.1 21.3

TPR (acceptable)

(percent) 82.8 74.2 82.6 86.0 82.8 76.3 71.9

TNR (not acceptable)

(percent) 63.9 69.4 57.6 58.3 63.9 63.9 64.5

Note: The deflection parameter is based on a survey at the middle of the slab and LTE calculated at the joint 

approach.

Table 80. Variables in the CI4 final model (based on transverse cracking)

(9,000 lb (4,086 kg)).

Variables (bi) ai p-value

CI4 -0.254 0.0003759

Class 9 volume -0.001012 0.001084

Constant 3.630 0.0000003134

Cutoff 0.7

Table 81. Variables in the D1 final model (based on transverse cracking)

(9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D1 -0.006694 0.168

Class 9 volume -0.001017 0.001709

Total pavement thickness 0.225 0.0786

Constant 0.209 0.886

Cutoff 0.728
140

Table 82. Variables in the LTEA final model (based on transverse cracking)

(9,000 lb (4,086 kg)).

Variables (bi) ai p-value

LTEA 3.27 0.0001506

Constant -0.766 .0135

Cutoff 0.766

Table 83. Statistics of calibrated models based on transverse cracking of rigid pavements

(9,000 lb (4,086 kg)).

Deflection Parameter

Final Model

D1 D1

FWD test location Edge corner slab Edge midslab

Area ROC 0.774 0.703

Hosmer-Lemeshow 

significance test 0.353 0.168

Calibration—correct cases

(percent) 79.2 72.2

Validation—correct cases

(percent) 100.0 83.3

Error type I (false acceptable)

(percent) 9.6 11.1

Error type II (false not 

acceptable) (percent) 11.2 16.7

TPR (acceptable) (percent) 84.8 77.2

TNR (not acceptable) (percent) 63.6 58.8

Table 84. Variables in the D1 final model for FWD testing at edge corner slab

(based on transverse cracking) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D1 -0.006451 0.0001714

Class 9 volume -0.0007631 0.006384

Constant 3.328 0.0000000470

Cutoff 0.708

Table 85. Variables in the D1 final model for FWD testing at edge midslab

(based on transverse cracking) (9,000 lb (4,086 kg)).

Variables (bi) ai p-value

D1 -0.01000 0.0005496

Class 9 volume -0.0008483 0.004314

Constant 3.347 0.0000005382

Cutoff 0.713
141

RIGID PAVEMENT STRUCTURAL ANALYSIS FOR 12,000-LB (5,448-KG) 

FWD LOAD

Models Based on Roughness Performance (12,000 lb (5,448 kg))

Table 86. Statistics of calibrated models based on roughness of rigid pavements

(12,000 lb (5,448 kg)).

Deflection Parameter

Primary Model Evaluation Final Model

CI4 D6 CI6 I1 CI4 I1 LTEA

Area ROC 0.663 0.630 0.621 0.638 0.663 0.638 0.620

Hosmer-Lemeshow 

significance test 0.049 0.626 0.659 0.214 0.049 0.214 0.177

Calibration—correct 

cases (percent) 64.1 62.1 61.4 69.0 64.1 69.0 60.8

Validation—correct 

cases (percent) 57.1 57.1 71.4 71.4 57.1 71.4 66.7

Error Type I (false 

acceptable) (percent) 9.7 13.1 16.6 17.2 9.7 17.2 13.3

Error Type II (false not 

acceptable) (percent) 26.2 24.8 22.1 13.8 26.2 13.8 25.9

TPR (acceptable)

(percent) 60.8 62.9 67.0 79.4 60.8 79.4 61.9

TNR (not acceptable)

(percent) 70.8 60.4 50.0 47.9 70.8 47.9 58.7

Note: The deflection parameter is based on a survey at the middle of the slab and LTE calculated at the joint 

approach.

Table 87. Variables in the CI4 final model (based on roughness) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

CI4 -0.117 0.007378

Class 9 volume -0.0004607 0.06459

Constant 2.148 0.0000447

Cutoff 0.695

Table 88. Variables in the I1 final model (based on roughness) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

I1 160.521 0.008563

Class 9 volume -0.0005612 0.03519

Constant -0.293 0.576

Cutoff 0.62

Table 89. Variables in the LTEA final model (based on roughness) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

LTEA 1.903 0.01053

Constant -0.434 0.371

Cutoff 0.697
142

Table 90. Statistics of calibrated models based on roughness of rigid pavements

(12,000 lb (5,448 kg)).

Deflection Parameter

Final Model

D1 D1

FWD test location Edge corner slab Edge midslab

Area ROC 0.654 0.710

Hosmer-Lemeshow 

significance test 0.479 0.573

Calibration—correct cases

(percent) 60.7 70.9

Validation—correct cases

(percent) 57.1 71.4

Error Type I (false 

acceptable) (percent) 12.9 13.5

Error Type II (false not 

acceptable) (percent) 26.4 15.6

TPR (acceptable) (percent) 61.1 76.8

TNR (not acceptable)

(percent) 60.0 58.7

Table 91. Variables in the D1 final model for FWD testing at edge corner slab 

(based on roughness) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D1 -0.003005 0.003249

Class 9 volume -0.0003201 0.185

Constant 1.961 0.000007846

Cutoff 0.707

Table 92. Variables in the D1 final model for FWD testing at edge midslab 

(based on roughness) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D1 -0.009806 0.00004818

Class 9 volume -0.0007354 0.009784

Constant 3.422 0.0000004192

Cutoff 0.664
143

Models Based on Faulting at Joints Performance (12,000 lb (5,448 kg))

Table 93. Statistics of calibrated models based on faulting at joints of rigid pavements

(12,000 lb (5,448 kg)).

Deflection Parameter

Primary Model Evaluation Final Model

D6 I1 Hogg D6 LTEA

Area ROC 0.644 0.643 0.592 0.634 0.608

Hosmer-Lemeshow 

significance test 0.131 0.640 0.596 0.222 0.745

Calibration—correct cases

(percent) 64.9 61.9 56.6 61.9 58.8

Validation—correct cases

(percent) 50.0 66.7 33.3 50.0 50.0

Error type I (false acceptable)

(percent) 17.2 9.7 14.0 12.7 13.0

Error type II (false not 

acceptable) (percent) 17.9 28.4 29.5 25.4 28.2

TPR (acceptable) (percent) 72.4 56.3 53.7 60.9 57.5

TNR (not acceptable) (percent) 51.1 72.3 61.7 63.8 61.4

Note: Deflection parameter based on survey at the middle of the slab and LTE calculated at joint approach.

Table 94. Variables in the D6 final model (based on faulting at joints) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D6 -0.008789 0.06896

Subgrade type -0.579 0.139

Constant 1.734 0.002499

Cutoff 0.651

Table 95. Variables in the LTEA final model (based on faulting at joints)

(12,000 lb (5,448 kg)).

Variables (bi) ai p-value

LTEA 1.106 0.144

Subgrade type -0.335 0.3899

Constant 0.172 0.773

Cutoff 0.677
144

Table 96. Statistics of calibrated models based on faulting at joints of rigid pavements

(12,000 lb (5,448 kg)).

Deflection Parameter

Final Model

D1 D1

FWD test location Edge corner slab Edge midslab

Area ROC 0.702 0.695

Hosmer-Lemeshow 

significance test 0.103 0.572

Calibration—correct cases

(percent) 64.9 61.832

Validation—correct cases

(percent) 60.0 83.333

Error type I (false acceptable)

(percent) 9.2 10.687

Error type II (false not 

acceptable) (percent) 26.0 27.481

TPR (acceptable) (percent) 60.9 58.621

TNR (not acceptable) (percent) 72.7 68.182

Table 97. Variables in the D1 final model for FWD testing at edge corner slab

(based on faulting at joints) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D1 -0.003291 0.002071

Subgrade type -0.825 0.04834

Constant 2.286 0.000006551

Cutoff 0.691

Table 98. Variables in the D1 final model for FWD testing at edge midslab

(based on faulting at joints) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D1 -0.007078 0.001048

Subgrade type -0.883 0.03558

Constant 2.764 0.000009804

Cutoff 0.7
145

Models Based on Transverse Cracking Performance (12,000 lb (5,448 kg))

Table 99. Statistics of calibrated models based on transverse cracking of rigid pavements

(12,000 lb (5,448 kg)).

Deflection Parameter

Primary Model Evaluation Final Model

CI4 D1 Hogg TA7 CI4 D1 LTEA

Area ROC 0.778 0.749 0.709 0.739 0.775 0.735 0.683

Hosmer-Lemeshow 

significance test 0.353 0.396 0.008 0.107 0.200 0.139 0.493

Calibration—correct 

cases (percent) 74.4 73.6 69.4 77.5 74.4 72.1 66.1

Validation—correct 

cases (percent) 66.7 50.0 50.0 66.7 83.3 50.0 80.0

Error Type I (false 

acceptable) (percent) 7.8 8.5 9.7 11.6 9.3 9.3 11.8

Error Type II (false not 

acceptable) (percent) 17.8 17.8 21.0 10.9 16.3 18.6 22.0

TPR (acceptable)

(percent) 75.0 75.0 71.1 84.8 77.2 73.9 69.9

TNR (not acceptable)

(percent) 73.0 70.3 64.7 59.5 67.6 67.6 55.9

Note: Deflection parameter based on survey at the middle of the slab and LTE calculated at joint approach.

Table 100. Variables in the CI4 final model (based on transverse cracking)

(12,000 lb (5,448 kg)).

Variables (bi) ai p-value

CI4 -0.231 0.00007858

Class 9 volume -0.001029 0.001282

Constant 3.9796 0.0000001201

Cutoff 0.71

Table 101. Variables in the D1 final model (based on transverse cracking)

(12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D1 -0.008441 0.07225

Class 9 volume -0.001027 0.001734

Total pavement thickness 0.1948 0.1398

Constant 0.943 0.5641

Cutoff 0.73
146

Table 102. Variables in the LTEA final model (based on transverse cracking)

(12,000 lb (5,448 kg)).

Variables (bi) ai p-value

LTEA 2.679 0.001196

Constant -0.5943 0.2463

Cutoff 0.736

Table 103. Statistics of calibrated models based on transverse cracking of rigid pavements

(12,000 lb (5,448 kg)).

Deflection Parameter

Final Model

D1 D1

FWD test location Edge corner slab Edge midslab

Area ROC 0.768 0.694

Hosmer-Lemeshow 

significance test 0.403 0.131

Calibration—correct cases

(percent) 77.6 67.460

Validation—correct cases

(percent) 100.0 66.667

Error Type I (false acceptable)

(percent) 8.8 7.937

Error Type II (false not 

acceptable) (percent) 13.6 24.603

TPR (acceptable) (percent) 81.7 66.304

TNR (not acceptable) (percent) 65.6 70.588

Table 104. Variables in the D1 final model for FWD testing at edge corner slab

(based on transverse cracking) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D1 -0.005252 0.0002574

Class 9 volume -0.0007991 0.005173

Constant 3.409 0.00000009316

Cutoff 0.725

Table 105. Variables in the D1 final model for FWD testing at edge midslab

(based on transverse cracking) (12,000 lb (5,448 kg)).

Variables (bi) ai p-value

D1 -0.006136 0.01611

Class 9 volume -0.02948 0.0187

Total PCC thickness 0.1211 0.3503

Constant 2.662 0.1164

Cutoff 0.718
147

APPENDIX C

FLEXIBLE PAVEMENT STRUCTURAL ANALYSIS

Models Based on Rutting Performance for Flexible Pavements

1 = 0.039 mil

Figure 67. Graph. Sensitivity of rutting acceptable probability to deflection parameter CI3

for flexible pavements.

μm
148

1 = 0.039 mil

Figure 68. Graph. Sensitivity of rutting acceptable probability to deflection parameter D1

for flexible pavements.

1 MPa = 145.0377 psi

Figure 69. Graph. Sensitivity of rutting acceptable probability to deflection parameter 

Hogg for flexible pavements.

μm
149

Models Based on Fatigue Cracking Performance for Flexible Pavements

1 1/ = 25.4 1/mil

Figure 70. Graph. Sensitivity of fatigue cracking acceptable probability to deflection 

parameter I1 for flexible pavements.

1 MPa = 145.0377 psi

Figure 71. Graph. Sensitivity of fatigue cracking acceptable probability to deflection 

parameter Hogg for flexible pavements.

μm
150

RIGID PAVEMENT STRUCTURAL ANALYSIS FOR 9,000-LB (4,086-KG) FWD LOAD

Models Based on Roughness Performance for Rigid Pavements (9,000 lb (4,086 kg))

1 = 0.039 mil

Figure 72. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

CI5 for rigid pavements (9,000 lb (4,086 kg)).

1 1/ = 25.4 1/mil

Figure 73. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

I1 for rigid pavements (9,000 lb (4,086 kg)).

μm

μm
151

Figure 74. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

LTEA for rigid pavements (9,000 lb (4,086 kg)).

Models Based on Faulting at Joints Performance for Rigid Pavements (9,000 lb (4,086 kg))

1 = 0.039 mil

Figure 75. Graph. Sensitivity of faulting at joints acceptable probability to deflection 

parameter D6 for rigid pavements (9,000 lb (4,086 kg)).

μm
152

Figure 76. Graph. Sensitivity of faulting at joints acceptable probability to deflection 

parameter LTEA for rigid pavements (9,000 lb (4,086 kg)).

Models Based on Transverse Cracking Performance for Rigid Pavements (9,000 lb 

(4,086 kg))

1 = 0.039 mil

Figure 77. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter CI4 for rigid pavements (9,000 lb (4,086 kg)).

μm
153

1 = 0.039 mil

Figure 78. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter D1 for rigid pavements (9,000 lb (4,086 kg)).

Figure 79. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter LTEA for rigid pavements (9,000 lb (4,086 kg)).

μm
154

RIGID PAVEMENT STRUCTURAL ANALYSIS FOR 12,000-LB (5,488-KG) 

FWD LOAD

Models Based on Roughness Performance for Rigid Pavements (12,000 lb (5,445 kg))

1 = 0.039 mil

Figure 80. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

CI4 for rigid pavements (12,000 lb (5,445 kg)).

1 1/ = 25.4 1/mil

Figure 81. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

I1 for rigid pavements (12,000 lb (5,445 kg)).

μm

μm
155

Figure 82. Graph. Sensitivity of roughness acceptable probability to deflection parameter 

LTEA for rigid pavements (12,000 lb (5,445 kg)).

Models Based on Faulting at Joints Performance for Rigid Pavements (12,000 lb (5,445 kg))

1 = 0.039 mil

Figure 83. Graph. Sensitivity of faulting at joints acceptable probability to deflection 

parameter D6 for rigid pavements (12,000 lb (5,445 kg)).

μm
156

Figure 84. Graph. Sensitivity of faulting at joints acceptable probability to deflection 

parameter LTEA for rigid pavements (12,000 lb (5,445 kg)).

Models Based on Transverse Cracking Performance for Rigid Pavements 

(12,000 lb (5,445 kg))

1 = 0.039 mil

Figure 85. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter CI4 for rigid pavements (12,000 lb (5,445 kg)).

μm
157

1 = 0.039 mil

Figure 86. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter D1 for rigid pavements (12,000 lb (5,445 kg)).

Figure 87. Graph. Sensitivity of transverse cracking acceptable probability to deflection 

parameter LTEA for rigid pavements (12,000 lb (5,445 kg)).

μm

159

APPENDIX D

The mechanistic validation was conducted using linear elastic models to predict the responses of 

the pavement (stresses, strains and deflections) to load. The software KENPAVE, developed by 

Huang, was used to model typical flexible and rigid pavement structures.(28) The mechanistic 

responses were then used to predict performance using the MEPDG.(27)

MECHANISTIC-EMPIRICAL ANALYSIS OF FLEXIBLE PAVEMENTS

Several pavement structures were simulated using the KENLAYER computer program, which is 

part of the KENPAVE software.(28) The intention was to evaluate different asphalt concrete and 

base layer thicknesses at different stiffnesses and different subgrade moduli. A factorial study 

was designed and is presented in table 18.

The combination of all parameters in the factorial experiment resulted in 1,296 sections. It was 

necessary to find a common variable for comparing the mechanistic responses among different 

combinations of the input parameters. The choice was the SN used in the 1993 AASHTO Guide 

for Design of Pavement Structures.

(8)

The SN gives a quantitative description of the structural capacity of the different layers in a 

pavement section. It is a function of layer thicknesses, layer coefficients, and drainage 

coefficients. The layer coefficients are measures of the relative ability of a unit thickness of a 

given material to function as a structural component of the pavement. The SN and layer 

coefficients for a three-layer system can be computed using the following equations:

Figure 88. Equation. Computation of SN.

Figure 89. Equation. Computation of the layer coefficient a2 for base course.

Where a1 and a2 are the layer coefficients of the asphalt concrete and base layers, respectively, 

D1 and D2 are the layer thicknesses in inches, and m2 is the base layer drainage coefficient, 

assumed as unity for simplicity. SN is a dimensionless variable. In figure 89, E2 refers to Mr of 

the base course in pounds per square inch. Figure 90 describes the trends between deflection 

parameter I2 and the SN. For simplicity, the data were grouped by subgrade modulus. I2 is 

the deflection parameter chosen for the final structural logistic model based on roughness 

performance. Figure 91 describes the trends between deflection parameter CI3 and the SN. 

CI3 is the deflection parameter chosen for the final structural logistic model based on rutting 

performance. Figure 92 describes the trends between I1 and SN. I1 is the deflection parameter 

chosen for the final structural logistic model based on fatigue cracking.

SN = a1D1 + a2D2m2

a2 = 0.249(log E2) - 0.977
160

11/ = 25.4 1/mil

1 psi = 6.89 kPa

Figure 90. Graph. Deflection parameter I2 as a function of SN for a flexible pavement with 

HMA modulus of 500,000 psi (3,445,000 kPa).

11/ = 25.4 1/mil

1 psi = 6.89 kPa

Figure 91. Graph. Deflection parameter CI3 as a function of SN for a flexible pavement 

with HMA modulus of 500,000 psi (3,445,000 kPa).

μm

μm
161

11/ = 25.4 1/mil

1 psi = 6.89 kPa

Figure 92. Graph. Deflection parameter I1 as a function of SN for a flexible pavement with 

HMA modulus of 500,000 psi (3,445,000 kPa).

Comparison with MEPDG Predicted Performance

The MEPDG performance prediction models were used to compare predicted distress 

performance at the end of the design life with the estimated structural condition obtained from 

the logistic structural model. This task was accomplished by applying the MEPDG models using 

the mechanistic responses calculated by KENPAVE.

Two models were considered—rutting and fatigue cracking. At first, the roughness model was 

also in the scope. However, this particular model requires additional site factors that often 

dominate the analysis. Therefore, comparison between the outcome of the structural logistic 

model based on roughness and predicted roughness performance was not included in this 

exercise. The calculations were performed in Microsoft Excel® and not within the MEPDG 

software due to computational time required to run all scenarios. Since the objective is the 

comparison and trend evaluation, this assumption had no impact on the outcome or conclusions.

The equation in figure 93 predicts the number of load repetitions to fatigue cracking failure,

where is the tensile strain at the bottom of the asphalt surface layer and E is the elastic modulus 

of the asphalt layer. k'1 and C are parameters calculated using equations in figure 94 through 

figure 96 where Va is the percentage of air voids and Vb is the percentage of binder content. 

Figure 93. Equation. Calculation of number of load repetitions to fatigue failure.

μm

εt

Nf = 0.00432k1

'

C�

1

εt

�

3.9492 �

1

E

�

1.281
162

Figure 94. Equation. Calculation of correction for different asphalt layer thickness effects.

Figure 95. Equation. Calculation of laboratory to field adjustment factor.

Figure 96. Equation. Calculation of parameter M.

The damage related to fatigue cracking, D, is computed using the Miner’s law and bottom- up 

cracking in percentage of total lane area is obtained through the equation in figure 97 in which 

C1, C'1, C2 and, C'2 are constants.

Figure 97. Equation. Fatigue cracking prediction.

Figure 32 describes the sensitivity of I1 structural logistic model probability based on fatigue 

cracking to MEPDG predicted fatigue cracking performance for flexible pavements. The trends 

agree with expectations; high probabilities of good structural condition are associated with 

low levels of fatigue cracking. As the probability decreases, the predicted area of fatigue 

cracking increases.

The analysis using the rutting model was simplified, and only rutting at the asphalt concrete 

surface layer was used. The current MEPDG model for asphalt concrete rutting is provided in 

figure 98 where is the plastic strain, is the elastic strain, T is temperature (Fahrenheit), N is 

the number of load applications, and k1 is a constant that depends on depth at which the elastic 

strain is calculated and is given by equations in figure 99 and figure 100. The total rutting in 

the asphalt layer is calculated by integrating the calculated plastic strain over the thickness of 

the layer.

Figure 98. Equation. Calculation of permanent deformation.

Figure 99. Equation. Calculation of k1.

Figure 100. Equation. Calculation of C1 and C2.

k1

' = 1

0.000398+ 0.003602

1+e11.02-3.49hac

C = 10M

M = 4.84 � Vb

Va + Vb

- 0.69�

FCbottom = � 6000

1+e

�C1C1

'

+C2C2

' log10(D*100)�

� �

1

60�

εp εr

εp

εr

= k1*10-3.35412T1.5606N0.4791

k1 = (C1+C2*depth)*0.328196depth

C1 = -0.1039*hac

2 + 2.4868*hac - 17.342

C2=0.0172*hac

2 - 1.7331*hac + 27.428
163

Figure 101 describes the sensitivity of CI3 structural logistic model probability based on rutting 

to MEPDG predicted AC rutting performance for flexible pavements. In this plot, the trends 

agree with expectations; high probabilities of good structural condition are associated with small 

permanent deformation. As the probability decreases, predicted AC rutting increases.

1 inch = 25.4 mm

1 psi = 6.89 kPa

Figure 101. Graph. Sensitivity of CI3 structural logistic model probability based on rutting 

performance to MEPDG predicted rutting for flexible pavements.

MECHANISTIC-EMPIRICAL ANALYSIS OF RIGID PAVEMENTS

Several pavement structures were simulated using the KENSLAB computer program, which is

part of the KENPAVE software. The intention was to evaluate different JPCP slab thicknesses 

and subgrade moduli and the consequences to the outcome of the structural logistic models. A 

factorial study was designed and is presented in table 19.

The deflection parameters of the best logistic models developed were computed for the structures 

simulated in the factorial experiment. Only the FWD test at the center of the slab was evaluated. 

The objective was to verify if trends would agree with expected outcomes from the models. At 

first, the deflection parameters were plotted against the slab thickness (i.e., considered as 

reference for the strength of the pavement section). Figure 31 shows the trends between 

deflection parameter I1 and slab thickness for three subgrade moduli. I1 was chosen for the final 

structural logistic model based on roughness performance. The results indicate that I1 increased

as slab thickness increased, as expected.

Figure 102 shows the trends between deflection parameter D6 and slab thickness. D6 was chosen 

for the final structural logistic model based on faulting performance. D6 is decreased as slab 

thickness increased, as expected. However, the sensitivity reduced when the subgrade modulus 

was stiffer.
164

11/ = 25.4 1/mil

1 psi = 6.89 kPa

Figure 102. Graph. Sensitivity of deflection parameter D6 to slab thickness.

Figure 103 shows the trends between CI4 and slab thickness. CI4 was chosen for the final 

structural logistic model based on transverse slab cracking. CI4 is sensitive to slab thickness, 

and the trend indicates that the value decreased as slab thickness increased, as expected.

11/ = 25.4 1/mil

1 psi = 6.89 kPa

Figure 103. Graph. Sensitivity of deflection parameter CI4 to slab thickness.

μm

μm
165

Comparison with MEPDG Predicted Performance

In the case of rigid pavements, the MEPDG was used to generate the performance predictions. 

There were only 15 scenarios to run, and the rigid pavement analysis was performed much faster 

than the flexible pavement analysis.

Figure 33 shows the sensitivity of I1 structural logistic model probability based on roughness to 

the MEPDG predicted roughness performance for rigid pavements. It can be seen that the trends 

agree with expectations; high probabilities of good structural condition are associated with low 

values of IRI. As the probability decreased, the predicted IRI increased. This plot confirms that 

the structural logistic model is capable of providing an assessment of structural condition that is 

tied to an expectation of performance.

Figure 104 shows the sensitivity of D6 structural logistic model probability based on faulting to 

MEPDG predicted faulting performance for rigid pavements. Again in this plot, the trends agree 

with expectations; high probabilities of good structural condition are associated with low faulting 

values. As the probability decreases, predicted joint faulting increases. It is important to note that 

in this particular model, although the trends agree with expectation, the variation in probability 

of acceptable structural condition is small when compared to previous models.

1 psi = 6.89 kPa

Figure 104. Graph. Sensitivity of D6 structural logistic model probability based on faulting

performance to MEPDG predicted faulting for rigid pavements.

Figure 105 shows the sensitivity of CI4 structural logistic model probability based on slab 

cracking to MEPDG predicted slab cracking performance for rigid pavements. The x-axis is 

presented in log scale to improve the visualization. The trends agree with expectations; high 

probabilities of good structural condition are associated with low to no slab cracking. As the 

probability decreases, predicted percentage of cracked slab increases.
166

1 psi = 6.89 kPa

Figure 105. Graph. Sensitivity of CI4 structural logistic model probability based on slab 

cracking performance to MEPDG predicted slab cracking for rigid pavements.
167

APPENDIX E

Table 106. Information about the different States used in the analysis.

State Section ID

AC 

Thickness 

(inches)

Mean 

Deflection 

(mils)

Standard 

Deviation

Length 

(mi)

Test 

Spacing 

(mi)

New 

Mexico

US70 EB

6 7.54 1.89 2.3 0.1

6.8 7.06 2.17 37.6 0.1

7 6.3 2.117 19.8 0.1

US70 WB

5.5 8.26 1.952 3.1 0.1

9.2 9.72 2.435 16.5 0.1

5 7.36 2.214 37.7 0.1

5.5 7.08 2.811 4.3 0.1

5.5 7.22 2.289 15.3 0.1

US550 NB

9.71 7.87 1.268 6.8 0.1

9.94 7.64 3.449 15.8 0.1

9.43 5.5 1.835 10.3 0.1

9.95 4.68 1.047 6.3 0.1

9.15 7.2 2.657 21.4 0.1

9.46 11.34 4.379 14 0.1

9.35 4.33 1.381 9.7 0.1

9.77 4.49 1.294 16.1 0.1

9.49 5.75 0.76 16.4 0.1

US550 SB

13.4 10.7 3.775 19.8 0.1

9.6 7.2 2.748 8.5 0.1

9.61 7 3.566 29.3 0.1

9.4 10.9 5.232 5.6 0.1

9.6 5.8 3.347 37.7 0.1

9.7 5.7 0.857 15.7 0.1

Oregon

I-5 7.151 2.421 0.9 0.1

OR38 10.442 3.728 8.65 0.1

US101 13.794 4.466 3.35 0.1

16.869 6.663 8.65 0.1

OR18 7.386 2.713 37 0.1

OR221 22.482 6.691 16.7 0.1

OR99E

6.948 2.272 2.2 0.1

7.192 2.553 2.2 0.1

9.402 4.075 9.85 0.1

US26

6.675 1.88 1.5 0.1

4.308 2.263 1.6 0.1

8.907 3.391 4.95 0.1

9.376 2.272 5.35 0.1

US97 8.9 2.945 4.25 0.1
168

Kansas

4

8 13.87 4.114 6.3 0.1 8 14.06 3.837 5.2 0.1

8.7 10.6 2.336 3.9 0.1

7.3 12.93 3.305 2.9 0.1

5.7 11.14 3.447 2.1 0.1

56

13 8.37 3.212 5.9 0.1

14.5 5.17 1.254 8.4 0.1

11.5 9.76 2.591 12.9 0.1

99

10.2 11.85 2.539 8.1 0.1

7.7 15.26 4.628 5.1 0.1

7.1 14.42 3.886 2.8 0.1 7 16.98 3.669 7.3 0.1

7.8 15.86 3.523 7.6 0.1

9.2 10.88 3.387 2.3 0.1

170

13.1 6.24 2.879 1.9 0.1

7.1 15.2 4.851 10.5 0.1

8.2 15.9 3.338 7.2 0.1

569 9.06 2.257 5.7 0.1

31 6.4 13.97 3.135 9.7 0.1

7.7 14.91 5.287 4.3 0.1

56 7.5 11.43 3.539 3.7 0.1

8.8 8.26 2.3 8.8 0.1

59

7.4 9.66 3.702 7.3 0.1

12 5.32 1.642 6.2 0.1

12.1 9.28 4.273 2.9 0.1

12.97 2.59 3.9 0.1

13.8 5.36 2.473 7.9 0.1

10.5 6.54 1.886 6.1 0.1

39

4.9 16.78 4.818 6.7 0.1 5 18.2 3.728 1.8 0.1

6.3 14.97 7.157 4.7 0.1

75

5 14.07 3.855 2.9 0.1

8.9 10.4 2.338 7.5 0.1

54 9.2 7.34 2.399 5.3 0.1

58

8 10.65 3.659 9.4 0.1

6.9 11.64 3.354 11.6 0.1
169

75

7.2 4.27 0.782 3.9 0.1

17.5 8.35 2.14 4.2 0.1

15.7 7.3 1.732 3.9 0.1

10.8 5.51 1.754 4.1 0.1

11.2 7.32 2.975 11.9 0.1

11.2 5.18 1.377 2.2 0.1

14.4 6.16 1.423 1.9 0.1

10.8 6.29 1.589 4.9 0.1

Note: Blank cells indicate that no thickness was available.

1 inch = 25.4 mm

1 = 0.039 mil

1 mile = 1.61 km

μm
170

Table 107. Errors in percentage for 50, 70, and 80 percent reliability for section lengths up 

to 10 mi (16.1 km).

Probability

Length 

(mi)

Spacing (mi)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

50 percent

1 8.98 11.77 14.27 16.57 18.72 20.75 22.69 24.55 26.34

2 6.39 8.34 10.06 11.64 13.12 14.51 15.84 17.11 18.33

3 5.24 6.81 8.20 9.47 10.66 11.77 12.84 13.85 14.83

4 4.55 5.90 7.09 8.18 9.20 10.15 11.06 11.92 12.76

5 4.08 5.28 6.34 7.30 8.20 9.05 9.85 10.61 11.35

6 3.73 4.82 5.78 6.66 7.47 8.23 8.96 9.65 10.32

7 3.46 4.46 5.35 6.15 6.90 7.60 8.27 8.91 9.52

8 3.24 4.17 5.00 5.75 6.44 7.10 7.72 8.31 8.88

9 3.05 3.93 4.71 5.41 6.07 6.68 7.26 7.81 8.35

10 2.90 3.73 4.46 5.13 5.75 6.33 6.87 7.40 7.90

70 percent

1 11.11 14.30 17.12 19.70 22.10 24.36 26.50 28.56 30.53

2 7.91 10.12 12.07 13.85 15.50 17.04 18.51 19.91 21.26

3 6.48 8.27 9.84 11.27 12.59 13.83 15.00 16.12 17.20

4 5.63 7.17 8.51 9.73 10.86 11.92 12.93 13.88 14.80

5 5.04 6.41 7.61 8.69 9.69 10.63 11.52 12.36 13.17

6 4.61 5.85 6.94 7.92 8.83 9.67 10.48 11.24 11.97

7 4.28 5.42 6.42 7.32 8.15 8.94 9.67 10.37 11.05

8 4.00 5.07 6.00 6.84 7.62 8.34 9.03 9.68 10.30

9 3.78 4.78 5.65 6.44 7.17 7.85 8.49 9.10 9.69

10 3.59 4.54 5.36 6.11 6.79 7.43 8.04 8.62 9.17

80 percent

1 12.39 15.83 18.85 21.59 24.14 26.54 28.81 30.99 33.07

2 8.82 11.21 13.29 15.18 16.93 18.57 20.13 21.61 23.03

3 7.23 9.16 10.83 12.35 13.76 15.07 16.32 17.50 18.63

4 6.28 7.93 9.37 10.67 11.87 13.00 14.06 15.07 16.03

5 5.63 7.10 8.37 9.53 10.59 11.58 12.52 13.42 14.27

6 5.15 6.48 7.64 8.68 9.65 10.55 11.40 12.20 12.97

7 4.77 6.00 7.07 8.03 8.91 9.74 10.52 11.26 11.97

8 4.47 5.61 6.61 7.50 8.32 9.09 9.82 10.51 11.16

9 4.22 5.29 6.22 7.06 7.84 8.56 9.24 9.88 10.50

10 4.00 5.02 5.90 6.70 7.42 8.10 8.75 9.36 9.94

1 mi = 1.61 km
171

Table 108. Errors in percentage for 90, 95, and 99.5 percent reliability for section lengths 

up to 10 mi (16.1 km).

Probability

Length 

(mi)

Spacing (mi)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

90 percent

1 14.18 17.94 21.24 24.22 26.98 29.57 32.02 34.35 36.59

2 10.10 12.71 14.98 17.03 18.93 20.70 22.37 23.96 25.48

3 8.28 10.38 12.21 13.86 15.38 16.80 18.13 19.41 20.62

4 7.19 9.00 10.56 11.97 13.27 14.48 15.63 16.71 17.75

5 6.44 8.05 9.44 10.69 11.84 12.91 13.92 14.88 15.80

6 5.89 7.35 8.61 9.74 10.78 11.75 12.67 13.54 14.36

7 5.46 6.80 7.97 9.01 9.97 10.86 11.70 12.49 13.25

8 5.11 6.36 7.45 8.42 9.31 10.14 10.92 11.66 12.36

9 4.82 6.00 7.02 7.93 8.76 9.54 10.27 10.96 11.62

10 4.58 5.69 6.65 7.51 8.30 9.03 9.72 10.38 11.00

95 percent

1 15.65 19.69 23.21 26.39 29.32 32.07 34.66 37.13 39.50

2 11.15 13.95 16.37 18.56 20.57 22.45 24.22 25.90 27.51

3 9.14 11.40 13.35 15.10 16.72 18.22 19.64 20.98 22.27

4 7.93 9.87 11.55 13.05 14.43 15.71 16.92 18.07 19.16

5 7.11 8.83 10.32 11.65 12.87 14.01 15.08 16.09 17.06

6 6.50 8.07 9.41 10.62 11.72 12.75 13.72 14.64 15.51

7 6.03 7.47 8.71 9.82 10.83 11.78 12.67 13.51 14.31

8 5.64 6.99 8.14 9.17 10.12 11.00 11.82 12.60 13.35

9 5.33 6.59 7.67 8.64 9.53 10.35 11.12 11.86 12.55

10 5.06 6.25 7.27 8.19 9.03 9.80 10.53 11.22 11.88

99.5 percent

1 19.43 24.17 28.27 31.95 35.33 38.48 41.44 44.26 46.94

2 13.84 17.12 19.95 22.47 24.79 26.94 28.96 30.88 32.71

3 11.34 13.99 16.26 18.29 20.15 21.87 23.49 25.02 26.48

4 9.85 12.12 14.07 15.80 17.39 18.86 20.24 21.55 22.79

5 8.83 10.85 12.57 14.11 15.51 16.82 18.04 19.19 20.29

6 8.07 9.90 11.47 12.86 14.13 15.31 16.41 17.46 18.45

7 7.48 9.17 10.61 11.89 13.06 14.14 15.16 16.11 17.02

8 7.01 8.58 9.92 11.11 12.20 13.20 14.14 15.03 15.88

9 6.61 8.09 9.35 10.47 11.48 12.43 13.31 14.14 14.93

10 6.28 7.67 8.86 9.92 10.88 11.77 12.60 13.39 14.14

1 mi = 1.61 km
172

Figure 106. Graph. Comparison between measured error and predicted error for all 

Kansas sections at 0.2-mi (0.322-km) spacing.

Figure 107. Graph. Comparison between measured error and predicted error for all 

Kansas sections at 0.5-mi (0.805-km) spacing.
173

Figure 108. Graph. Comparison between measured error and predicted error for all 

Kansas sections at 1-mi (1.61-km) spacing.

Figure 109. Graph. Comparison between measured error and predicted error for all 

Oregon sections at 0.2-mi (0.322-km) spacing.
174

Figure 110. Graph. Comparison between measured error and predicted error for all 

Oregon sections at 0.5-mi (0.805-km) spacing.

Figure 111. Graph. Comparison between measured error and predicted error for all 

Oregon sections at 1-mi (1.61-km) spacing
APPENDIX F

Table 109. Description of the Maryland sections used in the example.

ID

Road 

Name

Mile 

Post

Initial

Mile Post

End

HMA 

Thickness

(inches)

Total 

Thickness

(inches)

Bound 

Layer AADTT

Class 5

(percent)

Class 9

(percent)

Road 

Classification

Pavement 

Age at the 

Time of 

FWD 

Testing

FWD Test 

Date

1 IS 68 E 37.25 40.27 11.96 23.96 No 4186 20.85 47.43 Rural interstate 9 5/23/2007

2 IS 68 W 37.25 38.2 9 23 No 4186 20.85 47.43 Rural interstate 9 5/23/2007

3 IS 68 W 38.2 40.27 11.38 23.38 No 4186 20.85 47.43 Rural interstate 9 5/23/2007

4 I 68 E 4.76 7.6 15 19 No 3926 27.43 39.54 Urban interstate 11 6/10/2008

5 I 68 E 7.6 8.05 16.5 20.5 No 3926 27.43 39.54 Urban interstate 11 6/10/2008

6 US 40 W 0.37 1.78 7.5 15.5 No 12.5 52.01 8.25

Rural minor 

collector 15 9/24/2008

7 US 40 W 1.78 4.3 7 15 No 12.5 52.01 8.25

Rural minor 

collector 18 9/24/2008

8 US 40 W 4.3 5.77 6.5 14.5 No 12.5 52.01 8.25

Rural minor 

collector 16 9/24/2008

9 US 40 E 0.37 1.78 7.5 15.5 No 12.5 52.01 8.25

Rural minor 

collector 15 9/24/2008

10 US 40 E 1.78 4.3 7 15 No 12.5 52.01 8.25

Rural minor 

collector 18 9/24/2008

11 US 40 E 4.3 5.77 6.5 14.5 No 12.5 52.01 8.25

Rural minor 

collector 16 9/24/2008

12 MD 2 S 8.06 9.9 6 15 No 1944 47.74 15.3

Rural minor 

arterial 9 7/23/2007

13 MD 2 S 9.9 11.8 6.5 15.5 No 1944 47.74 15.3

Rural minor 

arterial 10 7/23/2007

14 MD 2 S 11.8 12.04 5.5 17.5 No 1944 47.74 15.3

Rural minor 

arterial 10 7/23/2007

15 MD 2 N 8.06 9.9 6 15 No 1944 47.74 15.3

Rural minor 

arterial 9 7/10/2007

16 MD 2 N 9.9 11.8 6.5 15.5 No 1944 47.74 15.3

Rural minor 

arterial 11 7/23/2007

17 MD 2 N 11.8 12.04 5.5 17.5 No 1944 47.74 15.3

Rural minor 

arterial 10 7/23/2007

17

5
22 MD 45 N 4.4 5.05 9.5 13.5 No 1390 42.44 11.94

Urban other 

principal arterial 23 6/26/2009

23 MD 45 N 5.05 5.15 9.5 13.5 No 1390 42.44 11.94

Urban other 

principal arterial2 6/26/2009

24 MD 45 S 4.4 5.05 9.5 13.5 No 1390 42.44 11.94

Urban other 

principal arterial 23 6/26/2009

42 MD 265 N0 1.755 14 No 204.75 52.01 8.25

Rural minor 

collector 16 6/15/2010

43 MD 265 S0 1.755 14 No 204.75 52.01 8.25

Rural minor 

collector 16 6/15/2010

44 MD 5 N 3.688 5.274 10.5 22.5 No 2090 33.67 34

Rural other 

principal arterial 15 6/18/2010

45 MD 225 E 1.56 3.519 13 No 1442.5 49.19 11.49

Rural major 

collector 16 5/25/2010

46 MD 225 W 1.56 3.519 13 No 1442.5 49.19 11.49

Ruralmajor 

collector 16 5/25/2010

47 MD 335 N 6.56 11.415 13 No 275.5 47.74 15.3

Rural minor 

arterial 11 7/22/2008

48 MD 335 S 6.56 11.415 13 No 275.5 47.74 15.3

Rural minor 

arterial 11 7/21/2008

49 US 50 E 4.65 4.85 11 19 No 2085 33.67 34

Rural other 

principal arterial 11 6/17/2009

50 US 50 E 4.85 6.06 9.75 15.75 Yes 2085 33.67 34

Rural other 

principal arterial 11 6/17/2009

51 US 50 W 4.65 4.8 10 18 No 2085 33.67 34

Rural other 

principal arterial6 6/17/2009

56 I 70 E 8.82 13.63 10.5 25.5 Yes 6373.5 27.43 39.54 Urban interstate 14—

57 I 68 E 18 22.26 18.5 22.5 No 4224 20.85 47.43 Rural interstate 10—

58 I 68 W 18 22.26 18.5 22.5 No 4224 20.85 47.43 Rural interstate 10—

82 MD 235 N 7.67 8.9 6.5 15.5 No 440 47.74 15.3

Rural minor 

arterial 29—

83 MD 235 N 8.9 9.27 8.5 17.5 No 440 47.74 15.3

Rural minor 

arterial6—

84 MD 235 S 7.67 8.9 6.5 15.5 No 440 47.74 15.3

Rural minor 

arterial 29—

85 MD 235 S 8.9 9.27 8.5 17.5 No 440 47.74 15.3

Rural minor 

Arterial6—

86 MD 238 N 4.09 7.163 12 No 260 52.01 8.25

Rural minor 

collector 31 5/25/2010

176
87 MD 238 S 4.09 7.16

3 12 No 260 52.01 8.25

Rural minor 

collector 31 5/25/2010

88 MD 470 S0 1.351 10 No 91 52.01 8.25

Rural minor 

collector 24 8/22/2006

89 MD 470 S 1.35 2.35 2.5 11.5 No 91 52.01 8.25

Rural minor 

collector 15 8/22/2006

90 MD 470 S 2.35 3.751 10 No 91 52.01 8.25

Rural minor 

collector 24 8/22/2006

91 MD 470 N0 1.351 10 No 91 52.01 8.25

Rural minor 

collector 24 8/22/2006

92 MD 470 N 1.35 2.35 2.5 11.5 No 91 52.01 8.25

Rural minor 

collector 15 8/22/2006

93 MD 470 N 2.35 3.751 10 No 91 52.01 8.25

Rural minor 

collector 24 8/22/2006

101 MD 63 N0 3.88 6.5 14.5 No 98 52.01 8.25

Rural minor 

collector 23 6/30/2010

102 MD 63 S0 3.88 6.5 14.5 No 98 52.01 8.25

Rural minor 

collector 23 6/30/2010

108 MD 367 E 1.75 2.158 14.5 No 272 49.19 11.49

Rural major 

collector9 10/2/2008

109 MD 367 E 2.15 2.68 16.5 Yes 272 49.19 11.49

Rural major 

collector9 10/2/2008

113 MD 367 W 1.75 2.158 14.5 No 272 49.19 11.49

Rural major 

collector9 10/2/2008

114 MD 367 W 2.15 2.68 16.5 Yes 272 49.19 11.49

Rural major 

collector9 10/2/2008

— Indicates that information was not available.

1 inch = 25.4 mm

177
Table 110. FWD test data for all of the Maryland sites.

ID

Load 

(kPa)

D1

( )

D2

( )

D3

( )

D4

( )

D5

( )

D6

( )

D7

( )

D8

( )

D9

( )

1 697.98 152.95 110.48 91.02 73.89 58.37 37.29 24.29 16.59 11.97

2 685.36 280.26 223.65 193.91 158.89 124.49 77.71 48.47 31.42 20.97

3 696.36 156.42 103.64 84.88 66.74 50.77 29.90 18.57 12.61 9.55

4 651.62 193.35 146.56 121.75 96.39 73.73 42.09 23.39 13.82 8.79

5 645.99 187.96 120.23 91.86 70.53 53.17 31.67 19.81 14.05 10.50

6 651.71 196.43 150.28 119.85 90.17 71.50 45.85 29.00 19.69 14.48

7 642.96 319.15 252.87 204.29 157.68 121.82 71.05 44.03 29.28 19.78

8 646.07 348.02 252.84 192.86 138.52 100.55 57.44 35.54 23.44 15.55

9 666.16 256.38 194.73 153.52 111.60 80.06 43.49 24.95 16.13 11.18

10 650.25 307.22 247.16 202.77 156.12 119.60 70.95 42.59 27.98 20.10

11 637.96 427.17 345.69 286.39 220.61 168.56 100.82 64.03 42.52 29.95

12 652.76 349.17 270.40 216.23 165.89 130.19 89.24 66.27 53.55 44.28

13 665.03 308.16 253.90 217.53 178.17 145.12 101.36 73.60 56.96 45.75

14 670.64 276.61 222.38 183.90 143.89 113.03 75.18 54.36 42.93 35.56

15 657.40 326.83 257.17 209.99 165.15 131.14 90.46 66.79 53.39 43.93

16 660.28 347.26 275.62 230.87 182.19 143.33 95.05 67.55 53.20 43.79

17 659.63 378.33 294.77 237.93 183.52 142.05 91.44 63.63 48.45 38.67

22 646.80 370.69 271.62 210.35 154.82 113.20 66.54 42.95 31.44 25.15

23 654.74 354.69 241.76 180.80 134.11 97.28 55.42 34.49 25.70 19.96

24 649.22 326.06 242.79 190.16 142.39 105.39 62.85 41.33 30.58 24.14

42 647.67 488.30 393.12 319.89 248.67 192.00 121.67 83.83 62.07 48.11

43 652.37 486.40 401.50 333.08 258.36 197.46 123.58 83.46 61.96 48.24

44 663.07 346.53 272.43 216.75 161.84 120.89 73.11 47.91 35.90 27.98

45 655.55 267.17 208.77 171.20 136.86 108.56 71.09 48.53 35.49 27.97

46 660.32 272.34 205.92 167.05 132.43 103.28 66.39 44.72 32.77 25.94

47 636.96 526.30 389.25 303.91 229.15 174.37 108.82 74.84 57.47 46.23

48 635.08 506.31 369.30 287.20 214.94 162.87 102.00 70.65 54.74 44.04

49 668.93 183.68 141.65 119.59 104.56 91.65 71.54 55.46 44.58 36.79

50 661.45 276.42 209.93 168.29 140.80 120.72 88.40 64.80 49.52 38.57

μm μm μm μm μm μm μm μm μm

178
51 674.00 145.54 95.15 73.96 67.92 63.91 55.37 47.09 39.73 32.82

56 676.85 86.08 77.00 71.25 64.81 58.48 47.53 38.34 31.16 24.47

57 683.34 89.72 72.55 64.76 58.33 52.04 41.04 31.77 24.68 65.16

58 687.30 91.63 78.28 70.30 62.40 54.98 42.53 32.64 24.49 70.31

82 680.88 180.01 153.57 135.39 113.14 89.60 58.42 39.77 29.56 23.51

83 685.72 188.76 161.65 142.09 120.25 98.30 65.93 44.56 31.21 24.38

84 685.95 171.67 148.69 131.27 110.68 91.85 61.81 43.54 31.90 25.01

85 686.95 286.16 245.47 210.67 156.01 125.07 79.71 51.36 36.02 27.18

86 637.34 681.44 533.49 411.59 295.53 212.38 122.38 80.32 61.65 48.93

87 643.13 541.75 430.59 344.85 262.69 199.39 125.30 85.90 64.65 49.00

88 636.46 775.11 620.40 490.11 349.81 241.91 123.61 73.31 54.79 44.56

89 629.90 863.83 690.09 543.28 382.99 262.89 140.09 89.87 68.12 54.43

90 637.88 699.13 548.46 424.64 293.76 199.88 104.05 66.58 51.85 41.87

91 632.25 856.79 677.76 528.26 371.96 254.37 126.84 75.86 55.89 47.20

92 629.75 834.83 664.03 528.14 379.22 268.20 143.79 89.92 66.83 53.02

93 625.65 866.70 658.32 487.73 325.88 216.68 109.35 69.71 53.90 43.94

101 670.32 397.30 306.75 241.88 177.22 129.20 72.97 45.44 33.09 25.86

102 660.16 436.23 338.29 264.54 193.49 140.30 79.78 51.36 38.33 30.34

108 654.17 274.04 230.29 199.87 166.29 136.51 93.05 63.67 45.16 34.01

109 645.53 292.99 229.98 182.90 136.88 102.64 63.84 43.88 33.34 27.16

113 649.83 297.21 245.17 210.41 173.99 142.37 97.60 69.18 51.85 41.02

114 642.40 294.13 224.84 174.29 125.89 93.17 57.82 40.94 32.40 26.35

1 psi = 6.89 kPa 1 μm = 0.039 mil

179

181

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HRDI-30/12-12(500)E Recycled

Recyclable