Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Curl and Warp Analysis of the 

LTPP SPS-2 Site in Arizona

Publication No. FHWA-HRT-12-068 December 2012
FOREWORD 

This study examined the roughness and roughness progression of 21 test sections on the Long-Term 

Pavement Performance (LTPP) Specific Pavement Studies (SPS)-2 site in Arizona over the first 

16 years of the experiment. The site included 12 test sections from the standard experiment and 

9 supplemental test sections selected by the Arizona Department of Transportation. 

Traditional profile analyses revealed roughness caused by transverse and longitudinal cracking 

on some test sections and some localized roughness caused by built-in defects. However, the 

analyses showed that curl and warp contributed to, and in some cases dominated, the roughness 

on many of the test sections. In addition, roughness did not increase steadily with time because 

of diurnal and seasonal changes in slab curl and warp. 

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-12-068 

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

4. Title and Subtitle 

Curl and Warp Analysis of the LTPP SPS-2 Site in Arizona 

5. Report Date 

December 2012 

6. Performing Organization Code 

7. Author(s) 

Steven M. Karamihas and Kevin Senn 

8. Performing Organization Report No. 

UMTRI-2012-28 

9. Performing Organization Name and Address 

Nichols Consulting Engineers 

1885 S. Arlington Ave., Suite 111 

Reno, NV 89509 

10. Work Unit No. (TRAIS) 

11. Contract or Grant No. 

DTFH61-06-C-00027 

12. Sponsoring Agency Name and Address 

Turner-Fairbank Highway Research Center 

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

16. Abstract 

This study examined the roughness and roughness progression of 21 test sections on the LTPP SPS-2 site in 

Arizona over the first 16 years of the experiment. The site included 12 test sections from the standard experiment 

and 9 supplemental test sections selected by the Arizona Department of Transportation. 

Traditional profile analyses revealed roughness caused by transverse and longitudinal cracking on some test sections 

and some localized roughness caused by built-in defects. However, the analyses showed that curl and warp contributed 

to, and in some cases dominated, the roughness on many of the test sections. In addition, roughness did not increase 

steadily with time because of diurnal and seasonal changes in slab curl and warp. 

This study applied objective profile analyses to quantify the level of curl and warp on each section. These automated 

algorithms estimated the gross strain gradient needed to deform each slab into the shape present in the measured 

profile and produced a pseudo strain gradient (PSG) value. The levels of curl and warp within each profile are 

summarized by the average PSG value. 

For the jointed concrete test sections, variations in average PSG over time explained many of the changes in roughness 

over time. This included diurnal variations in slab curl, which often caused the overall progression in roughness to 

appear disorderly throughout the experiment. PSG analysis also revealed that the overall level of curl and warp 

increased throughout the life of the experiment, with commensurate increases in the roughness. 

This limited study demonstrated the potential value of applying the methods herein to other jointed portland cement 

concrete pavements, including other SPS-2 sites. 

17. Key Word 

Road roughness, Longitudinal profile, International Roughness 

Index, LTPP, Pavement testing, Pavement rehabilitation, 

Jointed concrete pavement, Slab curl and warp 

18. Distribution Statement 

No restrictions. This document is available to 

the public through the National Technical 

Information Service, Springfield, VA 22161 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 

Unclassified 

21. No. of Pages 

110

22. Price 

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

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha 

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

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

MASS 

oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

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

TEMPERATURE (exact degrees) o

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

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx 

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH

mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2

 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac 

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

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

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for th International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E e 380. 

(Revised March 2003)
iii 

TABLE OF CONTENTS 

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

DATA COLLECTION AND ANALYSES ..................................................................................3

PROFILE DATA SYNCHRONIZATION ............................................................................3

DATA QUALITY SCREENING ............................................................................................4

SUMMARY ROUGHNESS VALUES ...................................................................................5

TRADITIONAL PROFILE ANALYSES ..............................................................................6

CURL AND WARP ANALYSIS ............................................................................................7

PSG Progression ..................................................................................................................8

Relationship Between PSG and IRI ...................................................................................11

Effect of Curling on IRI .....................................................................................................15

FAULTING ANALYSIS .......................................................................................................23

SUMMARY ..................................................................................................................................25

LOW-STRENGTH SECTIONS, STANDARD EXPERIMENT .......................................25

HIGH-STRENGTH SECTIONS, STANDARD EXPERIMENT......................................27

SUPPLEMENTAL SECTIONS ...........................................................................................28

AC SECTIONS.......................................................................................................................28

RECOMMENDATIONS .............................................................................................................29

APPENDIX A. DATA EXTRACTION......................................................................................31

CROSS CORRELATION .....................................................................................................31

SYNCHRONIZATION .........................................................................................................31

LONGITUDINAL DISTANCE MEASUREMENT ...........................................................32

APPENDIX B. DATA QUALITY SCREENING .....................................................................35

APPENDIX C. ROUGHNESS VALUES ...................................................................................49

APPENDIX D. TRADITIONAL PROFILE ANALYSES .......................................................69

SECTION 0213.......................................................................................................................69

SECTION 0214.......................................................................................................................75

SECTION 0215.......................................................................................................................76

SECTION 0216.......................................................................................................................77

SECTION 0217.......................................................................................................................77

SECTION 0218.......................................................................................................................79

SECTION 0219.......................................................................................................................79

SECTION 0220.......................................................................................................................79

SECTION 0221.......................................................................................................................80

SECTION 0222.......................................................................................................................81

SECTION 0223.......................................................................................................................81

SECTION 0224.......................................................................................................................81

SECTION 0260.......................................................................................................................82

SECTION 0261.......................................................................................................................83

SECTION 0262.......................................................................................................................83

SECTION 0263.......................................................................................................................84

SECTION 0264.......................................................................................................................85
iv 

SECTION 0265.......................................................................................................................85

SECTION 0266.......................................................................................................................85

SECTION 0267.......................................................................................................................86

SECTION 0268.......................................................................................................................86

APPENDIX E. JOINT FINDING ...............................................................................................87

STEP 1: FILTER THE PROFILES .....................................................................................87

STEP 2: NORMALIZE .........................................................................................................87

STEP 3: SEEK THE NEGATIVE SPIKES.........................................................................88

STEP 4: WEED OUT LESSER SPIKES .............................................................................88

STEP 5: AGGREGATE ACROSS THE REPEAT MEASUREMENTS .........................88

STEP 6: SORT THE LIST ....................................................................................................88

STEP 7: CONSOLIDATE GROUPS OF NEARBY SPIKES ...........................................88

STEP 8: TRIM THE LIST ....................................................................................................89

STEP 9: EVALUATE EACH GROUP ON THE LIST .....................................................90

STEP 10: DESIGNATE ONE OF THE GROUPS AS A JOINT LOCATION ...............90

STEP 11: SEEK OTHER JOINTS DOWNSTREAM ........................................................90

STEP 12: SEEK OTHER JOINTS UPSTREAM ...............................................................91

DISCUSSION .........................................................................................................................91

APPENDIX F. PSG ESTIMATION ...........................................................................................93

WESTERGAARD ..................................................................................................................93

SLAB-BY-SLAB ANALYSIS ...............................................................................................94

Step 1: Crop .......................................................................................................................94

Step 2: Shift........................................................................................................................95

Step 3: Detrend ..................................................................................................................95

Step 4: Estimate Pavement Properties ...............................................................................96

Step 5: Curve Fit ................................................................................................................96

SUMMARY INDEX ..............................................................................................................97

ACKNOWLEDGEMENTS ........................................................................................................99

REFERENCES ...........................................................................................................................101

 
v 

LIST OF FIGURES 

Figure 1. Graph. IRI Progression for Section 0213 .........................................................................5

Figure 2. Graph. IRI Progression for Section 0215 .........................................................................6

Figure 3. Graph. Left Profile PSG Values from Visit 09 of Section 0213 ......................................8

Figure 4. Graph. Average PSG versus Time for Left Side of Section 0213 ....................................9

Figure 5. Graph. Average PSG versus Time for Section 0223 ......................................................10

Figure 6. Graph. Average PSG versus Time for Section 0214 ......................................................11

Figure 7. Graph. Right PSG Values from Visits 01 and 10 of Section 0214 .................................11

Figure 8. Graph. IRI versus PSG for Right Side of Section 0215 (FHWA Data) .........................12

Figure 9. Graph. IRI versus PSG for Right Side of Section 0215 (LTPP SMP Data) ...................14

Figure 10. Graph. Left IRI Progression for Section 0213 ..............................................................16

Figure 11. Graph. Right IRI Progression for Section 0213 ...........................................................16

Figure 12. Graph. Left IRI Progression for Section 0215 ..............................................................17

Figure 13. Graph. Right IRI Progression for Section 0215 ...........................................................17

Figure 14. Graph. Left IRI Progression for Section 0217 ..............................................................18

Figure 15. Graph. Right IRI Progression for Section 0217 ...........................................................18

Figure 16. Graph. Left IRI Progression for Section 0219 ..............................................................19

Figure 17. Graph. Right IRI Progression for Section 0219 ...........................................................19

Figure 18. Graph. Left IRI Progression for Section 0221 ..............................................................20

Figure 19. Graph. Right IRI Progression for Section 0221 ...........................................................20

Figure 20. Graph. Left IRI Progression for Section 0223 ..............................................................21

Figure 21. Graph. Right IRI Progression for Section 0223 ...........................................................21

Figure 22. Graph. Faulting for Section 0262 .................................................................................23

Figure 23. Graph. Faulting for Section 0265 .................................................................................24

Figure 24. Graph. Consistency in Longitudinal Distance Measurement .......................................33

Figure 25. Graph. Comparison of HRI to MRI ..............................................................................49

Figure 26. Graph. IRI Progression for Section 0213 .....................................................................58

Figure 27. Graph. IRI Progression for Section 0214 .....................................................................59

Figure 28. Graph. IRI Progression for Section 0215 .....................................................................59

Figure 29. Graph. IRI Progression for Section 0216 .....................................................................60

Figure 30. Graph. IRI Progression for Section 0217 .....................................................................60

Figure 31. Graph. IRI Progression for Section 0218 .....................................................................61

Figure 32. Graph. IRI Progression for Section 0219 .....................................................................61

Figure 33. Graph. IRI Progression for Section 0220 .....................................................................62

Figure 34. Graph. IRI Progression for Section 0221 .....................................................................62

Figure 35. Graph. IRI Progression for Section 0222 .....................................................................63

Figure 36. Graph. IRI Progression for Section 0223 .....................................................................63

Figure 37. Graph. IRI Progression for Section 0224 .....................................................................64

Figure 38. Graph. IRI Progression for Section 0260 .....................................................................64

Figure 39. Graph. IRI Progression for Section 0261 .....................................................................65

Figure 40. Graph. IRI Progression for Section 0262 .....................................................................65

Figure 41. Graph. IRI Progression for Section 0263 .....................................................................66

Figure 42. Graph. IRI Progression for Section 0264 .....................................................................66

Figure 43. Graph. IRI Progression for Section 0265 .....................................................................67

Figure 44. Graph. IRI Progression for Section 0266 .....................................................................67
vi 

Figure 45. Graph. IRI Progression for Section 0267 .....................................................................68

Figure 46. Graph. IRI Progression for Section 0268 .....................................................................68

Figure 47. Graph. Raw Profile from Visit 03 of Right Side of Section 0213 ................................69

Figure 48. Graph. Profile with Smoothing from Visit 03 of Right Side of Section 0213 .............70

Figure 49. Graph. Profile with Anti-Smoothing from Visit 03 of Right Side of Section 0213 .....70

Figure 50. Graph. Profile with Additional Anti-Smoothing from Visit 03 of Right Side of 

Section 0213...................................................................................................................................70

Figure 51. Graph. Changes in Curl on Section 0213 .....................................................................71

Figure 52. Graph. Slope Spectral Density of Section 0213 ...........................................................72

Figure 53. Graph. Slope Spectral Density of Section 0213 with Linear Scaling ...........................73

Figure 54. Graph. Right Elevation Profile for Three Repeats from Visit 12 of Section 0213 ......74

Figure 55. Graph. Right Roughness Profile for Three Repeats from Visit 12 of Section 0213 ....... 74

Figure 56. Graph. Right Elevation Profiles from Visit 01 of Section 0214...................................75

Figure 57. Graph. Right Elevation Profiles from Visit 10 of Section 0214...................................75

Figure 58. Graph. Profiles Leading to Section 0214 .....................................................................76

Figure 59. Graph. PSD Plots for Section 0215 ..............................................................................77

Figure 60. Graph. Right Elevation Profiles for Section 0217 ........................................................78

Figure 61. Graph. PSD Plots from Visit 08 of Section 0217 .........................................................79

Figure 62. Graph. Profile from Visit 04 of Section 0220 ..............................................................80

Figure 63. Graph. Right Elevation Profile for Five Repeats from Visit 15 of Section 0221 .........80

Figure 64. Graph. PSD of Left Slope for Section 0224 .................................................................81

Figure 65. Graph. Left Roughness Profile for Section 0260 .........................................................82

Figure 66. Graph. Left Elevation Profile for a Segment from Section 0260 .................................83

Figure 67. Graph. Left Elevation Profile from Visit 15 of Section 0262 ......................................84

Figure 68. Graph. Left Roughness Profile from Visit 15 of Section 0262 ....................................84

Figure 69. Graph. Right Roughness Profile for Section 0265 .......................................................85

Figure 70. Graph. Weigh-in-Motion Scale on Section 0267 .........................................................86

Figure 71. Graph. High-Pass Filtered, Normalized Profile ...........................................................87

Figure 72. Equation. Relationship of Slab Elevation to Position ..................................................94

Figure 73. Equation. PSG ..............................................................................................................94

Figure 74. Graph. Measured Slab Profile for Section 0215 ...........................................................95

Figure 75. Graph. Detrended Slab Profile for Section 0215 ..........................................................95

Figure 76. Graph. Curve Fit for Section 0215 ...............................................................................97

 
vii 

LIST OF TABLES 

Table 1. Arizona SPS-2 Site Structural Factors ...............................................................................1

Table 2. Profile Measurement Visits of the SPS-2 Site ...................................................................3

Table 3. Seasonal Visits of Section 0215 .........................................................................................4

Table 4. Regression Results for IRI and PSG on Low-Strength Test Sections .............................13

Table 5. Regression Results for IRI and PSG on High-Strength Test Sections ............................15

Table 6. Summary Results, Low-Strength Sections ......................................................................26

Table 7. Summary Results, High-Strength Sections ......................................................................27

Table 8. Summary Results, Supplemental Sections .......................................................................28

Table 9. Selected Repeats for Section 0213 ...................................................................................36

Table 10. Selected Repeats for Section 0214 .................................................................................36

Table 11. Selected Repeats for Section 0215 .................................................................................37

Table 12. Selected Repeats for Section 0216 .................................................................................38

Table 13. Selected Repeats for Section 0217 .................................................................................38

Table 14. Selected Repeats for Section 0218 .................................................................................39

Table 15. Selected Repeats for Section 0219 .................................................................................39

Table 16. Selected Repeats for Section 0220 .................................................................................40

Table 17. Selected Repeats for Section 0221 .................................................................................40

Table 18. Selected Repeats for Section 0222 .................................................................................41

Table 19. Selected Repeat for Section 0223 ..................................................................................41

Table 20. Selected Repeats for Section 0224 .................................................................................42

Table 21. Selected Repeats for Section 0260 .................................................................................42

Table 22. Selected Repeats for Section 0261 .................................................................................43

Table 23. Selected Repeats for Section 0262 .................................................................................43

Table 24. Selected Repeats for Section 0263 .................................................................................44

Table 25. Selected Repeats for Section 0264 .................................................................................44

Table 26. Selected Repeats for Section 0265 .................................................................................45

Table 27. Selected Repeats for Section 0266 .................................................................................45

Table 28. Selected Repeats for Section 0267 .................................................................................46

Table 29. Selected Repeats for Section 0268 .................................................................................46

Table 30. Roughness Values ..........................................................................................................50

Table 31. Negative Spike Groups from Visit 15 of Section 0215 .................................................89

Table 32. Pavement Properties ......................................................................................................96

 
viii 

LIST OF ACRONYMS 

AC Asphalt concrete 

ADOT Arizona Department of Transportation 

BTB Bituminous-treated base 

DGAB Dense-graded aggregate base 

FHWA Federal Highway Administration 

GPS General Pavement Studies 

HRI Half-car Roughness Index 

IRI International Roughness Index 

LCB Lean concrete base 

LTPP Long-Term Pavement Performance 

MRI Mean Roughness Index 

PATB Permeable asphalt-treated base 

PBTB Permeable bituminous-treated base 

PCC Portland cement concrete 

PSD Power spectral density 

PSG Pseudo strain gradient 

RN Ride Number 

SEE Standard estimate of error 

SMP Seasonal Monitoring Program 

SPS Specific Pavement Studies 
1 

INTRODUCTION 

This report provides the results of profile and roughness analyses for the Long-Term Pavement 

Performance (LTPP) Specific Pavement Studies (SPS)-2 site in Arizona. The analyses emphasized 

the roles of curl and warp in the development of roughness. SPS-2 sites were established for the 

study of rigid pavement structural factors, including concrete slab thickness, concrete strength, base 

material, permeability, and lane width.(1) These test pavements were constructed on eastbound 

Interstate 10 from April 1993 through January 1994. The site includes 21 test sections and 

extends from milepost 106 to 109. Some properties of the sections are listed in table 1. 

Table 1. Arizona SPS-2 Site Structural Factors. 

Section 

Lane 

Width 

(ft) 

PCC 

Flexural 

Strength 

(psi) 

Layer Thickness 

(inches) Layer Type 

Layer 1 Layer 2 Layer 3 Layer 1 Layer 2 Layer 3

0213 14 550 8 6 PCC DGAB 

0214 12 900 8 6 PCC DGAB 

0215 12 550 11 6 PCC DGAB 

0216 14 900 11 6 PCC DGAB 

0217 14 550 8 6 PCC LCB 

0218 12 900 8 6 PCC LCB 

0219 12 550 11 6 PCC LCB 

0220 14 900 11 6 PCC LCB 

0221 14 550 8 4 4 PCC PATB DGAB 

0222 12 900 8 4 4 PCC PATB DGAB 

0223 12 550 11 4 4 PCC PATB DGAB 

0224 14 900 11 4 4 PCC PATB DGAB 

0260 — — 8.5 4 AC DGAB 

0261 — — 8.5 4 AC DGAB 

0262 14 550 8 6 PCC DGAB 

0263 14 550 8 4 4 PCC PBTB DGAB 

0264 12 550 8.5 4 4 PCC PBTB DGAB 

0265 12 550 8.5 6 PCC DGAB 

0266 14 550 12.5 4 PCC DGAB 

0267 14 550 11 4 PCC BTB 

0268 14 550 8 4 PCC BTB 

— Value unknown 

Blank cell indicates that layer is not present in section 

AC = Asphalt concrete 

BTB = Bituminous-treated base 

DGAB = Dense-graded aggregate base 

LCB = Lean concrete base 

PATB = Permeable asphalt-treated base 

PCC = Portland cement concrete 

PBTB = Permeable bituminous-treated base 
2 

Twelve sections, 0213–0224, were constructed as part of the standard SPS-2 experiment. These 

sections have the same design characteristics as the standard 12 sections that appear on several other 

SPS-2 sites within the LTPP study. They are all doweled jointed plain concrete pavements. This site 

also includes four undoweled sections with skewed joints, SPS-2A-type sections 0262–0265. Their 

doweled counterparts are 0213, 0221, 0223, and 0215, respectively. Three additional sections 

of doweled jointed plain concrete, 0266–0268, were included with specialized designs of interest 

to the Arizona Department of Transportation (ADOT). Asphalt concrete (AC) sections 0260 

and 0261 were also included by ADOT. 

This report seeks to characterize the surface roughness of these sections over time and link the 

observations to records of pavement distress and its development. Road profile measurements 

were collected on this site about once per year since the winter after it was opened to traffic. 

Profile data were also collected on section 0215 on 16 additional dates. 

This study applied algorithms for estimating the level of curl and warp present in the pavement 

and its effect on surface roughness. The algorithms included slab-by-slab quantification of curl 

and warp throughout the monitoring history of the site. The analysis framework for this was 

established in a recent Federal Highway Administration (FHWA) study of seasonal and diurnal 

changes in jointed concrete pavement roughness.(2) This method applies Westergaard’s theory to 

establish the likely shape of a curled slab and a curve fitting algorithm to quantify the level of 

curling in each slab. 

The study related aggregated measurements of curl and warp within each profile measurement 

to the International Roughness Index (IRI). The observed statistical relationship between changes 

in curl and warp and changes in IRI for a given section provided a way distinguish the long-term 

roughness caused by distress from short- and long-term changes in roughness associated with curl 

and warp. Estimates of curl and warp from the profiles also provide the opportunity to study 

underlying environmental causes, but that aspect was not explored in this study. 

This study also analyzed the profiles in detail using profile analysis methods employed in the study 

of other SPS sites in Arizona. (See references 3–7.) These methods include calculating roughness 

index values, examining the spatial distribution of roughness within a section, viewing profiles 

with post-processing filters, and examining spectral properties. The study applied the traditional 

analysis methods to the AC sections (0260 and 0261) in an attempt to treat them as control 

sections for comparison to the portland cement concrete (PCC) sections.
3 

DATA COLLECTION AND ANALYSES 

PROFILE DATA SYNCHRONIZATION 

Profile data were collected over the entire Arizona SPS-2 site during 15 visits, as shown in table 2. 

Raw profile data were available for all 15 visits. In each visit, a minimum of seven repeat profile 

measurements were made. The measurements for all visits included sections 0213–0224 and 

sections 0260–0268. 

Table 2. Profile Measurement Visits of the SPS-2 Site. 

Visit Date Time Repeats 

01 25-Jan-1994 06:10 9 

02 05-Mar-1995 11:21 9 

03 27-Jan-1997 11:23–12:49 9 

04 04-Dec-1997 11:06–13:07 7 

05 08-Dec-1998 10:29–11:27 7 

06 15-Nov-1999 11:39–12:39 7 

07 30-Nov-2000 13:38–15:01 9 

08 08-Nov-2001 11:09–12:40 9 

09 30-Oct-2002 12:41–14:07 9 

10 04-Feb-2004 13:47–15:12 9 

11 12-Dec-2004 16:16–18:37 9 

12 11-Aug-2006 04:18–06:26 9 

13-Aug-2006 00:17–04:28 9 

13 30-Dec-2007 10:06–13:21 9 

14 20-Sep-2008 00:37–03:36 9 

15 25-Jan-2010 16:09–19:00 9 

Note: In visit 12, one portion of the site was measured on the first 

date and the remaining portion was measured two days later. 

Profile data were also collected over section 0215 on 16 additional dates as part of the Seasonal 

Monitoring Program (SMP). On most of the measurement dates for this section, profiles were 

collected in the morning and the afternoon. In others, the profiles were collected in the early and 

late morning. In this report, each group of runs is treated as a distinct visit. Table 3 lists the dates 

and times of each visit. These visits covered 4 seasons in 1998 and 12 consecutive seasons starting 

in the winter of 2001. 

Profiles of individual test sections were extracted directly from the raw measurements and aligned 

using an automated trace comparison algorithm. This was done for two reasons. First, profiles were 

collected at a sample interval of 0.98 inches in visits 03–08 and S01–S14 and at a sample interval 

of about 0.77 inches in visits 09–11 and S15–S28. These data appeared in the database after the 

application of an 11.8-inch moving average and decimation to a sample interval of 5.91 inches. The 

raw data contained the more detailed profiles. Second, this study depended on consistency of the 

profile starting and ending points with the construction layout and consistency of the section limits 

with time. Appendix A describes the extraction of individual test section profiles from the raw 

measurements and the process of ensuring the profiles had consistent alignment. 
4 

Table 3. Seasonal Visits of Section 0215. 

Visit Date Repeats Time

S01 15-Jan-1998 7 11:33–11:53 

S02 15-Jan-1998 5 16:43–16:52 

S03 13-Apr-1998 5 10:13–10:30 

S04 13-Apr-1998 5 15:20–15:31 

S05 09-Jul-1998 5 08:23–08:45 

S06 09-Jul-1998 5 12:11–12:26 

S07 30-Sep-1998 5 11:59–12:15 

S08 30-Sep-1998 7 14:34–15:05 

S09 09-Dec-2001 7 09:21–09:46 

S10 09-Dec-2001 9 14:58–15:30 

S11 24-Jan-2002 7 10:12–10:38 

S12 24-Jan-2002 9 14:56–15:33 

S13 15-Mar-2002 7 09:40–10:11 

S14 15-Mar-2002 7 14:30–15:01 

S15 09-Oct-2002 9 08:43–09:34 

S16 09-Oct-2002 9 13:47–14:35 

S17 20-Dec-2002 9 09:05–09:43 

S18 20-Dec-2002 9 13:24–14:08 

S19 07-Mar-2003 9 09:24–09:54 

S20 07-Mar-2003 9 13:57–14:37 

S21 25-Jul-2003 9 04:24–05:06 

S22 25-Jul-2003 9 08:34–09:12 

S23 24-Nov-2003 9 09:32–10:17 

S24 24-Nov-2003 9 14:23–15:04 

S25 14-Dec-2003 9 10:33–11:10 

S26 14-Dec-2003 9 15:16–15:56 

S27 22-Apr-2004 9 04:59–05:38 

S28 22-Apr-2004 9 09:49–10:25 

S29 15-Jul-2004 9 04:17–04:50 

S30 15-Jul-2004 9 09:02–09:40 

S31 09-Sep-2004 9 08:35–09:05 

S32 09-Sep-2004 9 15:53–16:25 

DATA QUALITY SCREENING 

Each visit of each test section included five, seven, or nine repeat profile measurements. Data 

quality screening was performed to select five repeat profile measurements per section from each 

visit. Among the group of available runs, the five measurements that exhibited the best agreement 

with each other were selected. Agreement between two profiles was judged by cross correlating 

the profiles after applying the IRI filter rather than the overall IRI values. This method compares 

the profile traces rather than the overall index. Achieving high correlation requires that the details 

of the profile shape affecting roughness agree as well as the overall roughness level.(8)

The average correlation level produced by these calculations provided a numerical assessment of 

the repeatability within each set of repeat measurements. Overall, most sets of selected repeat 

measurements exhibited good repeatability. In some cases, localized surface distress reduced 
5 

repeatability. The inconsistency in profiles in these areas occurred because of slight variations in the 

lateral tracking position of the profiles as the profiler passed over transversely inconsistent surface 

features. The most prominent example of this inconsistency occurred in the later visits of 

section 0213 on the left side of the lane. 

Appendix B describes the process of selecting five repeat measurements for each visit of each 

section and provides a list of the selected profiles with a repeatability score. Appendix C provides 

the standard deviation of left and right IRI values for each set of repeat measurements. 

SUMMARY ROUGHNESS VALUES 

Appendix C provides roughness progression plots for all 21 test sections. These plots show the left 

and right IRI values from each visit over the 16-year monitoring period. Appendix C also lists the 

IRI, Half-car Roughness Index (HRI), and Ride Number (RN) of each section for each visit. These 

roughness values are the average of the five repeat measurements selected by data quality screening. 

The measurements are not necessarily the same five repeat measurements selected for the LTPP 

public database. Appendix C also provides the standard deviation of IRI over the five repeat 

measurements. This helps identify erratic roughness values that are the result of transverse 

variations in the profile caused by surface distresses. 

Figure 1 and figure 2 show left and right IRI values for sections 0213 and 0215 over their monitoring 

period. The graph for section 0213 includes 30 summary IRI values, 2 per visit over 15 visits. The 

graph for section 0215 includes extra IRI values from the seasonal visits listed in table 3. The 

figures show the IRI values versus time in years. In this case, years is defined as the number of 

years between the measurement date and the date the site was opened to traffic (1-Oct-1993). 

© ADOT 

Figure 1. Graph. IRI Progression for Section 0213. 

Right

Left

Section 0213

0

25

50

75

100

125

150

175

200

225

0 2 4 6 8 10 12 14 16 18

Time (years)

IRI (in/mi)
6 

© ADOT 

Figure 2. Graph. IRI Progression for Section 0215. 

On section 0213, the IRI increases overall, but the roughness does not increase consistently as 

time progresses. For example, the IRI values in visit 01 (0.32 years) are greater than the values in 

visit 02 (1.42 years), and the IRI values in visit 12 (12.86 years) are much greater than in visit 11 

(11.20 years) or visit 13 (14.25 years). In addition, the right IRI increases over the last three visits, 

whereas the left IRI does not. The analyses in this report show that the first two observations are 

due to diurnal changes in curl and warp and the third is not. 

On section 0215, the IRI progression reverses direction many times. The eras from 4 to 6 years and 

8 to 11 years include several pairs of IRI values from two different times on the same day and a 

series of seasonal measurements. Of the 16 diurnal pairs collected on section 0215 (listed in table 3), 

the later set of repeat measurements produced IRI values that were between 2.2 inches/mi above 

and 19.0 inches/mi below the earlier set of repeat measurements from the same day. In addition, 

the four seasonal visits that took place in year 9 produced a range of IRI values of 27.2 inches/mi 

on the left side and 20.5 inches/mi on the right side. 

The analyses in the next sections aim to explain the inconsistent progression in IRI on all the test 

sections and show that some short-term changes in IRI are due to curl and warp and others are not. 

TRADITIONAL PROFILE ANALYSES 

This study applied typical diagnostic profile analyses such as inspection of filtered elevation profile 

plots, roughness profile plots, and power spectral density plots to explain the roughness, roughness 

distribution, and roughness progression of each section. Appendix D provides detailed findings 

from these analyses that support the discussion of each section in the summary. 

0

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40

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80

100

120

140

160

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0215

Time (years)

IRI (in/mi)
7 

These analyses showed that slab curl and warp contributed to, and in some cases dominated, the 

roughness of many of the test sections. In addition, changes in curl and warp offered a possible 

explanation for the disorderly progression in roughness with time that occurred on some of the 

test sections. For example, section 0215 exhibited a very unsteady progression in roughness with 

time, including large diurnal and seasonal changes in years 4–6 and 8–12. 

The analyses in the following sections helped account for changes in slab curl and warp to 

determine what share of the roughness of each profile was due to slab effects. 

CURL AND WARP ANALYSIS 

Statistical analysis segregated the portion of roughness caused by curl and warp within a profile 

from the rest of the irregularities. The levels of curl and warp present within each profile were 

estimated using slab-by-slab analysis of local profile segments. The procedure quantified the 

level of curl and warp on each slab using a pseudo strain gradient (PSG). PSG is the gross strain 

gradient required to deform a slab into the shape that appears within the measured slab profile 

from a flat baseline. 

The PSG value for each slab was derived using a curve fit between the measured profile and an 

expected curled slab shape using the Westergaard equation. The Westergaard equation requires 

estimates of pavement mechanical properties (summarized by the radius of relative stiffness). 

As such, the idealized slab shape was different for each test section. Estimates of these 

properties were developed using the LTPP database. 

Appendix E describes the process of identifying the slab boundaries, and appendix F describes 

the methodology for estimating PSG given the measured profile and pavement mechanical 

properties for each slab. Figure 3 shows results for a left-side profile of section 0213 collected 

in visit 09 (20-Oct-2002). The figure shows the PSG value for each slab along the profile, where 

slabs 0 and 33 straddle the boundaries of the section and slabs -1 and 34 are outside the section 

boundaries. The figure shows PSG in units of microstrain per inch ( /inch). Negative values 

indicate upward curl, which means that the slab edges have a higher elevation than the center. 


8 

Figure 3. Graph. Left Profile PSG Values from Visit 09 of Section 0213. 

Figure 3 provides an example of the variation in upward curl along the left profile of section 0213. 

For the purposes of examining trends over time, the average PSG value summarizes the overall 

curl and warp observed for the entire section. The average PSG value is -95.5 /inch for the profile 

in figure 3. This is a weighted average, where the PSG of each slab contributes to the section average 

in proportion to the length that appears within the section. Thus, the PSG of slabs -1 and 34 do not 

affect the average, and the PSG of slabs 0 and 33 influence the average less than slabs 1–32. 

Because this study includes five repeat measurements from each visit of each section, the average 

PSG values are further averaged over the five repeat measurements. For example, the five left-side 

profiles of section 0213 from visit 09 (30-Oct-2002) yielded sectionwide average PSG values of 

-95.5 to -93.0 /inch, with an average value of -94.5 /inch. Unless otherwise specified, the 

PSG values provided in this report are averaged over five repeat profile measurements. 

PSG Progression 

Figure 4 shows the variation in average PSG for the left side of section 0213 throughout the 

experiment. The value of -94.5 /inch, previously discussed for visit 09, appears on the plot 

9.08 years into the experiment. 

0 5 10 15 20 25 30 35

Slab Number

-160

-140

-120

-100

-80

-60

-40

-20

0

PSG (/inch)



 


9 

Figure 4. Graph. Average PSG versus Time for Left Side of Section 0213. 

The data in figure 4 provide a way to examine the gross changes in curl and warp over time for 

the left profile of section 0213. The levels of downward curl shown in figure 4 and the left IRI 

shown in figure 1 follow similar trends, including the following: 

 Curling is more severe in visit 01 (0.32 years) than in visit 02 (1.42 years), and the IRI is 

higher in visit 01 than in visit 02. 

 Curling is more severe in visit 09 (9.08 years) than in the two visits before and the two 

visits afterward, and the IRI is higher in visit 09 than in the two visits before and the two 

visits afterward. 

 Curling is greater in visits 12 (12.86 years) and 14 (14.97 years) than in visits 11 (11.20 years), 

13 (14.25 years), and 15 (16.32 years), and the IRI is higher in visits 12 and 14 than in 

visits 11, 13, and 15. 

Indeed, the variations in absolute average IRI over time imitate many of the details of the variations 

in PSG over time for the left side of section 0213. 

Inspection of PSG values versus time showed a similar relationship between PSG and IRI over 

most of the test sections in the experiment. In some cases, variation in PSG was proportional to 

variation in IRI but only over the early part of the experiment and during eras of the pavement 

life where distress remained constant. The following section examines the relationship between 

PSG and IRI in detail. 

Several trends in the variation of PSG over time on multiple sections help explain the disorderly 

progression in IRI shown in the figures in appendix C. First, on many of the test sections, like 

section 0213, the upward curl was much more severe in visit 01 (25-Jan-1994) than in visit 02 

-120

-100

-80

-60

-40

-20

0

0 2 4 6 8 10 12 14 16 18

Time (years)

Average PSG (/inch)
10 

(5-Mar-1995) or the PSG reversed from negative (upward curl) in visit 01 to positive (downward 

curl) in visit 02. Visit 01 was conducted at about 6 a.m., and visit 02 was conducted at 11 a.m. 

Second, PSG values were more negative in visits 12 (11-Aug-2006) and 14 (20-Sep-2008) than in 

visits 11 (12-Dec-2004), 13 (30-Dec-2007), and 15 (25-Jan-2010) on sections 0213, 0215–0219, 

0220, 0222, and 0262–0268. This indicates a decrease in upward curling in visits 11, 13, and 15 

compared to visits 12 and 14. Visits 12 and 14 occurred shortly after midnight, and visits 11, 13, and 

15 occurred after sunrise. Section 0214 also exhibited a decrease in downward curl in visits 12 and 14. 

Third, sections 0215, 0219, 0223, 0224, and 0264–0266 exhibited a net increase in the magnitude 

of upward curl over the life of the experiment. The trend was not orderly on any of the test sections, 

and it typically included the short-term variations discussed for visits 01 and 02 and visits 11–15. 

Figure 5 provides an example, showing the average PSG for the left- and right-side profiles of 

each visit for section 0223. Diurnal cycles in temperature and sunlight explain the short-term 

variations in PSG but not the trend toward increasing upward curl over the life of the experiment. 

Figure 5. Graph. Average PSG versus Time for Section 0223. 

In contrast to the rest of the test sections, section 0214 exhibited a trend from upward curl at the 

start of the experiment to increasingly downward curl at the end. As shown in figure 6, the PSG 

values increased most aggressively from negative to positive in years 4–10. Figure 7 shows that 

the slabs curled upward throughout the section in visit 01 (0.32 years). However, the trend toward 

downward curl is strongest near the start of the section in visit 10 (10.34 years) and becomes 

increasingly weak toward the end of the section. A decrease in severity of map cracking from 

the beginning to the end of the section may explain this trend. 

-50

-40

-30

-20

-10

0

10

0 2 4 6 8 10 12 14 16 18

Time (years)

Right

Left

Average PSG (/inch)
11 

Figure 6. Graph. Average PSG versus Time for Section 0214. 

Figure 7. Graph. Right PSG Values from Visits 01 and 10 of Section 0214. 

Relationship Between PSG and IRI 

This section addresses the penalty to IRI caused by curling. On the low-strength sections, a very 

strong statistical relationship was found between variations in PSG and variations in IRI. Using this 

relationship, the roughness caused by slab curl was separated from the roughness caused by other 

sources. This provided a way to look for increases in IRI caused by surface deterioration without 

the erratic changes caused by variations in curl and warp over time. This also provided a way to 

directly estimate the improvement in IRI that is possible with a reduction in slab curl. 

Originally, the study sought to relate PSG to IRI theoretically. For example, an artificial profile 

constructed using a pattern of 15-ft-long slabs with profiles equivalent to the Westergaard equations 

-80

-60

-40

-20

0

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40

60

0 2 4 6 8 10 12 14 16 18

Time (years)

Right

Left

Average PSG (/inch)

visit 10

visit 01

-100

-50

0

50

100

150

0 5 10 15 20 25 30 35

Slab Number

Right PSG (/inch)
12 

showed increases in IRI of 1.74 inches/mi per 1 /inch increase in PSG when the radius of relative 

stiffness was 39.37 inches. However, statistical observations using measured profiles showed that 

the variation in IRI with PSG was roughly three-quarters as large. This is because more roughness 

appeared at transitions between slabs in the theoretical profile, where the slope break between slabs 

was sharper. In the measured profiles, the slope at slab ends was not as large, most likely due to the 

influence of dowel bars and slab weight, which were not included in the model that produced the 

theoretical slab profile. 

Instead, the statistical relationship between IRI and PSG was derived using detailed profile 

measurements collected for the FHWA project “Inertial Profile Data for Pavement Performance 

Analysis.”(2) Measurements from the FHWA study include 124 profiles of sections 0213–0224 

collected over a 1-year cycle. The measurements include four seasonal visits (17-Aug-2003, 

13-Dec-2003, 9-Mar-2004, and 3-Jul-2004) and four rounds of measurement per visit (before 

sunrise, after sunrise, mid-afternoon, and after sunset). Seven or more repeat profiles were 

collected in each of the 16 rounds of measurement. One of the data collection rounds 

commenced less than 11 h after LTPP visit 11 (12-Dec-2003). 

The FHWA profile measurements occurred throughout a diverse mix of ground temperature, air 

temperature, weather, and intensity of solar radiation. Thus, large changes were observed in curl 

and warp without large changes in other surface conditions that affect IRI, such as distress. 

Unfortunately, the profiles from the FHWA study did not cover sections 0260–0268. 

Figure 8 shows the relationship between IRI and PSG on the right side of section 0215 using the 

FHWA data set. The figure shows a distinct IRI-PSG pair for each of 122 passes by the profiler. 

A least-squares linear fit indicates that the IRI changes 1.3754 inches/mi per 1 /inch of change 

in PSG, with a standard estimate of error (SEE) of 2.23 inches/mi. The close relationship observed 

depends on using measurements collected over a relatively short portion of the pavement life so 

that changes do not occur because of other contributors to the IRI, such as surface distress. The 

high correlation is also due to the large range of observed PSG values. 

Figure 8. Graph. IRI versus PSG for Right Side of Section 0215 (FHWA Data). 



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0 10 20 30 40 50 60

PSG (/inch)

IRI = 66.81 + 1.3754•PSG

Standard Error Estimate: 2.23 in/mi

122 samples

R2 = .93

IRI (in/mi)
13 

Figure 8 provides noteworthy insight into the contribution of curl and warp to the roughness of 

section 0215. The PSG values for the right side covered a range of 30–55 /inch in just 1 year, 

and the IRI exhibited a commensurate variation of 38 inches/mi. Further, the plot suggests that if 

the apparent curl were eliminated, the IRI of the right side would be about 67 inches/mi, which is 

less than half the peak value. 

Linear regression of IRI against PSG demonstrated a similar level of correlation for the low-strength 

test sections in the standard experiment. Table 4 lists the slope, intercept, SEE, and correlation 

coefficient for the left- and right-side profiles of these sections. 

Table 4. Regression Results for IRI and PSG on Low-Strength Test Sections. 

Section Side 

Slope

((inches/mi)/( /inch))

Intercept 

(inches/mi)

SEE 

(inches/mi) R2

0213 Left 0.8969 39.97 1.19 0.99 

Right 0.8859 48.95 4.64 0.86 

0217 Left 1.0511 50.90 2.51 0.96 

Right 1.1348 42.11 2.15 0.96 

0221 Left 0.8307 42.03 3.60 0.90 

Right 0.9346 36.00 2.52 0.96 

0215 Left 1.3182 60.40 1.84 0.95 

Right 1.3754 66.81 2.23 0.93 

0219 Left 1.4938 52.02 4.02 0.92 

Right 1.5094 69.97 2.17 0.98 

0223 Left 1.3995 52.27 2.83 0.94 

Right 1.3686 60.36 2.14 0.96 

In table 4, the test sections are listed in order of surface layer thickness. This illustrates the similarity 

in the IRI-PSG slope among structurally similar pavements. A similar dependence of the slope on 

radius of relative stiffness appeared in the theoretical calculations. At a higher radius of relative 

stiffness, IRI is higher for the same strain gradient in an artificial profile constructed using the 

Westergaard equation. The consistency between this trend and the influence of radius of relative 

stiffness on the IRI-PSG slope derived empirically is a sign that the Westergaard equation may 

have been an appropriate choice of an idealized profile on the low-strength test sections. 

The dependence of IRI on PSG was also characterized using LTPP data from section 0215. This 

was possible because section 0215 is in SMP, and data collected from November 2001 through 

December 2004 included 3 regular profiling visits and 24 seasonal visits. Figure 9 shows the linear 

regression for IRI against PSG for the 135 associated profiler passes. The slope, intercept, and 

SEE are all exceptionally similar to the observations from the FHWA data. For the left side, the 

LTPP data produced a slope of 1.442 inches/mi per 1 inch. 




14 

Figure 9. Graph. IRI versus PSG for Right Side of Section 0215 (LTPP SMP Data). 

The agreement between figure 8 and figure 9 demonstrates that the IRI-PSG relationship derived 

from one data set may be applied to data from another, so long as appropriate measurement practices 

are followed. (An analytical procedure with this quality is called “transportable” in the classic road 

roughness literature.(9)) The consistency between data sets also indicates that the SMP produced 

sufficient data to investigate the IRI-PSG relationship and other rigid SMP test sections may also 

produce sufficient data for this analysis. 

Unfortunately, the regression for the high-strength sections often produced low correlation. Table 5 

lists the statistics produced by the FHWA data set for the high-strength sections. In some cases, the 

low overall range in PSG values over the 16 rounds of testing caused low correlation to IRI. Curl and 

warp also caused only a small share of the overall roughness on many of the high-strength sections, 

which often led to poor curve fits in the slab-by-slab analysis. High correlation (and low SEE) 

existed for the right-side profiles on sections 0218, 0220, and 0222. However, the variations in 

IRI over the monitoring period were low relative to the SEE for these sections as compared to 

the low-strength sections. 

0

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40

60

80

100

120

140

160

0 10 20 30 40 50 60

PSG (/inch)

IRI (in/mi)

IRI = 66.38 + 1.3860•PSG

Standard Error Estimate: 2.14 in/mi

135 samples

R2 = .93
15 

Table 5. Regression Results for IRI and PSG on High-Strength Test Sections. 

Section Side 

Slope

((inches/mi)/( /inch))

Intercept 

(inches/mi)

SEE 

(inches/mi) R2

0214 Left 0.3726 74.32 5.85 0.02 

Right 0.8089 44.30 1.87 0.72 

0218 Left 0.2879 71.08 3.39 0.19 

Right 1.0129 41.36 2.07 0.90 

0222 Left 0.5281 60.37 4.85 0.72 

Right 0.7001 41.51 2.29 0.96 

0216 Left 3.3459 49.39 3.80 0.54 

Right 0.8603 82.18 2.12 0.21 

0220 Left 0.8482 65.20 5.86 0.18 

Right 1.1765 53.60 2.04 0.88 

0224 Left 0.6488 69.75 7.43 0.26 

Right 0.5674 65.18 2.15 0.80 

Effect of Curling on IRI 

For the low-strength sections, the relationship between IRI and PSG was sufficient to support 

empirical estimates of the contributions curl and warp make to each IRI value. This was done by 

obtaining the absolute average PSG value for a given visit of a given section, applying the slope 

from table 4 to it, and subtracting the result from the raw IRI value. Graphically, this is equivalent 

to placing a point in the appropriate location on an IRI versus PSG plot such as figure 8 and using 

the IRI-PSG slope to project the point to the IRI axis. 

The product of the PSG and the slope from table 4 is the portion of the IRI associated with curl, 

warp, and other profile features that consistently appear with the same shape as the Westergaard 

equation. The balance is the roughness linked to other sources, such as built-in defects and 

surface distress. Figure 10 through figure 21 provide the results of this method for the lowstrength test sections. 


16 

Figure 10. Graph. Left IRI Progression for Section 0213. 

Figure 11. Graph. Right IRI Progression for Section 0213. 

0

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0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Left IRI (in/mi)

Time (years)

0

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225

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Right IRI (in/mi)

Time (years)
17 

Figure 12. Graph. Left IRI Progression for Section 0215. 

Figure 13. Graph. Right IRI Progression for Section 0215. 

0

20

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160

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Left IRI (in/mi)

Time (years)

0

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160

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Right IRI (in/mi)

Time (years)
18 

Figure 14. Graph. Left IRI Progression for Section 0217. 

Figure 15. Graph. Right IRI Progression for Section 0217. 

0

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120

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Curl Influence Removed

IRI

Left IRI (in/mi)

Time (years)

0

10

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40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Right IRI (in/mi)

Time (years)
19 

Figure 16. Graph. Left IRI Progression for Section 0219. 

Figure 17. Graph. Right IRI Progression for Section 0219. 

0

20

40

60

80

100

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140

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Curl Influence Removed

IRI

Left IRI (in/mi)

Time (years)

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Right IRI (in/mi)

Time (years)
20 

Figure 18. Graph. Left IRI Progression for Section 0221. 

Figure 19. Graph. Right IRI Progression for Section 0221. 

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16 18

Time (years)

Curl Influence Removed

IRI

Left IRI (in/mi)

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Right IRI (in/mi)

Time (years)
21 

Figure 20. Graph. Left IRI Progression for Section 0223. 

Figure 21. Graph. Right IRI Progression for Section 0223. 

This analysis depends on some key assumptions. First, the idealized slab shape must be appropriate. 

If so, the individual curve fits for slab profiles will have high quality, like the example in appendix F. 

Second, empirical derivation of IRI-PSG slope requires measurements over a large range of PSG 

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Left IRI (in/mi)

Time (years)

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Right IRI (in/mi)

Time (years)
22 

values. Third, these analyses used the average absolute PSG value as a basis for comparison to 

IRI. As such, the quality of the relationship breaks down for test sections where some slabs curl 

upward and others curl downward. This was often the case in visit 02 (1.42 years). Lastly, the method 

may overestimate the influence of curl and warp on IRI if other roughness is present that appears 

consistently as a pattern with the same characteristic length as the joint spacing. It is important to 

monitor the quality of the curve fits and qualitatively look for potential features of this type. 

Figure 10 and figure 11 provide sample results for section 0213. The figures show the progression 

in left and right IRI and the portion of the IRI that remained after removing the influence of curl 

and warp. On section 0213, the overall IRI values increased over time, but they were erratic. This 

analysis shows that, without curl and warp, the roughness on the left side was steady throughout the 

experiment, and the roughness on the right side was steady over the first 11 years of the experiment. 

Since longitudinal cracking caused the increase in IRI on the right side after 11 years, it also 

contributed to the roughness in the plot after removing the influence of curl and warp (see 

appendix D). The right side of section 0213 provides an example of using the IRI-PSG 

relationship to distinguish the roughness progression caused by curl and warp from the 

roughness progression caused by surface distress. 

Figure 12 and figure 13 provide sample results for section 0215, including the seasonal visits. As 

on section 0213, the raw IRI values increased erratically on section 0215, with additional scatter 

caused by IRI values that differed between morning and afternoon passes. For example, seasonal 

visits S11 and S12 (8.31 years) produced an IRI on the left side of 121.8 inches/mi at 10 a.m. and 

111.6 inches/mi at 3 p.m. With the influence of curl and warp removed, these values changed to 

58.0 and 57.7 inches/mi, respectively. 

With the influence of curl and warp removed, the IRI values for section 0215 progressed much 

less erratically. Further, the overall IRI level held steady over the experiment. This suggests that 

a long-term increase in upward curl and warp caused net increases in raw IRI of 35 inches/mi on 

the left side and 39 inches/mi on the right side. 

Figure 14 through figure 21 show the results for sections 0217, 0219, 0221, and 0223. These sections 

also exhibited erratic changes in IRI caused by curl and warp. With the influence of curl and warp 

removed, the IRI values were much lower and either increased slowly or held steady throughout 

the experiment, with two exceptions. On the left side of sections 0219 and 0223, the IRI values were 

much higher in visits 09 (9.08 years) and 10 (10.34 years) than in the previous and following visits, 

even after removing the influence of curl and warp (see figure 16 and figure 20). This is because 

other factors caused the increased roughness. 

On both sections, spectral analysis for the left side profiles revealed additional content in the 

8–11-ft wavelength range in visits 09 (9.08 years) and 10 (10.34 years) that did not appear in other 

visits. This phenomenon appeared prominently on sections 0214, 0216, 0218, 0219, 0223, and 0224 

and to a lesser extent on sections 0215, 0217, 0220, and 0222. In many cases, this effect increased 

the IRI of some but not all repeat measurements. Appendix D provides an example for section 0224, 

where the effect was strongest. On many of these sections, the IRI progression plots (appendix C) 

or the standard deviation of IRI for the left side (appendix B) showed some evidence of this effect, 
23 

but the influence of curl and warp obscured it. The source of additional roughness in the 8–11-ft 

wavelength range is not clear, but the affected test sections all appear as a group along the site. 

FAULTING ANALYSIS 

Traditional profile analysis also revealed that faulting contributed heavily to the roughness of 

some test sections. A simple algorithm provided faulting estimates at each joint. This included 

an algorithm for finding the joints, as described in appendix E, and a simple calculation of the 

difference in elevation downstream of the joint and elevation upstream of the joint. 

To exclude the narrow dips at the joint from the calculation, the faulting algorithm excluded 6 inches 

of profile on either side of the joint and used the average elevation over 6 inches of profile on 

either side of the excluded area. In visits 01 (0.32 years) and 02 (1.42 years), only one profile 

point appeared within this range for the approach and leave slabs. In later visits, the calculation 

included at least six points on either side of the joint. 

All test sections except 0262 and 0265 produced average faulting values of less than 0.05 inches 

throughout the experiment. As described in appendix D, sections 0262 and 0265 faulted, the 

severity of faulting grew throughout the experiment, and the increase in IRI with time was 

primarily due to faulting. Figure 22 and figure 23 show the faulting estimates for the left and 

right profiles on these sections. 

Figure 22. Graph. Faulting for Section 0262. 

0

.05

.10

.15

.20

0 2 4 6 8 10 12 14 16 18

Time (years)

Right

Left

Average Faulting (inches)
24 

Figure 23. Graph. Faulting for Section 0265. 

-.05

0

.05

.10

.15

0 2 4 6 8 10 12 14 16 18

Time (years)

Right

Left

Average Faulting (inches)
25 

SUMMARY 

This study examined the roughness and roughness progression of 21 test sections on the LTPP 

SPS-2 site in Arizona. The site included 12 test sections from the standard experiment and 

9 supplemental test sections selected by ADOT. The standard test sections included a matrix of 

variations in surface layer thickness, surface layer strength, and base type. The supplemental 

sections included four test sections that were similar to their counterparts from the standard 

experiment but without dowel bars. The supplemental test sections also included three other 

jointed plain concrete pavement designs of interest to ADOT and two AC test sections. 

Traditional profile analyses revealed roughness caused by transverse and longitudinal cracking on 

some test sections and some localized roughness caused by built-in defects. However, spectral 

analysis and filtered profile plots showed that curl and warp contributed to, and in some cases 

dominated, the roughness on many of the test sections. In addition, the progression of roughness 

throughout the experiment often followed a disorderly trend because of diurnal and seasonal 

changes in slab curl and warp. This study applied objective profile analyses to quantify the level 

of curl and warp on each section. These automated algorithms estimated the gross strain gradient 

needed to deform each slab into the shape present in the measured profile and produced a PSG 

value. The levels of curl and warp within each profile are summarized by the average PSG value. 

For the 19 jointed concrete test sections, variations in average PSG over time and slab-by-slab PSG 

along the pavement explained many of the changes in IRI over time. This included diurnal variations 

in slab curl, which often caused the overall progression in IRI to appear disorderly throughout the 

experiment. PSG analysis also revealed that the level of curl and warp increased overall throughout 

the life of the experiment, with commensurate increases in the IRI. 

LOW-STRENGTH SECTIONS, STANDARD EXPERIMENT 

Table 6 summarizes the observations for the low-strength sections in the base experiment. The table 

lists key structural factors of each section and provides the net change in IRI values from the initial 

visit (0.32 years) to the final visit (16.32 years) for the left and right side. The table also lists the 

net change in PSG values from the initial to the final visit and the prevailing direction of curl in 

the final visit. For these test sections, a negative value indicates an increase in upward curl and a 

positive value indicates a decrease in upward curl. 
26 

Table 6. Summary Results, Low-Strength Sections. 

Section 0213 0217 0221 0215 0219 0223

PCC Flexural Strength (psi) 550 550 550 550 550 550 

Surface Layer Thickness (inches) 8 8 8 11 11 11 

Base Type DGAB LCB PATB DGAB LCB PATB 

Direction of Curl Up Up Up Up Up Up 

IRI Change (inches/mi) 

Left 20 -12 9 34 20 28 

Right 101 -7 11 38 24 22 

PSG Change ( /inch) 

Left -26 24 -8 -33 -10 -28 

Right -12 16 -10 -35 -6 -24 

IRI Change, Curl Removed (inches/mi) 

Left -3 12 2 -6 6 -6 

Right 72 9 2 -5 12 -5 

DGAB = Dense-graded aggregate base 

LCB = Lean concrete base 

PATB = Permeable asphalt-treated base 

PCC = Portland cement concrete 

Table 6 shows that a strong relationship exists between the change in PSG and the change in IRI, 

even though the specific relationship depends on the pavement structural properties (see table 4). 

For example, the highest change in PSG of the 11-inch-thick sections occurred on section 0215, 

which showed the highest change in IRI. Further, section 0217, where the level of curl decreased, 

showed a net decrease in IRI. 

On the six low-strength test sections in the standard experiment, the correlation between IRI and PSG 

was very high. This permitted statistical analysis that isolated the portion of the overall roughness 

caused by curl and warp from the remainder of the roughness. With the influence of curl and warp 

removed, the balance of roughness often followed a more orderly trend. This allowed investigation 

of sources of roughness, such as distress, that were otherwise obscured by the influence of curl 

and warp. It also identified instances in which the roughness progressed due solely to changes 

in curl and warp, where the test section had not deteriorated despite the increase in overall IRI. 

Table 6 also lists the change in IRI with the influence of curl removed. In this case, the balance 

of the roughness held steady throughout the monitoring period on sections 0215, 0217, and 0221. 

This was also the case on sections 0219 and 0223, with the exception of two left IRI values from 

years 9 and 10 that stood out as higher than the rest. Profile analysis showed that the additional 

roughness was isolated to the 8–11-ft wavelength range. Otherwise, the curl-removed IRI on these 

sections held steady at a relatively low value or increased slightly from an initially low value. 

With the influence of curl and warp removed, the balance of the roughness on section 0213 held 

steady throughout the experiment on the left side but increased after 11 years on the right side. 

Patches of narrow dips caused by longitudinal cracking appeared in the left-side profiles in the 

second half of the monitoring period, and they caused localized roughness starting in year 12 of 

the experiment. 


27 

Other observations from the low-strength sections include the following: 

 Section 0213: Section 0213 included a long bump followed by a long dip in all profiles. 

This feature of the profile included a 0.9-inch transition from the peak of the bump to the 

lowest part of the dip over 40 ft of pavement. 

 Section 0217: Section 0217 included transverse and longitudinal cracking starting in year 3 

of the experiment. The transverse cracks caused narrow dips in the profiles at some mid-slab 

positions that increased in severity throughout the rest of the monitoring period. 

 Section 0221: One of the slabs within section 0221 experienced severe aggregate loss 

early in the experiment. The distress surveys listed scaling along the right side of the slab. 

This area and a few others were sealed with fiberglass by year 14. Nevertheless, the slab 

with the most severe aggregate loss caused localized roughness in the right-side profiles 

by the end of the monitoring period. 

HIGH-STRENGTH SECTIONS, STANDARD EXPERIMENT 

Table 7 lists summary results for the high-strength sections. As a group, the high strength 

sections exhibited smaller increases in roughness. As in the low-strength group, the sections 

with lean concrete base (LCB) either increased in roughness less than counterparts with other 

base types or decreased in roughness. 

Table 7. Summary Results, High-Strength Sections. 

Section 0214 0218 0222 0216 0220 0224

PCC Flexural Strength (psi) 900 900 900 900 900 900 

Surface Layer Thickness (inches) 8 8 8 11 11 11 

Base Type DGAB LCB PATB DGAB LCB PATB 

Direction of Curl 

Initial (0.32 years) Up Up Up Up Up Up 

Final (16.32 years) Down Up Up Down Up Up 

IRI Change (inches/mi) 

Left 15 -14 4 3 3 20 

Right 19 -15 -1 18 3 16 

PSG Change ( /inch) 

Left 103 48 1 32 14 -13 

Right 103 56 8 27 6 -15 

DGAB = Dense-graded aggregate base 

LCB = Lean concrete base 

PATB = Permeable asphalt-treated base 

Table 7 lists the net change in PSG for each section. On sections 0218, 0220, and 0222, a positive 

number indicates a reduction in upward curl. The IRI either reduced or held steady on these sections. 

On sections 0214 and 0216, a positive value indicates a change from upward curl at the start of 

the experiment to downward curl at the end. On section 0214, the transition toward downward 

curl was more aggressive on the first half of the section, and a group of slabs in the second half 

of the section maintained a reduced level of upward curl. In this case, the effect on IRI depended 

on the initial level of downward curl. On section 0224, upward curl increased overall. 


28 

SUPPLEMENTAL SECTIONS 

Table 8 lists summary results for the supplemental sections. Sections 0262–0265 match the designs 

of sections 0213, 0221, 0223, and 0215, respectively, except that they are undoweled. All of the 

supplemental sections were curled upward (on average) in the initial visit (0.32 years) and the final 

visit (16.32 years), but some exhibited downward curl in the second visit (1.42 years). Sections 0262 

and 0265 faulted, and the faulting progressed from virtually none to an average value of about 

0.15 inches on section 0262 and 0.10 inches on section 0265. 

Table 8. Summary Results, Supplemental Sections. 

Section 0262 0263 0264 0265 0266 0267 0268

PCC Flexural Strength (psi) 550 550 550 550 550 550 550 

Surface Layer Thickness (inches) 8 8 8.5 8.5 12.5 11 8 

Base Type DGAB PBTB PBTB DGAB DGAB BTB BTB 

Direction of Curl Up Up Up Up Up Up Up 

IRI Change (inches/mi) 

Left 123 19 23 49 24 -2 9 

Right 162 9 31 91 19 -14 7 

PSG Change ( /inch) 

Left -52 -13 -21 -32 -20 -8 -17 

Right -49 -18 -19 -33 -19 -6 -12 

BTB = Bituminous-treated base 

DGAB = Dense-graded aggregate base 

PATB = Permeable asphalt-treated base 

PCC = Portland cement concrete 

AC SECTIONS 

The IRI increased on section 0260 by 64 inches/mi on the left side and 9 inches/mi on the right side. 

Two areas of localized roughness on the left side of the section account for the increase in IRI. 

These areas included small potholes, patching, longitudinal cracks, and pools of sealant. 

The IRI increased on section 0261 by 17 inches/mi on the left side and 58 inches/mi on the right side. 

Dips appeared at several transverse cracks starting 10 years into the experiment that exacerbated the 

roughness of the section in both wheel paths. In addition, a distressed area on the right side 

developed into a pothole. This caused localized roughness in the final profiling visit. 


29 

RECOMMENDATIONS 

This report demonstrated the potential for isolating the effect of curl and warp from other sources of 

roughness in the study of long-term pavement performance due to the strong statistical relationship 

between changes in IRI and changes in PSG. This report also demonstrated that long-term increases 

in IRI may be caused solely by changes in curl and warp and do not necessarily indicate structural 

failure or increased surface distress. However, the statistical methods used in this study required a 

high volume of profile measurements. Refinement of the methods for more general applications 

with broader validity and less ambitious data requirements requires further study. The following 

investigations are recommended: 

 Study structural models other than the original Westergaard equations that may improve 

the prediction of slab profiles near the joints on pavements with dowels. This may also 

permit the theoretical determination of the IRI-PSG slope and reduce measurement effort. 

 Apply the method to other SPS-2 and General Pavement Studies (GPS)-3 sites to generalize 

the IRI-PSG relationship for each pavement design. This would reduce the measurement 

effort needed to apply the methods investigated in this study and provide the same detailed 

assessment of the long-term behavior of pavements at other SPS-2 and GPS-3 sites. 

 Seek a refinement to the method that permits full analysis on high-strength sections and 

on pavement for which curl and warp is a small contributor to IRI. This may require an 

alternative method of estimating the dependence of IRI on PSG or the development of an 

alternative to PSG. 

 Refine the process of obtaining the radius of relative stiffness and quantify the sensitivity 

of the results to the quality of the estimate. 

 Investigate a version of the method that relates raw PSG, rather than average absolute 

PSG, to IRI. 

 Relate PSG to environmental factors.

31 

APPENDIX A. DATA EXTRACTION 

This appendix describes the process of extracting profile measurements for each test section from 

longer measurements that cover multiple test sections. The process described ensured that repeat 

measurements within a given visit and sets of repeat measurements from multiple visits have 

consistent boundaries. 

CROSS CORRELATION 

Searching for the longitudinal offset between repeat profile measurements that provides the 

best agreement between them is a helpful way to refine the synchronization. This can be done by 

inspecting filtered profile plots, but it is very time consuming. Visual assessment is also somewhat 

subjective when two profiles do not agree well, which is often the case when measurements are 

made several years apart. Rather than visual inspection, an automated procedure was used for 

finding the longitudinal offset between measurements. 

The procedure is based on a customized version of cross correlation.(10) In this procedure, a 

basis measurement that is considered to have the correct longitudinal positioning is designated. 

A candidate profile is then searched for the longitudinal offset that provides the highest cross 

correlation to the basis measurement. A high level of cross correlation requires a good match of 

profile shape, the location of isolated rough spots, and overall roughness level. Therefore, the 

correlation level is often only high when the two measurements are synchronized. Great care was 

required for the profiles in this study, because local peaks in correlation were observed every 15 ft, 

where joints from the two profiles aligned. However, the highest correlation level was only observed 

when the profiles were truly synchronized. When the optimal offset is found, a profile is extracted 

from the candidate measurement with the proper overall length and endpoint positions. For the 

rest of this discussion, this process will be referred to as automated synchronization. 

For this application, cross correlation was performed after the IRI filter was applied to the profiles 

rather than using unfiltered profiles. This helped assign the proper weighting to relevant profile 

features. In particular, it increased the weighting of short-wavelength roughness that may appear 

at joints. This enhanced the effectiveness of the automated synchronization procedure. The longwavelength content within the IRI output helped ensure the longitudinal positioning was nearly 

correct, and the short-wavelength content was able to leverage roughness near joints to fine-tune 

the positioning. 

SYNCHRONIZATION 

In visits 01–11, the profiler covered all test sections in each pass with a single, long run. In 

visits 12–15, the profiler covered portions of the site in each pass, and the site was split into 

either four or five groups of test sections. 

Profiles of individual test sections were extracted from the raw measurements using the 

following steps: 

1. Establish a basis measurement for each section from visit 08. This was done using the event 

markers from a raw measurement. The first repeat measurement was used for this purpose. 
32 

Event markers appeared at the start of every section and at the end of every section except 

section 0214. The locations of the event markers were compared to the layout provided in the 

construction report.(1) They exhibited a linear relationship with a bias of less than 0.014 percent, 

and no individual section starting point differed by more than 5 ft. All of the sections were 

assumed to begin at the appropriate event marker and continue for 500 ft. 

2. Automatically synchronize the other eight repeats from visit 08 to the basis set. 

3. Automatically synchronize the measurements from the previous visit to the current basis set. 

4. Replace the basis set with a new set of synchronized measurements from the first repeat of 

the current visit. 

5. Repeat steps 3 and 4 until visit 01 is complete. 

Data for visits 09–15 were provided after visits 01–08 were synchronized. Visits 09–15 were 

synchronized using steps 3–5 but going forward in time. 

LONGITUDINAL DISTANCE MEASUREMENT 

When the longitudinal placement of the individual sections within each measurement were compared 

to the layout within the basis set, the slope of the linear fit ranged from 0.9995 to 1.0000. Thus, the 

longitudinal distance measurement for the nine profile measurements of visit 08 was consistent 

within 0.05 percent. This is a very high level of agreement in longitudinal distance measurement. 

Figure 24 shows the disagreement in longitudinal distance measurement for visits 01–11 using the 

original basis set as a reference. In visits 12–15, the site was not covered in a single, long run in 

each pass, so the visits were excluded from this analysis. In the figure, a range of disagreement for 

each visit exists because up to nine repeat profile measurements were made. The variation between 

repeat measurements within a visit appears as the width of each bar in the figure. Because the 

longitudinal distance measurement was based on the rotation of a drive wheel, the variations were 

most likely caused by variations in speed, lateral wander, and tire inflation pressure.(11) If tire 

inflation pressure were the dominant cause, the disagreement would grow more positive with 

each successive repeat measurement as the tire heated up. This is because the tire rolling radius 

would increase, and the profiler would register less wheel rotation for the same travel distance. 

This appeared to be the case for visits 04–10, but the effect was never greater than 0.10 percent 

of the overall distance. 
33 

© ADOT 

Figure 24. Graph. Consistency in Longitudinal Distance Measurement. 

The variation between visits in figure 24 was caused by differences in distance measurement 

instrument calibration. The longitudinal distance measured by a profiler is not a true horizontal 

distance. It includes additional components because the profiler must travel up and down undulations 

in the road. This component can be minimized by calibrating the profiler to true horizontal distance. 

However, if a profiler operates on a road with grade changes and roughness that are not similar to 

the site used for longitudinal distance measurement calibration, some error will exist. For consistent 

results, tire inflation pressure must also be close to the level used during calibration. 

Modest inconsistency in longitudinal distance measurement between visits is not critical as long as 

the profiles of individual sections are extracted using event markers rather than longitudinal distance 

from the start of each profile measurement. A high level of inconsistency, however, could interfere 

with comparisons between profile features and distress surveys. Errors in profile index values, such 

as IRI, are also roughly of the same order as errors in longitudinal distance measurement.(11)

Figure 24 shows that longitudinal distance was measured with a very high level of agreement 

throughout all 11 visits.

2

4

6

8

10

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

11

1

3

5

7

9

Disagreement in Longitudinal Distance (percent)

Visit Number

35 

APPENDIX B. DATA QUALITY SCREENING 

A screening process was performed to select five repeat profile measurements from each visit of 

each section. The five measurements selected from the group of either five, seven, or nine available 

runs were those that exhibited the best agreement with each other. In this case, agreement between 

any two profile measurements was judged by cross correlating them after applying the IRI filter.(10)

In this method, the IRI filter is applied to the profiles, then the output signals, rather than the overall 

index, are compared. High correlation by this method requires that the overall roughness is in 

agreement, as well as the details of the profile shape that affect IRI. The IRI filter was applied 

before correlation in this case for the following reasons: 

 Direct correlation of unfiltered profiles places a premium on long-wavelength content but 

ignores much of the contribution of short-wavelength content. 

 Correlation of IRI filter output emphasizes profile features in (approximate) proportion to 

their effect on the overall roughness. 

 Correlation of IRI filter output provides a good tradeoff between emphasizing localized 

rough features at distressed areas in the pavement and placing too much weight on shortduration, narrow features (spikes) that are not likely to agree between measurements. 

This is because the IRI filter amplifies short-wavelength content but attenuates 

macrotexture, megatexture, and spikes. 

 A relationship has been demonstrated between the cross correlation level of IRI filter 

output and the expected agreement in overall IRI.(10)

The method was performed with a special provision for correcting modest longitudinal distance 

measurement errors. 

Each comparison between profiles produced a single value that summarized their level of agreement. 

When 9 repeat profile measurements were available, they produced a total of 36 correlation values. 

Any subgroup of 5 measurements could be summarized by averaging the appropriate 10 correlation 

values. The subgroup that produced the highest average was selected, and the other repeats were 

excluded from the analyses discussed in this report. Table 9 through table 29 list the selected 

repeats for each visit of each section and the composite correlation level produced by them. 

The process used for selecting five repeat measurements from a larger group is similar to the practice 

within LTPP except that it uses composite agreement in profiles rather than the overall index value. 

The correlation levels listed in table 9 through table 29 provide a repeatability score and appraise 

the agreement between profile measurements for each visit of each section. When two profiles 

produce a correlation level above 0.82, their IRI values are expected to agree within 10 percent most 

(95 percent) of the time. Above this threshold, the agreement between profiles is usually acceptable 

for studying the influence of distresses on the profile. When two profiles produce a correlation level 

above 0.92, they are expected to agree within 5 percent most of the time. Above this threshold, the 

agreement between profiles is good. Correlation above 0.92 often depends on consistent lateral 

tracking of the profiler and may be very difficult to achieve on highly distressed surfaces. The IRI 

values in this report are the average of five observations, which tightens the tolerance even further. 
36 

Table 9. Selected Repeats for Section 0213. 

Visit Repeat Number Composite Correlation 

01 2 3 6 7 8 0.935 

02 2 5 6 7 9 0.902 

03 1 3 5 6 8 0.971 

04 1 3 4 5 7 0.953 

05 1 2 5 6 7 0.965 

06 1 3 4 5 6 0.963 

07 4 5 6 7 9 0.948 

08 1 2 4 7 9 0.936 

09 1 3 4 5 7 0.948 

10 1 2 6 7 8 0.947 

11 2 3 4 7 9 0.900 

12 1 4 5 7 8 0.853 

13 1 2 3 4 5 0.812 

14 1 3 4 5 6 0.771 

15 1 4 5 7 9 0.769 

Table 10. Selected Repeats for Section 0214. 

Visit Repeat Numbers Composite Correlation 

01 2 3 5 6 8 0.909 

02 2 4 6 7 8 0.822 

03 2 3 4 5 8 0.912 

04 1 3 4 5 7 0.900 

05 1 3 4 5 6 0.903 

06 2 3 4 6 7 0.926 

07 1 2 5 6 8 0.953 

08 1 2 5 6 7 0.950 

09 1 3 5 6 8 0.937 

10 2 3 5 6 8 0.935 

11 3 5 6 7 8 0.924 

12 2 3 4 7 8 0.945 

13 4 5 6 8 9 0.959 

14 1 3 4 7 8 0.927 

15 2 4 5 6 9 0.955 
37 

Table 11. Selected Repeats for Section 0215. 

Visit Repeat Numbers Composite Correlation 

01 1 3 4 5 8 0.930

02 1 3 5 7 8 0.920

03 5 6 7 8 9 0.962

04 1 3 4 5 7 0.922

05 1 2 4 6 7 0.967

06 1 2 4 6 7 0.955

07 1 3 4 8 9 0.976

08 4 5 6 7 9 0.987

09 3 5 6 7 8 0.943

10 1 3 5 8 9 0.933

11 1 2 3 5 7 0.948

12 2 4 5 6 7 0.981

13 2 3 4 7 9 0.976

14 1 2 7 8 9 0.969

15 2 3 4 5 8 0.965

S01 2 3 4 5 7 0.936

S02 1 2 3 4 5 0.966

S03 1 2 3 4 5 0.955

S04 1 2 3 4 5 0.921

S05 1 2 3 4 5 0.937

S06 1 2 3 4 5 0.959

S07 1 2 3 4 5 0.936

S08 2 3 4 5 6 0.959

S09 1 2 3 4 7 0.977

S10 1 3 4 5 9 0.972

S11 2 3 5 6 7 0.979

S12 1 2 3 6 8 0.983

S13 1 3 4 5 7 0.979

S14 2 3 5 6 7 0.965

S15 4 5 6 7 9 0.960

S16 1 2 3 4 5 0.965

S17 1 2 3 4 6 0.976

S18 1 4 7 8 9 0.947

S19 2 3 5 6 9 0.963

S20 2 4 6 7 9 0.960

S21 1 3 4 5 6 0.972

S22 3 4 6 7 9 0.975

S23 3 4 5 8 9 0.964

S24 1 4 5 6 9 0.957

S25 1 2 4 7 9 0.975

S26 1 2 4 5 6 0.973

S27 1 2 3 8 9 0.972

S28 4 6 7 8 9 0.961

S29 1 2 3 4 8 0.973

S30 2 4 6 7 8 0.978

S31 3 4 6 7 8 0.978

S32 1 2 3 4 6 0.976
38 

Table 12. Selected Repeats for Section 0216. 

Visit Repeat Numbers Composite Correlation 

01 3 5 6 8 9 0.922 

02 3 5 7 8 9 0.892 

03 1 2 3 5 7 0.927 

04 1 2 4 5 6 0.930 

05 1 2 3 5 6 0.951 

06 2 3 4 5 6 0.948 

07 2 3 4 6 9 0.968 

08 2 3 4 6 8 0.957 

09 1 2 4 5 8 0.930 

10 1 3 4 6 7 0.937 

11 2 4 5 6 9 0.910 

12 1 4 6 7 8 0.949 

13 2 4 7 8 9 0.954 

14 2 3 6 8 9 0.938 

15 1 2 3 4 8 0.948 

Table 13. Selected Repeats for Section 0217. 

Visit Repeat Numbers Composite Correlation 

01 4 6 7 8 9 0.925 

02 1 4 5 6 8 0.876 

03 3 4 6 8 9 0.951 

04 2 3 4 6 7 0.916 

05 1 2 3 6 7 0.915 

06 1 2 4 5 7 0.939 

07 4 5 6 8 9 0.963 

08 1 2 3 6 9 0.957 

09 1 2 3 4 5 0.921 

10 1 2 3 7 9 0.907 

11 1 2 6 7 9 0.875 

12 1 3 5 6 7 0.957 

13 2 3 4 6 9 0.911 

14 1 2 5 7 9 0.933 

15 1 5 6 7 9 0.838 
39 

Table 14. Selected Repeats for Section 0218. 

Visit Repeat Numbers Composite Correlation 

01 1 2 5 7 9 0.898 

02 2 4 5 8 9 0.818 

03 1 3 6 7 9 0.909 

04 1 3 4 5 7 0.891 

05 1 2 3 4 5 0.888 

06 2 3 4 6 7 0.923 

07 1 2 3 6 9 0.944 

08 1 3 4 7 8 0.951 

09 2 3 5 6 7 0.892 

10 1 2 4 7 9 0.906 

11 1 2 3 6 7 0.889 

12 4 5 6 7 9 0.928 

13 2 3 6 8 9 0.931 

14 1 3 7 8 9 0.947 

15 1 3 6 7 8 0.921 

Table 15. Selected Repeats for Section 0219. 

Visit Repeat Numbers Composite Correlation 

01 3 5 6 7 9 0.902 

02 1 2 5 6 8 0.870 

03 2 4 7 8 9 0.931 

04 1 3 4 6 7 0.920 

05 1 2 3 5 7 0.928 

06 2 3 4 6 7 0.942 

07 2 4 6 8 9 0.955 

08 1 2 5 6 8 0.954 

09 1 2 3 7 9 0.923 

10 1 2 5 6 8 0.932 

11 4 5 6 7 8 0.936 

12 1 4 6 7 8 0.970 

13 2 3 4 8 9 0.954 

14 1 3 4 5 6 0.951 

15 4 5 6 7 9 0.931 
40 

Table 16. Selected Repeats for Section 0220. 

Visit Repeat Numbers Composite Correlation 

01 5 6 7 8 9 0.910 

02 3 4 5 6 9 0.871 

03 1 2 6 7 8 0.917 

04 1 3 4 6 7 0.898 

05 2 3 4 6 7 0.950 

06 1 2 5 6 7 0.950 

07 1 2 5 7 9 0.935 

08 2 3 4 5 6 0.958 

09 1 2 3 6 8 0.915 

10 2 3 4 6 7 0.929 

11 1 2 5 6 9 0.938 

12 3 4 6 7 8 0.936 

13 2 3 6 7 9 0.932 

14 2 4 5 6 7 0.944 

15 1 3 6 8 9 0.936 

Table 17. Selected Repeats for Section 0221. 

Visit Repeat Numbers Composite Correlation 

01 1 4 6 8 9 0.890 

02 4 6 7 8 9 0.838 

03 1 2 4 6 9 0.901 

04 1 2 4 5 6 0.882 

05 1 2 3 5 6 0.936 

06 1 2 4 5 7 0.946 

07 1 2 5 6 9 0.932 

08 1 5 6 8 9 0.946 

09 1 5 6 7 8 0.825 

10 1 3 4 6 8 0.861 

11 2 4 5 6 7 0.857 

12 3 4 5 6 7 0.943 

13 1 2 3 5 6 0.907 

14 1 2 3 4 6 0.949 

15 2 5 7 8 9 0.934 
41 

Table 18. Selected Repeats for Section 0222. 

Visit Repeat Numbers Composite Correlation 

01 4 5 6 8 9 0.898 

02 1 4 5 6 7 0.816 

03 1 3 5 6 9 0.942 

04 1 3 5 6 7 0.857 

05 2 3 4 6 7 0.929 

06 2 3 4 5 7 0.920 

07 2 4 5 6 8 0.943 

08 2 4 5 7 8 0.948 

09 1 2 4 6 7 0.900 

10 1 2 3 5 6 0.880 

11 2 3 4 6 8 0.853 

12 2 3 6 7 8 0.935 

13 2 3 5 6 9 0.931 

14 2 3 4 6 7 0.914 

15 2 6 7 8 9 0.910 

Table 19. Selected Repeat for Section 0223. 

Visit Repeat Numbers Composite Correlation 

01 1 2 6 7 9 0.892 

02 1 3 4 8 9 0.893 

03 4 5 6 7 9 0.934 

04 3 4 5 6 7 0.948 

05 1 2 3 6 7 0.943 

06 1 2 3 4 6 0.953 

07 1 2 3 6 8 0.956 

08 3 4 5 6 9 0.960 

09 3 6 7 8 9 0.949 

10 1 2 3 5 8 0.914 

11 5 6 7 8 9 0.946 

12 2 4 5 6 9 0.972 

13 2 3 4 8 9 0.956 

14 3 5 6 8 9 0.965 

15 3 4 6 8 9 0.951 
42 

Table 20. Selected Repeats for Section 0224. 

Visit Repeat Numbers Composite Correlation 

01 3 4 6 8 9 0.894 

02 4 5 6 8 9 0.837 

03 2 3 4 6 7 0.907 

04 1 2 3 4 5 0.863 

05 1 2 3 6 7 0.873 

06 2 3 5 6 7 0.921 

07 2 3 5 6 7 0.940 

08 2 4 6 7 8 0.932 

09 1 2 4 5 8 0.917 

10 2 4 6 8 9 0.960 

11 1 2 4 7 9 0.873 

12 1 2 6 7 8 0.939 

13 5 6 7 8 9 0.950 

14 3 6 7 8 9 0.905 

15 1 2 3 5 9 0.918 

Table 21. Selected Repeats for Section 0260. 

Visit Repeat Numbers Composite Correlation 

01 1 2 3 4 7 0.939 

02 3 5 6 8 9 0.899 

03 1 2 5 6 8 0.932 

04 3 4 5 6 7 0.885 

05 1 2 4 5 7 0.921 

06 2 4 5 6 7 0.920 

07 1 3 4 6 9 0.952 

08 2 3 6 7 9 0.962 

09 1 3 4 6 8 0.921 

10 1 2 5 7 8 0.897 

11 1 2 5 6 7 0.837 

12 1 3 4 6 8 0.889 

13 1 3 5 6 8 0.799 

14 1 2 3 4 6 0.882 

15 1 3 4 5 6 0.866
43 

Table 22. Selected Repeats for Section 0261. 

Visit Repeat Numbers Composite Correlation 

01 3 5 6 8 9 0.916 

02 2 4 6 7 9 0.872 

03 5 6 7 8 9 0.910 

04 1 3 5 6 7 0.857 

05 3 4 5 6 7 0.926 

06 1 2 4 5 7 0.896 

07 3 4 5 6 7 0.937 

08 1 3 4 5 7 0.940 

09 1 2 3 4 9 0.866 

10 1 2 5 6 7 0.860 

11 1 4 5 6 7 0.766 

12 4 5 6 8 9 0.882 

13 2 3 4 7 8 0.893 

14 1 2 3 6 7 0.877 

15 1 2 3 5 9 0.922 

Table 23. Selected Repeats for Section 0262. 

Visit Repeat Numbers Composite Correlation 

01 4 5 6 8 9 0.867 

02 1 4 5 7 9 0.859 

03 2 3 5 6 7 0.965 

04 2 3 4 5 7 0.969 

05 1 2 3 4 5 0.981 

06 2 3 4 5 6 0.980 

07 2 5 6 8 9 0.981 

08 2 3 5 6 7 0.986 

09 1 2 3 4 6 0.976 

10 2 3 4 6 7 0.975 

11 2 3 4 6 7 0.978 

12 1 4 5 8 9 0.982 

13 2 3 5 7 9 0.949 

14 1 4 7 8 9 0.959 

15 1 2 5 8 9 0.974 
44 

Table 24. Selected Repeats for Section 0263. 

Visit Repeat Numbers Composite Correlation 

01 3 6 7 8 9 0.839 

02 1 6 7 8 9 0.813 

03 1 2 3 5 9 0.940 

04 1 2 3 4 5 0.936 

05 2 3 4 5 7 0.939 

06 1 2 3 4 6 0.942 

07 1 3 5 7 9 0.947 

08 2 3 5 7 9 0.944 

09 2 5 6 7 8 0.884 

10 1 2 4 5 9 0.932 

11 1 2 4 5 7 0.855 

12 2 3 4 6 7 0.949 

13 2 4 5 6 8 0.941 

14 2 3 5 7 8 0.939 

15 2 3 4 5 6 0.899 

Table 25. Selected Repeats for Section 0264. 

Visit Repeat Numbers Composite Correlation 

01 2 3 4 5 8 0.906 

02 1 5 6 7 8 0.931 

03 1 2 4 6 8 0.938 

04 2 3 4 5 6 0.940 

05 2 3 5 6 7 0.964 

06 1 2 3 6 7 0.951 

07 1 2 5 6 8 0.962 

08 1 4 5 6 7 0.969 

09 1 3 4 7 8 0.904 

10 3 4 5 7 8 0.894 

11 1 2 4 5 6 0.911 

12 1 3 6 8 9 0.968 

13 2 4 6 8 9 0.946 

14 1 2 4 6 7 0.962 

15 1 2 3 4 5 0.937 
45 

Table 26. Selected Repeats for Section 0265. 

Visit Repeat Numbers Composite Correlation 

01 1 2 4 5 8 0.915 

02 4 5 6 7 9 0.879 

03 1 3 4 6 7 0.958 

04 3 4 5 6 7 0.927 

05 1 4 5 6 7 0.950 

06 1 2 4 6 7 0.937 

07 2 4 6 7 8 0.976 

08 2 3 4 5 6 0.965 

09 2 3 4 5 7 0.923 

10 3 6 7 8 9 0.935 

11 2 4 5 6 7 0.916 

12 2 3 7 8 9 0.974 

13 3 4 6 8 9 0.966 

14 1 2 4 6 7 0.962 

15 1 2 3 6 7 0.977 

Table 27. Selected Repeats for Section 0266. 

Visit Repeat Numbers Composite Correlation 

01 1 4 6 7 9 0.886 

02 1 2 3 5 6 0.885 

03 1 2 7 8 9 0.941 

04 1 2 3 4 6 0.901 

05 1 2 3 4 6 0.972 

06 1 2 3 5 6 0.943 

07 1 4 6 7 8 0.958 

08 2 3 4 5 6 0.963 

09 3 4 7 8 9 0.902 

10 1 3 5 7 8 0.949 

11 1 4 5 7 9 0.934 

12 1 2 5 6 9 0.947 

13 1 2 4 5 8 0.960 

14 1 3 4 5 8 0.950 

15 1 3 4 5 6 0.937 
46 

Table 28. Selected Repeats for Section 0267. 

Visit Repeat Numbers Composite Correlation 

01 1 3 6 7 9 0.888 

02 4 5 6 7 8 0.878 

03 4 5 6 8 9 0.919 

04 1 2 3 4 6 0.872 

05 1 2 4 5 6 0.921 

06 2 3 4 5 7 0.949 

07 1 2 3 7 9 0.955 

08 1 4 6 7 9 0.960 

09 2 3 5 6 8 0.874 

10 2 3 5 7 9 0.930 

11 1 2 5 6 7 0.926 

12 1 2 4 6 9 0.869 

13 1 4 6 7 8 0.878 

14 1 2 4 5 6 0.907 

15 1 2 3 4 6 0.909 

Table 29. Selected Repeats for Section 0268. 

Visit Repeat Numbers Composite Correlation 

01 1 2 5 6 9 0.851 

02 1 3 5 6 8 0.813 

03 4 5 7 8 9 0.919 

04 1 2 4 6 7 0.863 

05 1 2 4 5 6 0.904 

06 2 3 5 6 7 0.956 

07 1 3 4 8 9 0.932 

08 2 3 6 7 9 0.947 

09 1 2 3 5 6 0.831 

10 1 5 6 8 9 0.924 

11 3 4 6 7 9 0.875 

12 2 3 6 7 8 0.939 

13 3 4 5 7 9 0.931 

14 1 2 5 6 9 0.883 

15 2 3 4 6 9 0.873 

Only 9 of the 347 sets of selected repeat measurements listed in table 9 through table 29 exhibited 

a composite correlation below 0.82. Measurements of sections 0215 and 0262 produced the highest 

repeatability scores, whereas some profiles from visit 02 and from later visits of section 0213 

produced the lowest scores. Fortunately, correlation was never low enough to impede the automated 

synchronization process. However, low repeatability scores prompted inspection of profile plots 

to help identify the cause. In visit 02, most of the profiles included short-wavelength content that 

was not correlated between repeat measurements. The effect was greatest in sections 0214, 0218, 

0222, 0263, and 0268. It is suspected that the effect was caused by coarse surface texture, but 

that cannot be verified. 
47 

Other observations were as follows: 

 Section 0213, visits 13–15: The right profiles of these visits included deep, narrow dips 

or patches of narrow dips that appeared in some areas in each profile with inconsistent 

size and placement. 

 Section 0260, later visits: Agreement between profiles was diminished by patches of 

uncorrelated deep, narrow dips in the left profiles from 50 to 65 ft from the start of the 

section and from 330 to 360 ft from the start of the section. This is an AC section. 

 Section 0261, visit 11: Localized roughness appeared on the right side from 474 to 479 ft 

from the start of the section in four of the five profiles and with inconsistent shape and 

placement on the left side from 355 to 375 ft from the start of the section. Visits 09 and 10 

also included inconsistent measurement of these features. This is an AC section. 

 Sections 0267 and 0268, visit 09: The short-wavelength content from the visit did not 

agree well, and the profiles included some extraneous narrow dips. 

49 

APPENDIX C. ROUGHNESS VALUES 

This appendix lists left IRI, right IRI, Mean Roughness Index (MRI), HRI, and RN values for each 

visit of each section. The roughness values are the average for five repeat runs. The five runs were 

selected from a group of as many as nine by automated comparison of profiles, as described in 

appendix B. Values of standard deviation are also provided for left and right IRI to reveal cases 

of high variability among the five measurements. However, the screening procedure used to 

select the five repeats usually helped reduce the level of scatter. 

The discussion of roughness in the main report emphasizes the left and right IRI. Nevertheless, the 

other indexes provide useful additional information. MRI is the average of the left and right IRI 

values. HRI is calculated by converting the IRI filter into a half-car model.(12) This is done by 

collapsing the left and right profile into a single profile in which each point is the average of the 

corresponding left and right elevation. The IRI filter is then applied to the resulting signal. HRI is 

similar to IRI except that side-to-side deviations in the profile are eliminated. The result is that the 

HRI value for a pair of profiles will always be lower than the corresponding MRI value. Comparing 

HRI and MRI values provides a crude indication of the significance of roll (i.e., side-by-side 

variation in profile) to the overall roughness. When HRI is low compared to MRI, roll is significant. 

This is common among asphalt pavements.(13) Certain types of pavement distress, such as 

longitudinal cracking, may also cause significant differences between HRI and MRI. 

Figure 25 compares HRI to MRI for the profile measurements on PCC sections. This includes 

1,585 pairs of roughness values and excludes AC sections 0260 and 0261. The figure shows a best-fit 

line with a zero intercept and a line of equality. The slope of the line is 0.914. A typical range for 

concrete pavement is 0.90–0.95. A better linear fit was found without forcing a zero intercept. A 

simple linear fit produced a slope of about 0.979 and an intercept of about -6.9 inches/mi. 

© ADOT 

Figure 25. Graph. Comparison of HRI to MRI. 

0

50

100

150

200

0 50 100 150 200

HRI = 0.906•MRI

Line of Equality

HRI (in/mi)

MRI (in/mi)
50 

RN has shown a closer relationship to road-user opinions than other indexes.(14) As such, it may 

help distinguish the segments from each other by ride quality. Further, the effect on RN may help 

quantify the impact of distress on ride when the roughness of a section is dominated by a particular 

type of distress. In particular, a very low RN value coupled with moderate IRI values indicates a 

high level of short-wavelength roughness and potential sensitivity to narrow dips and measurement 

errors caused by coarse surface texture. 

Table 30 provides the roughness values. The table also lists the date of each measurement and the 

time in years since the site was opened to traffic. Figure 26 through figure 46 show left and right 

IRI versus time in years for all 21 test sections. As before, years is defined as the number of years 

between the measurement date and the date the site was opened to traffic (1-Oct-1993). 

Table 30. Roughness Values. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0213 

25-Jan-94 0.32 91 1.7 97 1.5 94 86 3.63 

5-Mar-95 1.42 72 1.0 83 1.7 78 69 3.75 

27-Jan-97 3.32 103 0.9 110 1.1 107 101 3.53 

4-Dec-97 4.18 104 2.6 117 2.0 111 105 3.50 

8-Dec-98 5.19 108 1.1 117 1.5 112 107 3.46 

15-Nov-99 6.12 118 0.7 131 1.0 124 118 3.33 

30-Nov-00 7.16 107 1.1 119 1.4 113 106 3.42 

8-Nov-01 8.10 118 1.2 133 1.5 125 119 3.29 

30-Oct-02 9.08 124 0.6 119 2.4 122 116 3.36 

4-Feb-04 10.34 110 1.4 105 3.3 108 101 3.48 

12-Dec-04 11.20 103 1.2 117 3.2 110 103 3.32 

11-Aug-06 12.86 139 1.0 177 5.5 158 149 2.39 

30-Dec-07 14.25 114 0.8 147 6.9 131 121 2.56 

20-Sep-08 14.97 127 1.0 166 6.8 147 136 2.56 

25-Jan-10 16.32 111 1.3 198 3.5 155 140 2.00 

0214 

25-Jan-94 0.32 85 1.9 80 1.9 83 80 3.65 

5-Mar-95 1.42 55 0.5 59 1.7 57 50 3.78 

27-Jan-97 3.32 76 3.2 64 2.6 70 65 3.80 

4-Dec-97 4.18 70 2.6 69 1.9 70 65 3.79 

8-Dec-98 5.19 67 3.3 68 0.9 68 62 3.80 

15-Nov-99 6.12 85 2.0 71 1.8 78 71 3.70 

30-Nov-00 7.16 81 0.8 71 1.2 76 70 3.68 

8-Nov-01 8.10 79 2.5 79 0.5 79 73 3.62 

30-Oct-02 9.08 94 3.4 78 1.0 86 78 3.47 

4-Feb-04 10.34 101 3.1 87 1.4 94 85 3.38 

12-Dec-04 11.20 80 2.9 83 1.0 81 75 3.46 

13-Aug-06 12.87 81 1.9 83 0.8 82 75 3.44 

30-Dec-07 14.25 102 1.3 93 1.8 97 90 3.31 

20-Sep-08 14.97 96 3.0 85 1.7 91 84 3.39 

25-Jan-10 16.32 100 2.0 99 0.9 100 94 3.27 
51 

Table 30. Roughness Values—Continued. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0215 

25-Jan-94 0.32 89 0.8 91 1.4 90 80 3.66 

5-Mar-95 1.42 82 0.9 97 3.2 89 80 3.61 

27-Jan-97 3.32 98 0.7 102 1.4 100 91 3.60 

4-Dec-97 4.18 100 3.6 105 2.2 103 94 3.52 

15-Jan-98 4.29 89 0.8 101 2.3 95 86 3.61 

15-Jan-98 4.29 87 0.7 103 0.9 95 87 3.61 

13-Apr-98 4.53 92 0.9 99 1.7 96 86 3.60 

13-Apr-98 4.53 91 1.2 98 1.6 95 85 3.60 

9-Jul-98 4.77 96 1.7 107 2.3 101 91 3.54 

9-Jul-98 4.77 93 0.7 105 1.9 99 88 3.54 

30-Sep-98 5.00 105 1.1 114 2.3 109 100 3.47 

30-Sep-98 5.00 99 2.3 112 1.6 105 96 3.48 

8-Dec-98 5.19 109 1.2 110 2.1 109 101 3.46 

15-Nov-99 6.12 114 1.9 123 1.5 118 110 3.41 

30-Nov-00 7.16 111 0.5 119 1.4 115 106 3.44 

8-Nov-01 8.10 121 0.5 126 0.7 124 116 3.34 

9-Dec-01 8.19 125 0.3 129 0.6 127 120 3.32 

9-Dec-01 8.19 116 0.9 120 0.6 118 111 3.42 

24-Jan-02 8.31 122 1.2 127 0.9 124 117 3.34 

24-Jan-02 8.31 112 0.3 120 1.1 116 108 3.43 

15-Mar-02 8.45 130 1.2 133 1.3 132 125 3.27 

15-Mar-02 8.45 117 0.7 122 2.8 119 112 3.40 

9-Oct-02 9.02 140 1.3 132 3.0 136 130 3.24 

9-Oct-02 9.02 121 1.4 123 1.4 122 116 3.35 

30-Oct-02 9.08 131 6.1 122 1.1 127 119 3.33 

20-Dec-02 9.22 137 0.8 131 1.3 134 128 3.25 

20-Dec-02 9.22 125 4.4 120 1.6 123 115 3.37 

7-Mar-03 9.43 124 1.5 119 2.1 122 115 3.35 

7-Mar-03 9.43 112 0.7 112 2.0 112 105 3.45 

25-Jul-03 9.81 121 0.3 130 1.2 126 119 3.32 

25-Jul-03 9.81 119 1.0 126 1.0 122 115 3.33 

24-Nov-03 10.15 124 1.7 127 0.9 125 119 3.29 

24-Nov-03 10.15 117 1.2 120 2.2 118 112 3.39 

14-Dec-03 10.20 119 0.8 126 1.0 122 115 3.32 

14-Dec-03 10.20 115 1.4 119 0.6 117 110 3.39 

4-Feb-04 10.34 130 3.3 118 2.4 124 116 3.35 

22-Apr-04 10.56 133 0.4 139 2.1 136 129 3.22 

22-Apr-04 10.56 118 1.1 121 1.6 120 113 3.36 

15-Jul-04 10.79 132 1.3 142 1.7 137 131 3.21 

15-Jul-04 10.79 129 0.3 135 0.9 132 126 3.24 

9-Sep-04 10.94 135 0.1 145 0.7 140 134 3.18 

9-Sep-04 10.94 132 0.7 142 1.6 137 131 3.19 
52 

Table 30. Roughness Values—Continued. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0215 

12-Dec-04 11.20 108 1.9 120 1.3 114 107 3.39 

13-Aug-06 12.87 135 0.6 141 0.9 138 133 3.18 

30-Dec-07 14.25 122 0.5 123 1.0 123 116 3.32 

20-Sep-08 14.97 134 0.9 142 1.6 138 132 3.18 

25-Jan-10 16.32 124 1.5 129 1.0 126 119 3.28 

0216 

25-Jan-94 0.32 90 2.4 87 2.3 89 81 3.57 

5-Mar-95 1.42 83 1.5 89 1.8 86 75 3.54 

27-Jan-97 3.32 87 3.7 84 0.8 86 76 3.65 

4-Dec-97 4.18 86 0.7 85 2.5 85 76 3.61 

8-Dec-98 5.19 88 0.9 87 1.8 88 78 3.59 

15-Nov-99 6.12 93 2.7 86 0.6 89 79 3.63 

30-Nov-00 7.16 85 1.3 88 0.7 87 78 3.65 

8-Nov-01 8.10 85 1.2 91 1.3 88 78 3.62 

30-Oct-02 9.08 98 3.9 92 1.3 95 80 3.52 

4-Feb-04 10.34 99 3.2 99 1.6 99 84 3.47 

12-Dec-04 11.20 88 1.6 99 2.7 94 85 3.50 

13-Aug-06 12.87 88 1.4 99 1.5 94 85 3.49 

30-Dec-07 14.25 98 1.6 101 1.5 99 88 3.44 

20-Sep-08 14.97 100 2.8 97 0.4 99 85 3.47 

25-Jan-10 16.32 93 1.0 105 1.8 99 90 3.42 

0217 

25-Jan-94 0.32 93 0.5 82 1.1 87 79 3.59 

5-Mar-95 1.42 61 1.5 70 2.1 65 56 3.81 

27-Jan-97 3.32 83 0.7 78 1.3 80 71 3.76 

4-Dec-97 4.18 79 3.7 80 2.6 79 72 3.78 

8-Dec-98 5.19 82 3.2 78 2.8 80 72 3.76 

15-Nov-99 6.12 93 2.2 81 0.9 87 77 3.73 

30-Nov-00 7.16 85 1.6 75 0.6 80 70 3.81 

8-Nov-01 8.10 87 2.2 77 1.7 82 74 3.78 

30-Oct-02 9.08 87 1.5 74 0.8 80 70 3.73 

4-Feb-04 10.34 88 3.3 66 1.4 77 65 3.79 

12-Dec-04 11.20 84 4.3 74 2.0 79 69 3.75 

11-Aug-06 12.86 105 1.7 89 2.1 97 89 3.62 

30-Dec-07 14.25 80 2.5 74 1.6 77 66 3.60 

20-Sep-08 14.97 110 3.5 82 1.9 96 86 3.61 

25-Jan-10 16.32 81 1.6 75 3.0 78 68 3.26 
53 

Table 30. Roughness Values—Continued. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0218 

25-Jan-94 0.32 92 3.7 85 1.9 88 83 3.54

5-Mar-95 1.42 65 1.3 59 1.6 62 53 3.74

27-Jan-97 3.32 74 1.5 56 0.4 65 58 3.81

4-Dec-97 4.18 73 1.4 61 2.0 67 60 3.77

8-Dec-98 5.19 74 0.9 60 1.2 67 60 3.77

15-Nov-99 6.12 79 1.9 65 0.7 72 65 3.77

30-Nov-00 7.16 72 1.1 60 0.7 66 58 3.82

8-Nov-01 8.10 71 1.0 62 0.6 67 59 3.82

30-Oct-02 9.08 85 4.7 56 0.9 70 63 3.75

4-Feb-04 10.34 82 3.2 56 1.3 69 61 3.76

12-Dec-04 11.20 72 1.4 64 2.1 68 59 3.76

13-Aug-06 12.87 77 1.1 71 0.8 74 66 3.70

30-Dec-07 14.25 83 2.5 68 1.7 76 67 3.70

20-Sep-08 14.97 80 1.2 76 0.8 78 69 3.66

25-Jan-10 16.32 78 1.4 70 1.3 74 65 3.68

0219 

25-Jan-94 0.32 78 1.5 90 2.1 84 75 3.60

5-Mar-95 1.42 67 1.1 84 1.4 76 66 3.63

27-Jan-97 3.32 77 1.6 95 1.3 86 78 3.68

4-Dec-97 4.18 88 3.9 97 1.6 92 84 3.63

8-Dec-98 5.19 84 3.8 102 1.6 93 86 3.63

15-Nov-99 6.12 89 2.5 105 2.3 97 90 3.59

30-Nov-00 7.16 79 0.4 101 1.2 90 82 3.67

8-Nov-01 8.10 87 1.8 110 3.2 99 92 3.59

30-Oct-02 9.08 100 1.6 102 1.6 101 92 3.53

4-Feb-04 10.34 101 4.4 98 1.6 100 91 3.52

12-Dec-04 11.20 91 2.8 111 2.0 101 94 3.54

13-Aug-06 12.87 117 1.5 136 1.4 127 121 3.24

30-Dec-07 14.25 90 1.2 102 1.0 96 89 3.54

20-Sep-08 14.97 118 2.4 135 3.3 126 121 3.29

25-Jan-10 16.32 98 2.7 114 1.5 106 99 3.42

0220 

25-Jan-94 0.32 77 2.1 80 1.8 78 74 3.70

5-Mar-95 1.42 66 1.4 72 1.2 69 62 3.74

27-Jan-97 3.32 66 3.6 72 1.7 69 64 3.87

4-Dec-97 4.18 70 1.8 73 1.6 71 67 3.84

8-Dec-98 5.19 69 0.6 73 1.4 71 67 3.86

15-Nov-99 6.12 69 1.0 77 1.4 73 68 3.85

30-Nov-00 7.16 77 4.7 69 1.3 73 68 3.86

8-Nov-01 8.10 68 1.0 78 0.5 73 67 3.86

30-Oct-02 9.08 82 2.1 69 1.2 76 71 3.77

4-Feb-04 10.34 89 4.5 69 0.5 79 73 3.75

12-Dec-04 11.20 73 1.6 80 1.9 77 71 3.75

13-Aug-06 12.87 75 1.8 82 1.0 79 73 3.71

30-Dec-07 14.25 86 1.9 85 1.6 85 80 3.63

20-Sep-08 14.97 91 2.2 79 0.8 85 80 3.63

25-Jan-10 16.32 80 2.4 83 1.7 82 76 3.65
54 

Table 30. Roughness Values—Continued. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0221 

25-Jan-94 0.32 73 1.9 73 1.7 73 65 3.72

5-Mar-95 1.42 56 0.7 60 1.4 58 48 3.82

27-Jan-97 3.32 78 1.6 78 0.4 78 71 3.76

4-Dec-97 4.18 82 3.3 84 2.3 83 77 3.59

8-Dec-98 5.19 85 2.8 82 1.7 83 77 3.66

15-Nov-99 6.12 85 1.8 88 1.0 86 79 3.61

30-Nov-00 7.16 76 1.2 82 1.6 79 71 3.62

8-Nov-01 8.10 84 2.0 85 0.9 85 79 3.63

30-Oct-02 9.08 90 6.3 77 2.4 84 77 3.46

4-Feb-04 10.34 76 1.3 74 3.8 75 67 3.63

12-Dec-04 11.20 79 2.9 80 1.3 79 72 3.61

11-Aug-06 12.86 100 0.9 99 0.9 100 94 3.43

30-Dec-07 14.25 81 1.3 81 1.6 81 74 3.52

20-Sep-08 14.97 96 1.3 94 1.8 95 88 3.43

25-Jan-10 16.32 82 1.3 84 1.5 83 76 3.40

0222 

25-Jan-94 0.32 72 1.1 71 1.7 72 65 3.74

5-Mar-95 1.42 58 1.4 56 1.1 57 47 3.82

27-Jan-97 3.32 72 0.9 55 0.7 64 55 3.85

4-Dec-97 4.18 64 2.8 63 1.8 63 55 3.82

8-Dec-98 5.19 66 0.4 63 1.3 64 56 3.80

15-Nov-99 6.12 79 2.5 64 0.8 72 64 3.78

30-Nov-00 7.16 77 1.9 60 0.4 69 61 3.83

8-Nov-01 8.10 68 1.6 64 0.8 66 57 3.84

30-Oct-02 9.08 88 4.3 57 0.7 73 64 3.73

4-Feb-04 10.34 87 6.3 58 1.1 72 64 3.72

12-Dec-04 11.20 69 3.1 66 0.9 67 58 3.77

13-Aug-06 12.87 72 0.8 73 1.7 73 63 3.75

30-Dec-07 14.25 91 2.3 69 0.9 80 73 3.67

20-Sep-08 14.97 78 2.1 75 1.5 76 69 3.69

25-Jan-10 16.32 76 1.7 70 1.7 73 64 3.72

0223 

25-Jan-94 0.32 73 1.5 81 3.1 77 66 3.70

5-Mar-95 1.42 69 0.9 79 1.3 74 63 3.68

27-Jan-97 3.32 80 1.5 85 1.2 82 71 3.69

4-Dec-97 4.18 83 0.7 88 1.4 85 76 3.69

8-Dec-98 5.19 89 2.2 92 1.5 90 82 3.64

15-Nov-99 6.12 89 1.7 95 1.4 92 84 3.62

30-Nov-00 7.16 82 1.3 94 0.8 88 79 3.66

8-Nov-01 8.10 87 1.8 99 1.1 93 85 3.61

30-Oct-02 9.08 108 1.3 88 0.9 98 90 3.56

4-Feb-04 10.34 117 5.8 86 1.1 101 93 3.52

12-Dec-04 11.20 91 2.5 98 1.3 95 87 3.54

13-Aug-06 12.87 111 1.5 120 1.3 116 109 3.37

30-Dec-07 14.25 97 1.6 96 2.2 96 90 3.51

20-Sep-08 14.97 122 2.5 118 0.8 120 115 3.35

25-Jan-10 16.32 101 2.9 102 1.2 102 95 3.47
55 

Table 30. Roughness Values—Continued. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0224 

25-Jan-94 0.32 65 0.5 67 1.7 66 61 3.80

5-Mar-95 1.42 60 1.8 71 3.6 66 60 3.74

27-Jan-97 3.32 73 3.2 69 0.8 71 66 3.84

4-Dec-97 4.18 64 5.5 71 2.3 67 61 3.84

8-Dec-98 5.19 64 5.5 75 3.3 69 64 3.83

15-Nov-99 6.12 80 5.2 71 1.5 76 71 3.83

30-Nov-00 7.16 83 4.3 69 0.4 76 72 3.84

8-Nov-01 8.10 66 3.3 77 0.8 72 66 3.82

30-Oct-02 9.08 84 2.7 72 0.9 78 72 3.77

4-Feb-04 10.34 114 2.1 71 1.0 93 86 3.65

12-Dec-04 11.20 70 5.0 79 1.7 75 69 3.78

13-Aug-06 12.87 78 3.6 74 1.1 76 72 3.78

30-Dec-07 14.25 79 1.7 77 0.9 78 74 3.75

20-Sep-08 14.97 89 6.6 78 1.2 83 78 3.72

25-Jan-10 16.32 85 5.2 84 1.7 84 80 3.70

0260 

25-Jan-94 0.32 57 0.3 69 1.8 63 50 3.89

5-Mar-95 1.42 62 0.5 75 2.8 68 54 3.75

27-Jan-97 3.32 64 0.9 70 2.6 67 51 3.84

4-Dec-97 4.18 62 1.5 70 1.3 66 52 3.73

8-Dec-98 5.19 61 1.8 69 1.6 65 50 3.77

15-Nov-99 6.12 63 1.4 68 1.4 66 51 3.84

30-Nov-00 7.16 62 0.8 68 0.8 65 51 3.86

8-Nov-01 8.10 62 0.5 70 1.4 66 51 3.82

30-Oct-02 9.08 64 1.2 60 0.7 62 48 3.85

4-Feb-04 10.34 65 1.6 60 2.1 63 49 3.82

12-Dec-04 11.20 66 1.9 69 0.6 67 52 3.64

13-Aug-06 12.87 88 2.7 70 2.4 79 61 3.36

30-Dec-07 14.25 105 6.8 66 2.2 86 69 2.76

20-Sep-08 14.97 111 3.8 72 2.0 92 74 2.78

25-Jan-10 16.32 121 3.1 78 1.3 99 78 2.50

0261 

25-Jan-94 0.32 40 0.4 53 1.5 47 39 4.05

5-Mar-95 1.42 38 0.7 60 1.8 49 40 3.99

27-Jan-97 3.32 40 0.5 60 1.4 50 40 3.85

4-Dec-97 4.18 41 0.4 58 2.2 50 40 3.89

8-Dec-98 5.19 39 0.9 60 1.0 50 40 3.84

15-Nov-99 6.12 39 1.1 59 1.3 49 39 3.87

30-Nov-00 7.16 38 0.4 59 0.8 48 40 3.82

8-Nov-01 8.10 40 0.5 60 0.7 50 40 3.80

30-Oct-02 9.08 38 0.6 55 1.7 46 38 4.02

4-Feb-04 10.34 39 0.3 55 1.3 47 37 3.92

12-Dec-04 11.20 42 2.5 62 1.0 52 42 3.86

13-Aug-06 12.87 44 1.0 66 1.3 55 44 3.76

30-Dec-07 14.25 44 0.6 72 3.1 58 48 3.51

20-Sep-08 14.97 47 1.0 82 3.4 65 52 3.32

25-Jan-10 16.32 57 0.8 111 2.5 84 69 2.83
56 

Table 30. Roughness Values—Continued. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0262 

25-Jan-94 0.32 72 1.0 67 1.3 70 62 3.76

5-Mar-95 1.42 67 0.6 70 1.3 69 59 3.71

27-Jan-97 3.32 112 1.0 110 1.3 111 105 3.44

4-Dec-97 4.18 122 1.3 118 1.4 120 115 3.35

8-Dec-98 5.19 137 1.3 138 0.4 137 132 3.14

15-Nov-99 6.12 144 0.6 150 1.1 147 142 3.08

30-Nov-00 7.16 139 1.4 155 1.1 147 141 3.02

8-Nov-01 8.10 158 0.3 175 0.5 166 161 2.84

30-Oct-02 9.08 155 0.8 174 1.4 165 156 2.79

4-Feb-04 10.34 158 0.8 171 1.5 164 154 2.73

12-Dec-04 11.20 163 2.3 193 1.8 178 170 2.60

11-Aug-06 12.86 195 0.8 225 0.8 210 201 2.33

30-Dec-07 14.25 186 2.1 234 4.5 210 199 1.80

20-Sep-08 14.97 204 0.6 249 3.9 227 215 1.76

25-Jan-10 16.32 195 1.0 229 3.8 212 202 2.13

0263 

25-Jan-94 0.32 68 0.8 70 1.8 69 61 3.67

5-Mar-95 1.42 59 1.9 68 1.4 64 53 3.65

27-Jan-97 3.32 80 0.7 73 0.7 77 69 3.76

4-Dec-97 4.18 81 1.5 79 2.1 80 72 3.67

8-Dec-98 5.19 82 1.2 82 2.3 82 74 3.67

15-Nov-99 6.12 90 0.3 81 1.3 85 77 3.69

30-Nov-00 7.16 82 1.7 78 1.6 80 72 3.75

8-Nov-01 8.10 86 2.4 83 0.3 85 77 3.69

30-Oct-02 9.08 92 2.6 83 1.4 88 78 3.58

4-Feb-04 10.34 90 1.7 83 1.8 87 75 3.58

12-Dec-04 11.20 84 3.9 80 1.9 82 73 3.62

11-Aug-06 12.86 104 1.4 95 2.0 100 92 3.50

30-Dec-07 14.25 92 2.1 81 1.8 87 78 3.58

20-Sep-08 14.97 103 2.4 93 1.9 98 89 3.50

25-Jan-10 16.32 88 1.4 79 1.4 83 75 3.59

0264 

25-Jan-94 0.32 105 1.9 113 2.4 109 93 3.37

5-Mar-95 1.42 93 1.5 117 2.2 105 89 3.41

27-Jan-97 3.32 113 1.4 122 2.6 118 98 3.34

4-Dec-97 4.18 115 2.4 126 1.1 120 103 3.32

8-Dec-98 5.19 114 2.1 133 1.7 123 106 3.30

15-Nov-99 6.12 121 1.8 130 2.5 126 108 3.27

30-Nov-00 7.16 119 0.7 129 2.7 124 107 3.28

8-Nov-01 8.10 119 1.6 140 3.2 129 113 3.26

30-Oct-02 9.08 122 4.7 125 1.0 123 108 3.26

4-Feb-04 10.34 121 5.3 123 3.5 122 107 3.26

12-Dec-04 11.20 123 4.7 135 4.4 129 114 3.19

13-Aug-06 12.87 140 1.5 141 0.5 141 126 3.10

30-Dec-07 14.25 135 1.6 132 2.7 134 119 3.12

20-Sep-08 14.97 150 1.7 148 1.5 149 135 3.04

25-Jan-10 16.32 128 3.6 144 3.5 136 122 3.13
57 

Table 30. Roughness Values—Continued. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0265 

25-Jan-94 0.32 84 2.1 89 2.3 86 72 3.55

5-Mar-95 1.42 81 2.0 96 2.1 89 73 3.50

27-Jan-97 3.32 96 1.9 106 0.7 101 88 3.44

4-Dec-97 4.18 99 2.6 115 3.2 107 94 3.37

8-Dec-98 5.19 107 2.0 123 2.1 115 104 3.27

15-Nov-99 6.12 109 1.4 128 1.0 118 106 3.29

30-Nov-00 7.16 107 0.7 133 0.7 120 109 3.21

8-Nov-01 8.10 118 1.6 146 0.5 132 122 3.11

30-Oct-02 9.08 114 2.3 141 0.8 127 114 3.12

4-Feb-04 10.34 112 2.1 145 3.5 129 116 3.05

12-Dec-04 11.20 114 2.0 156 3.8 135 125 2.97

13-Aug-06 12.87 136 1.4 168 1.4 152 143 2.90

30-Dec-07 14.25 123 1.0 168 1.4 146 134 2.82

20-Sep-08 14.97 143 1.6 182 1.5 163 154 2.79

25-Jan-10 16.32 133 1.1 180 0.6 156 145 2.75

0266 

25-Jan-94 0.32 82 1.2 93 1.8 87 78 3.54

5-Mar-95 1.42 79 1.1 95 2.4 87 78 3.57

27-Jan-97 3.32 87 1.5 94 0.4 90 79 3.65

4-Dec-97 4.18 88 1.5 100 3.2 94 86 3.63

8-Dec-98 5.19 91 1.6 102 0.5 97 89 3.60

15-Nov-99 6.12 95 3.5 104 0.8 99 89 3.58

30-Nov-00 7.16 89 0.7 101 0.7 95 87 3.62

8-Nov-01 8.10 99 1.1 110 1.0 105 97 3.53

30-Oct-02 9.08 118 5.2 108 0.9 113 104 3.39

4-Feb-04 10.34 104 1.0 103 0.9 103 93 3.44

12-Dec-04 11.20 98 1.9 109 2.1 103 96 3.47

13-Aug-06 12.87 122 3.5 125 1.9 123 116 3.28

30-Dec-07 14.25 114 1.6 109 1.1 111 102 3.35

20-Sep-08 14.97 133 0.6 129 0.8 131 123 3.21

25-Jan-10 16.32 106 1.7 112 1.1 109 102 3.39

0267 

25-Jan-94 0.32 80 1.7 106 2.0 93 78 3.39

5-Mar-95 1.42 79 0.9 112 4.2 95 79 3.38

27-Jan-97 3.32 75 2.2 106 1.4 90 75 3.61

4-Dec-97 4.18 83 5.4 113 3.0 98 83 3.52

8-Dec-98 5.19 82 1.8 115 1.7 99 84 3.49

15-Nov-99 6.12 78 0.8 114 1.9 96 83 3.57

30-Nov-00 7.16 76 0.3 111 1.0 94 82 3.56

8-Nov-01 8.10 86 2.7 120 1.8 103 90 3.44

30-Oct-02 9.08 92 6.2 110 2.7 101 86 3.44

4-Feb-04 10.34 86 1.0 104 1.1 95 82 3.45

12-Dec-04 11.20 88 1.6 114 1.4 101 89 3.40

13-Aug-06 12.87 98 1.8 110 1.9 104 92 3.29

30-Dec-07 14.25 81 1.2 84 1.2 82 71 3.53

20-Sep-08 14.97 92 1.5 101 1.5 97 87 3.42

25-Jan-10 16.32 77 2.0 91 1.7 84 74 3.45
58 

Table 30. Roughness Values—Continued. 

Section Date Years 

Left IRI 

(inches/mi) 

Right IRI 

(inches/mi) 

MRI 

(inches/

mi) 

HRI 

(inches/

Average SD Average SD mi) RN 

0268 

25-Jan-94 0.32 85 2.0 94 0.5 89 73 3.39 

5-Mar-95 1.42 80 1.5 96 3.7 88 72 3.36 

27-Jan-97 3.32 91 1.2 92 1.2 91 75 3.53 

4-Dec-97 4.18 89 3.9 95 2.5 92 76 3.48 

8-Dec-98 5.19 93 3.2 98 3.0 95 79 3.45 

15-Nov-99 6.12 94 1.6 98 1.6 96 79 3.52 

30-Nov-00 7.16 92 0.5 97 1.9 95 78 3.48 

8-Nov-01 8.10 97 1.1 104 2.1 101 84 3.42 

30-Oct-02 9.08 102 4.7 96 2.8 99 84 3.40 

4-Feb-04 10.34 99 0.6 91 1.9 95 80 3.39 

12-Dec-04 11.20 97 3.5 98 2.1 97 80 3.35 

13-Aug-06 12.87 116 0.6 112 2.1 114 100 3.26 

30-Dec-07 14.25 99 2.2 94 1.3 97 80 3.40 

20-Sep-08 14.97 106 3.2 107 2.4 107 93 3.32 

25-Jan-10 16.32 94 2.1 100 0.8 97 80 3.33 

SD = Standard deviation 

© ADOT 

Figure 26. Graph. IRI Progression for Section 0213. 

Right

Left

Section 0213

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
59 

© ADOT 

Figure 27. Graph. IRI Progression for Section 0214. 

© ADOT 

Figure 28. Graph. IRI Progression for Section 0215. 

Right

Left

Section 0214

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0215

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
60 

© ADOT 

Figure 29. Graph. IRI Progression for Section 0216. 

© ADOT 

Figure 30. Graph. IRI Progression for Section 0217. 

Right

Left

Section 0216

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0217

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
61 

© ADOT 

Figure 31. Graph. IRI Progression for Section 0218. 

© ADOT 

Figure 32. Graph. IRI Progression for Section 0219. 

Right

Left

Section 0218

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0219

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
62 

© ADOT 

Figure 33. Graph. IRI Progression for Section 0220. 

© ADOT 

Figure 34. Graph. IRI Progression for Section 0221. 

Right

Left

Section 0220

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0221

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
63 

© ADOT 

Figure 35. Graph. IRI Progression for Section 0222. 

© ADOT 

Figure 36. Graph. IRI Progression for Section 0223. 

Right

Left

Section 0222

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0223

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
64 

© ADOT 

Figure 37. Graph. IRI Progression for Section 0224. 

© ADOT 

Figure 38. Graph. IRI Progression for Section 0260. 

Right

Left

Section 0224

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0260

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
65 

© ADOT 

Figure 39. Graph. IRI Progression for Section 0261. 

© ADOT 

Figure 40. Graph. IRI Progression for Section 0262. 

Right

Left

Section 0261

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0262

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Time (years)
66 

© ADOT 

Figure 41. Graph. IRI Progression for Section 0263. 

© ADOT 

Figure 42. Graph. IRI Progression for Section 0264. 

Right

Left

Section 0263

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0264

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
67 

© ADOT 

Figure 43. Graph. IRI Progression for Section 0265. 

© ADOT 

Figure 44. Graph. IRI Progression for Section 0266. 

Right

Left

Section 0265

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0266

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
68 

© ADOT 

Figure 45. Graph. IRI Progression for Section 0267. 

© ADOT 

Figure 46. Graph. IRI Progression for Section 0268. 

Right

Left

Section 0267

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Right

Left

Section 0268

Time (years)

IRI (in/mi)

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18
69 

APPENDIX D. TRADITIONAL PROFILE ANALYSES 

This appendix provides findings from traditional profile analyses applied to the LTPP SPS-2 site in 

Arizona. These tools helped study roughness, roughness distribution, and roughness progression of 

each section, including concentrated roughness-linked pavement distress. The analyses included 

viewing filtered elevation profile plots, roughness profiles, and power spectral density (PSD) plots. 

Sayers provides tutorial demonstrations of these methods.(15,16) Karamihas and Senn applied them 

to other SPS sites in Arizona. (See references 3–7.) 

This appendix discusses observations pertinent to IRI but only on those sections where the analyses 

yielded noteworthy observations. Section 0213 exhibited several features of interest and is used 

to provide detailed examples of phenomena that appeared on other sections. 

SECTION 0213 

A simple way to learn about the type of roughness that exists within a profile is to view the trace. 

However, key details of the profile are often not as obvious in a raw profile trace as they may be 

after the profile is filtered. Figure 47 shows the right-side profile of section 0213 from visit 03 

(27-Jan-1997). Several features are evident from this plot, but they are much more obvious when 

plotted with filters. 

Figure 47. Graph. Raw Profile from Visit 03 of Right Side of Section 0213. 

Figure 48 through figure 50 show the profile from figure 47 after application of various moving 

average filters. Each of the filters helps examine a distinct feature of the roughness on section 0213. 

0 100 200 300 400 500

Distance (feet)

-1

-.5

0

.5

Right Elevation (inches)
70 

Figure 48. Graph. Profile with Smoothing from Visit 03 of Right Side of Section 0213. 

Figure 49. Graph. Profile with Anti-Smoothing from Visit 03 of Right Side of Section 0213. 

Figure 50. Graph. Profile with Additional Anti-Smoothing from Visit 03 of Right Side 

of Section 0213. 

Figure 48 shows the profile after application of a smoothing filter with a base length of 25 ft. The 

filter greatly reduces the contribution of deviations that occur over 25 ft and shorter but preserves the 

trend. This plot shows a long bump followed by a long dip within the profile. This feature appears on 

both the left and right profiles throughout the monitoring history of section 0213, and it consistently 

smoothing, 25-foot base length

-.5

0

.5

Right Elevation (inches)

0 100 200 300 400 500

Distance (feet)

-.2

-.1

0

.1

.2

anti-smoothing, 25-foot base length

0 100 200 300 400 500

Distance (feet)

Right Elevation (inches)

0 100 200 300 400 500

Distance (feet)

anti-smoothing, 0.82-foot base length

-.1

-.05

0

.05
71 

contributes to the overall IRI of the section. Together, the bump and dip make up a feature so 

long that the native filters applied to the profile during measurement affect their shape, although 

the native filters preserve the roughness that most affects IRI. For example, the largest change in 

this plot occurred between visit 08 (8-Nov-2001) and 09 (30-Oct-2002), when the high-pass filter 

applied by the profiler had changed.(17)

Figure 49 shows the profile after application of an anti-smoothing filter with a base length of 25 ft. 

This filter greatly reduces the contribution of deviations that occur over 25 ft and longer, which 

eliminates the trend and makes the upward curl in the 15-ft-long slabs more obvious.1 In this plot, 

local peaks appear 15 ft apart, beginning about 9 ft from the start of the section and ending about 

489 ft from the start of the section. These peaks represent the joints that surround the 32 slabs. Even 

though the vertical scale is much smaller in figure 49 than in figure 48, the contribution to IRI 

is much larger. For example, IRI of the trace in figure 49 is 104.7 inches/mi, and IRI of the trace 

in figure 48 is 26.6 inches/mi. Although the trace in figure 48 covers a larger vertical scale, the 

rapid reversals in the trace in figure 49 create greater roughness. 

Figure 50 shows the profile after application of an anti-smoothing filter with a base length of 0.82 ft. 

Again, eliminating the longer wavelength content reduces the vertical range of the plot. This filter 

eliminates nearly all the content that affects IRI but retains the narrow dips that appear at the joints. 

Inspection of filtered elevation profiles showed that upward slab curl existed throughout the 

monitoring history of section 0213 and that the level of curl was not consistent. Figure 51 shows 

part of the left-side profile traces from visits 12 (13-Aug-2006) and 13 (30-Dec-2007). The figure 

shows a distinct set of upwardly curled slabs. The figure also shows that the extent of curling at 

each slab is greater in visit 12 than in visit 13. The level of curl that appears on a pavement section 

is determined by a combination of diurnal, seasonal, and long-term effects. However, a change in 

temperature gradient may explain the difference in the profiles, since visit 12 took place before 

sunrise and visit 13 took place after sunrise. 

Figure 51. Graph. Changes in Curl on Section 0213. 

 1

 Distortion of jointed concrete pavement slabs includes curling, which is typically associated with cyclic thermal gradients; warping, which 

is typically associated with cyclic and long-term changes in moisture gradient; and a small portion of built-in unevenness. In this appendix, the 

term curl is used as shorthand for all three sources of slab distortion. 

400 420 440 460 480 500

Distance (feet)

Left Elevation (inches)

11-Aug-2006

30-Dec-2007

-.2

-.1

0

.1

.2
72 

Over the 100 ft displayed in figure 51, IRI for visit 12 (13-Aug-2006) was 132.0 inches/mi, and IRI 

for visit 13 (30-Dec-2007) was 106.0 inches/mi. Over the entire section, the difference in IRI was 

25.6 inches/mi, which demonstrates the influence a visually modest change in the curling within a 

profile can have on the roughness of a pavement section (see figure 10 and figure 11). 

A PSD plot provides an alternative way of comparing the severity of slab curl within a profile. 

Figure 52 shows a PSD plot for the two profiles in figure 51. The plot is modified to show PSD 

of profile slope, rather than elevation, and it uses wavelength as the ordinate axis, instead of wave 

number (the reciprocal of wavelength). The plot displays spectral density in 24 bands per octave 

(i.e., 24 values for each increase in wavelength by a factor of 2, with uniform spacing along a 

logarithmic scale). The PSD plots for both visits include peaks at wavelengths of 15, 7.5, and 5 ft. 

The peak at 15 ft corresponds to the slab length. Additional peaks appear at 7.5 and 5 ft because 

the slabs do not curl into a sinusoidal profile. Instead, they curl into a shape that breaks down into 

an infinite series of sine waves that are as long as the slab, half as long, a third as long, and so on. 

Figure 52. Graph. Slope Spectral Density of Section 0213. 

Figure 52 displays the spectral content of the profile in a convenient manner in that values on the 

ordinate axis map directly to the characteristic length of known pavement features, such as joint 

spacing. The figure also shows that the influence of curling on variations in profile slope stands 

out over other profile features. However, the non-standard method of display in figure 52 distorts 

the relative contribution of each waveband to the overall profile. 

Figure 53 provides a more standard display of PSD. The figure displays both axes on a linear scale 

and provides spectral density versus wave number. When the plots are displayed in this manner, 

the area under the curve for any range of wave numbers is proportional to the contribution the 

range makes to the overall mean square. Over the range that affects IRI, shown in figure 53, 

slab curl dominates the roughness of the section in both visits. Figure 53 also provides a more 

2 5 10 2 5 100

Wavelength (feet)

0.1x10-7

0.1x10-6

0.1x10-5

0.1x10-4

0.1x10-3

0.1x10-2

PSD of Left Slope (feet/cycle)

11-Aug-2006

30-Dec-2007
73 

representative view of the difference between visit 12 (11-Aug-2006) and visit 13 (30-Dec-2007). 

At a wave number of 0.066 cycles/ft, which corresponds to a wavelength of 15 ft, the plot for 

visit 12 has a value of 0.00125 ft/cycle and the plot for visit 13 has a value of 0.00076 ft/cycle. In 

terms of root mean square, this waveband therefore accounts for 28 percent more roughness in 

visit 12 than in visit 13. 

Figure 53. Graph. Slope Spectral Density of Section 0213 with Linear Scaling. 

Section 0213 developed distress in the later part of the monitoring history. Starting in visit 12 

(11-Aug-2006), narrow dips and groups of densely spaced narrow dips appeared in the right-side 

profiles. The right-side profiles from visit 12 included narrow dips at 35–47, 143–160, 243–246, 255, 

and 317–330 ft from the start of the section. These areas correspond to locations where the distress 

survey showed longitudinal cracking starting in 2004. Starting in 2008, longitudinal cracks appeared 

either in or near the right wheel path over the first two-thirds of the section. The cracks grew in 

width from 2008 onward, and some include missing material replaced by asphalt by 2011. Typically, 

the dips within the profile appear where the cracks wander into the center of the wheel path. 

Figure 54 shows three repeat profiles from the right side of section 0213. The area from 143 to 

160 ft includes several deep dips. The most severe features in this area appear with the same 

shape in all three measurements. However, some details of the profiles in this area are not 

perfectly repeated because they are caused by longitudinal cracks. 

0 .1 .2 .3

Wave Number (cycles/foot)

PSD of Left Slope (feet/cycle) 11-Aug-2006

30-Dec-2007

0

0.5x10-3

0.1x10-2

0.15x10-2
74 

Figure 54. Graph. Right Elevation Profile for Three Repeats from Visit 12 of Section 0213. 

A roughness profile provides a way to quantify the severity of isolated disturbances in a profile, such 

as the dips shown in figure 54. A roughness profile provides a continuous report of road roughness 

using a given segment length.(18) Instead of summarizing the roughness by providing IRI for an 

entire pavement section, the roughness profile shows the details of how IRI varies with distance 

along the section. It does this by displaying IRI of every possible segment of a given base length 

along the pavement, using a sliding window. Figure 55 shows the roughness profile using a 25-ft 

base length for the profiles shown in figure 54. With a 25-ft base length, isolated roughness is easy 

to identify and the area with the narrow dips stands out as much rougher than the surrounding area. 

The peak value in this area was about 600–700 inches/mi. Since this 25-ft-long area accounts for 

one-twentieth of the section length, this area contributes 30–35 inches/mi to the overall IRI of the 

section for these repeat measurements. 

Figure 55. Graph. Right Roughness Profile for Three Repeats from Visit 12 of Section 0213. 

One of the repeat measurements shown in figure 55 also includes an area of higher roughness 

about 250 ft from the start of the section. This is another patch of dips on a longitudinal crack 

that only one pass detected due to small variations in the tracking position of the profiler. 

120 130 140 150 160 170 180

Distance (feet)

-2

-1.5

-1

-.5

0

.5

Right Elevation (inches)

0 100 200 300 400 500

Distance (feet)

0

200

400

600

800

Right Roughness Profile (in/mi)

repeat 1

repeat 4

repeat 5
75 

Inspection of roughness profiles showed that narrow dips at longitudinal cracks account for 

much of the increase in roughness after visit 11 (12-Dec-2004), although the dips were less 

severe overall in visit 13 than in visit 12. By visit 15 (25-Jan-2010), two additional areas of 

isolated roughness appeared along with the area shown in figure 55. 

SECTION 0214 

Section 0214 profiles included evidence of upward curl in early visits. However, the slabs in the 

first half of the section gradually changed from upward curl to downward curl, and the upward curl 

in the second half of the section diminished over time. The slabs changed most aggressively between 

visit 04 (4-Dec-1997) and visit 10 (4-Feb-2004). Figure 56 shows the right-side profile from visit 

01 (25-Jan-1994), and figure 57 shows right-side profiles from visit 10 over part of section 0214. 

In this part of the section, all of the slabs changed from upward to downward curl. 

Figure 56. Graph. Right Elevation Profiles from Visit 01 of Section 0214. 

Figure 57. Graph. Right Elevation Profiles from Visit 10 of Section 0214. 

Distress surveys noted map cracking on the section starting in 1997. The 1997 survey listed 

low-severity map cracking throughout the section. By 2008, the distress surveys listed high-severity 

map cracking in the first part of the section and map cracking in the wheel paths throughout the 

section. The 2008 distress survey also noted a rough transition from asphalt to concrete pavement 

upstream of section 0214 and proposed that the resulting dynamic loads imposed on section 0214 

may have contributed to the cracking. Figure 58 shows the profile leading to section 0214 in 

Right Elevation (inches)

-.1

0

.1 25-Jan-1994

0 20 40 60 80 100 120

Distance (feet)

0 20 40 60 80 100 120

Distance (feet)

-.3

-.2

-.1

0

.1

04-Feb-2004

Right Elevation (inches)
76 

visit 09 (30-Oct-2002). The figure shows a distance of 0 ft at the section start. The rough features 

60–80 ft upstream of the section would exacerbate truck dynamic loading. However, the role of 

dynamic loading in causing the map cracking is not clear. 

Figure 58. Graph. Profiles Leading to Section 0214. 

SECTION 0215 

Profile data for section 0215 included measurements on 16 additional SMP dates. On those dates, 

profiles were collected early (typically in the morning) and late (typically in the afternoon). Together 

with the 15 routine visits, the data include 47 sets of repeat measurements, with measurements 

every season in 1998 and from winter 2001 through winter 2004. Plotting of filtered profiles and 

PSD functions revealed that changes in slab curl caused most of the changes in the roughness of 

section 0215 over time. 

Figure 59 shows the PSD plot for profiles measured in visits S05 (9-Jul-1998, 08:45) and S30 

(15-Jul-2004, 09:07). The spectral content for these two profiles is very similar. In addition, the 

roughness level is about equal over the range shown in the figure, except at wavelengths equal to 

the slab length (15 ft) and half the slab length (7.5 ft). IRI for the earlier profile was 93.6 inches/mi, 

and IRI for the later profile was 129.4 inches/mi. Figure 59 shows that changes in slab curl caused 

most of the difference (see figure 12 and figure 13). 

-100 -80 -60 -40 -20 0

Distance (feet)

-.5

0

.5

1

1.5

Elevation (inches)

left

right
77 

Figure 59. Graph. PSD Plots for Section 0215. 

PSD plots of profiles from the 47 visits showed the following: 

 The overall level of slab curl exhibited an increasing trend over time, but the trend was 

not orderly. 

 The overall level of curl was higher in visits 12 (13-Aug-2006) and 14 (20-Sep-2008) 

than in visits 11 (12-Dec-2004), 13 (30-Dec-2007), and 15 (25-Jan-2010). Visits 12 and 14 

occurred shortly after midnight, and visits 11, 13, and 15 occurred after sunrise. 

 In many of the paired seasonal visits from the same date, the level of curl was higher in 

the early set of passes than on the following set of passes. This occurred in visits S01–S20, 

S27, and S28 but not in visits S21–S26, S29, and S30. 

 Variations in IRI between visits followed the same trend as the severity of the peak value 

in the PSD plot at a wavelength of 15 ft. 

SECTION 0216 

No specific observations are provided for section 0216. 

SECTION 0217 

The 1997 distress survey recorded longitudinal and transverse cracks, and the level of cracking 

increased throughout the monitoring period. The 2002 distress survey also listed “map cracking 

throughout (the) section.” 

0.1x10-6

0.1x10-5

0.1x10-4

0.1x10-3

0.1x10-2

09-Jul-1998

15-Jul-2004

2 5 10 2 5 100

Wavelength (feet)

PSD of Left Slope (feet/cycle)
78 

Narrow dips appeared in both the left and right profiles at positions in the middle third of 

some slabs starting in visit 09 (30-Oct-2002). The dips appeared in locations where the distress 

surveys included transverse cracks, although not every transverse crack caused a dip. In visit 15 

(25-Jan-2010), the most severe dips appeared 30 ft (0–1.3 inches deep), 407 ft (0–0.9 inches deep), 

466.5 ft (0–0.15 inches deep), and 481.5 ft (0–0.6 inches deep) from the start of the section in the 

left-side profiles and 42–45 ft (0–0.7 inches deep), 238 ft (0–0.4 inches deep), 450 ft (0–1.3 inches 

deep), and 478 ft (0–1.6 inches deep) from the start of the section in the right-side profiles. The 

construction report listed transverse cracking in the LCB 480 ft from the start of section 0217 but 

not at the other locations.(1) Inspection of roughness profiles showed that none of the dips caused 

the short (25-ft)-interval IRI to exceed 2.5 times the section average. 

Throughout the monitoring history, one slab along the right side of section 0217 contributed twice 

as much to the roughness of the section as the others. Figure 60 shows the right-side profiles from 

visit 01 (25-Jan-1994) and visit 14 (20-Sep-2008). Joints appear within the plot 444.3, 459.2, 

474.2, and 489.3 ft from the start of the section. The slab that extends from 459.2 to 474.2 ft has 

upward curvature that registers as upward curling to an automated curling analysis based solely on 

slab profile. However, the upward curvature of this slab may have another cause because (1) no 

other slab on section 0217 exhibited a similar level of curvature, (2) the overall curvature of 

this profile along this slab did not change significantly with time, and (3) the left side profiles 

were relatively flat. The cause of the upward curvature cannot be determined without additional 

information, and the curling analyses presented in this report depend more heavily on changes in 

slab shape with time than on the nominal profiles. 

Figure 60. Graph. Right Elevation Profiles for Section 0217. 

Profiles from section 0217 included noteworthy spectral content not caused by slab curl. Figure 61 

shows the PSD plot for the left profile from visit 08 (8-Nov-2001). Slab curl caused the spikes at 15, 

7.5, and 5 ft. Another spike appears at about 33 ft that rivals the others in amplitude. The contractor 

who built the test pavements confirmed that this was the approximate string line stake spacing. 

Content at this wavelength was strongest on section 0217, but lesser peaks appear in PSD plots 

from sections 0214, 0215, 0216, 0218, and 0220. 

440 450 460 470 480 490 500

Distance (feet)

-.3

-.2

-.1

0

.1

.2

Right Elevation (inches)

20-Sep-2008

25-Jan-1994
79 

Figure 61. Graph. PSD Plots from Visit 08 of Section 0217. 

SECTION 0218 

The construction report listed 11 transverse cracks in the LCB within the monitoring range of 

section 0218.(1) Plotting of filtered profiles revealed no localized roughness and no systematic 

appearance of cracks in the surface layer. 

SECTION 0219 

Transverse cracks appeared in mid-slab positions on section 0219 beginning in 2002 and on about 

half of the slabs by the end of the monitoring period. The profiles included narrow dips at some 

of these locations, particularly on the right side, starting in visit 09 (30-Oct-2002). By visit 15 

(25-Jan-2010) narrow dips appeared intermittently in the right-side profiles 195 ft (0–0.15 inches 

deep), 258 ft (0–0.2 inches deep), 316 ft (0–0.9 inches deep), 384 ft (0–0.3 inches deep), 406 ft 

(0–0.8 inches deep), and 466 ft (0–0.4 inches deep) from the start of the section. Distress surveys 

also noted map cracking over most of section 0219 by the end of the monitoring period, but the 

cracking was less obvious in the photos than on other sections. 

SECTION 0220 

Profiles from visit 04 (4-Dec-1997) included densely spaced positive and negative spikes at some 

joint locations on section 0220. Figure 62 shows an example. Similar disturbances appeared in the 

right-side profiles at the joints about 70, 115, 175, 220, 325, 384, 430, and 474 ft from the start of 

the section. These disturbances typically appeared in only one or two of the repeat measurements 

in visit 04 and sparingly in profiles from visit 05 (8-Dec-1998) but not in any of the other visits. 

They did not correspond to anything noted in the distress survey, although a distress survey in 

2003 noted seal damage at joints. The construction report listed 13 transverse cracks in the LCB 

left

right

2 5 10 2 5 100

Wavelength (feet)

0.1x10-7

0.1x10-6

0.1x10-5

0.1x10-4

0.1x10-3

Slope PSD (feet/cycle) ~33 feet
80 

within the monitoring range of section 0220.(1) Plotting of filtered profiles revealed no localized 

roughness and no systematic appearance of cracks on the surface. 

Figure 62. Graph. Profile from Visit 04 of Section 0220. 

SECTION 0221 

Distress surveys listed distress in the right wheel path of a slab from 410 to 425 ft from the 

start of section 0221 throughout the monitoring history and distress in neighboring slabs later in 

the monitoring period. In 1997, the survey noted “severe aggregate loss.” Every survey afterward 

showed scaling along the right side of that slab, and the survey in 2008 (including the photos) 

showed fiberglass patching at various locations. Figure 63 shows five repeat measurements of 

the right-side profile from visit 15 (25-Jan-2010). The dip 421 ft from the start of the section caused 

localized roughness, and the slab from 410 to 425 ft from the start of the section contributed to IRI 

3 times as aggressively as the rest of the section. 

Figure 63. Graph. Right Elevation Profile for Five Repeats from Visit 15 of Section 0221. 

260 270 280 290 300

Distance (feet)

-.2

-.1

0

.1

.2

.3

Right Elevation (inches)

400 410 420 430 440

Distance (feet)

-1.5

-1

-.5

0

.5

Right Elevation (inches)
81 

SECTION 0222 

Some profiles from visit 14 (20-Sep-2008) and visit 15 (25-Jan-2010) included a narrow dip up 

to 0.7 inches deep at a joint 325 ft from the start of section 0222. Nothing in the distress surveys 

distinguished this joint from the others, and the dips did not increase the roughness of the section. 

SECTION 0223 

No specific observations are provided for section 0223. 

SECTION 0224 

The left IRI value from visit 10 (4-Feb-2004) on section 0224 was 114 inches/mi. This value 

stood out because the right IRI was 71 inches/mi, the left IRI from visit 09 (30-Oct-2002) was 

84 inches/mi, and the left IRI from visit 11 (12-Dec-2004) was 70 inches/mi (see figure 12). As 

shown in figure 64, a change in spectral content for wavelengths near 8 ft accounts for most of 

the difference. Although no other obvious explanation could be found, this content is most likely 

not caused by changes in slab curl, since it only appears on the left side of the lane. The content 

within the PSD plot at a 15-ft wavelength was not affected strongly, and the high content for 

wavelengths near 8 ft is not as concentrated as the upper harmonics caused by slab curl in the 

PSD plots shown for other sections. Furthermore, the peaks and valleys of the approximately 

8-ft-long waves do not align with the joint locations in a consistent manner. 

Figure 64. Graph. PSD of Left Slope for Section 0224. 

2 5 10 2 5 100

Wavelength (feet)

0.1x10-7

0.1x10-6

0.1x10-5

0.1x10-4

0.1x10-3

PSD of Left Slope (feet/cycle) 04-Feb-2004

12-Dec-2004
82 

SECTION 0260 

The distress surveys reported low-severity raveling on section 0260 starting in 1995 and raveling 

with no severity qualification in both wheel paths starting in 2004. By 2008, the distress surveys 

reported significant distress in the left wheel path, and the photos showed fatigue, small potholes, 

patching, and pools of sealant in the left wheel path. The distress increased in severity by 2010, 

including more visible cracking along the left wheel path. These observations explain the steady 

rise in IRI of the left wheel path starting 11 years after the experiment began. 

Some areas within the profile showed clear evidence of surface distress. For example, the area from 

50 to 70 ft from the start of the section often included patches of narrow dips. The dips appeared 

starting in visit 06 (15-Nov-1999) on the left side and in visit 11 (12-Dec-2004) on the right side. 

The dips were not well repeated when they first appeared. However, by the end of the monitoring 

period, the profile over this segment had a consistent shape, which included a narrow dip 

0.7 inches deep and a 3-ft-wide dip that was nearly 0.2 inches deep. 

A rough area present since construction exists about 350 ft from the start of the section. Figure 65 

shows the roughness profile at various ages, starting with the first profiling visit. The plot uses a 25-ft 

base length. The rough area progressed from a peak value of 118 inches/mi in visit 01 (25-Jan-1994) 

to 735 inches/mi by visit 15 (25-Jan-2010). Since the base length is equal to one-twentieth of the 

section length, this represents a progression in the contribution to overall IRI of the roughest area 

from 5.9 inches/mi to more than 36 inches/mi. 

Figure 65. Graph. Left Roughness Profile for Section 0260. 

Figure 66 shows profiles from visits 01 (25-Jan-1994) and 15 (25-Jan-2010). The initial disturbance 

is visible in the plot, although distress was not recorded there until 2000. However, it is not clear 

if the initial disturbance caused the roughness to progress by increasing the loading experienced at 

certain locations (i.e., a hot spot), if the disturbance was evidence of structural defects at that location 

(i.e., a weak spot), or both. In either case, figure 65 shows that the roughest area within section 0260 

at the start of its service life progressed to the roughest area much later in its service life. (The peak 

value would stand out in the plot from visit 01 if not for the large vertical scale needed to 

accommodate the roughness in later visits.) 

25-Jan-1994

08-Nov-2001

11-Aug-2006

25-Jan-2010

0 100 200 300 400 500

Distance (feet)

0

200

400

600

800

Left Roughness Profile (in/mi)
83 

Figure 66. Graph. Left Elevation Profile for a Segment from Section 0260. 

SECTION 0261 

Distress surveys recorded longitudinal cracking in some areas of section 0261 starting in 1997 and 

transverse cracking at several locations after 2004. Dips appeared as depressions up to 5 ft wide 

with a narrow dip up to 1 ft wide in the majority of locations where the 2008 (and later) distress 

surveys showed transverse cracking. These dips appeared in the profiles starting with visit 11 

(12-Dec-2004), and they were prominent late in the experiment. The dips exacerbated the roughness 

progression. Late in the experiment, localized roughness appeared about 325 ft from the start of 

the section, where a pothole developed. 

The 1997 distress survey recorded the presence of six cores along the right wheel path near the 

end of the section. A longitudinal crack developed along the line of cores. This area was sealed, 

but the sealant eventually wore off. A series of bumps and dips appeared in the right-side profiles 

at that location that grew in roughness throughout the monitoring history. 

SECTION 0262 

Section 0262 faulted. Filtered profile plots showed that the faulting grew steadily throughout 

the experiment. Figure 67 shows five repeat profile measurements from a portion of section 0262 

in visit 15 (25-Jan-2010). The figure shows a consistent level of faulting along the section and 

among the repeat measurements. Faulting caused much of the roughness and its progression on 

section 0262. Figure 68 shows a very short (8-ft)-interval roughness profile for the same set of 

measurements covered in figure 67. The figure shows the average contribution to IRI of each 

8-ft-long segment as a function of the segment midpoint. The figure demonstrates that 

contributions to overall IRI of the section built up most aggressively at the joints. 

25-Jan-1994

25-Jan-2010

300 320 340 360 380 400

Distance (feet)

-.8

-.6

-.4

-.2

0

.2

.4

Left Elevation (inches)
84 

Figure 67. Graph. Left Elevation Profile from Visit 15 of Section 0262. 

Figure 68. Graph. Left Roughness Profile from Visit 15 of Section 0262. 

Starting in visit 12 (11-Aug-2006), the right-side profiles from section 0262 included a narrow dip 

at the joint 83 ft from the start of the section and a swatch of narrow dips over a half-slab from 129 to 

137 ft from the start of the section. Both of these features appeared in areas where distress surveys 

recorded longitudinal cracking. The roughness at joints caused by the faulting obscured the 

roughness of these dips. 

SECTION 0263 

Section 0263 developed very little faulting relative to the other test sections without dowels 

(0262, 0264, and 0265). In contrast, elevation profile plots showed a high level of slab curl. 

200 250 300 350 400

Distance (feet)

-.2

-.1

0

.1

.2

.3

Left Elevation (inches)

200 250 300 350 400

Distance (feet)

0

100

200

300

400

Left Roughness Profile (in/mi)
85 

SECTION 0264 

All profiles from the right side of section 0264 included a rise in elevation of more than 0.5 inches 

over a 7-ft distance starting 164 ft from the start of the section. The area that included this builtin feature was the roughest of the section throughout the experiment. 

SECTION 0265 

Section 0265 faulted. Filtered profile plots showed that the faulting grew steadily throughout the 

experiment. Like section 0262, faulting on section 0265 caused a large portion of the roughness 

progression. Figure 69 shows the roughness profile for section 0265 at various stages of the 

experiment. In this case, the roughness profile is plotted using a base length of 100 ft. Thus, every 

point along the plot represents IRI of a segment of pavement that starts 50 ft upstream and ends 

50 ft downstream of that location. The 100-ft base length helps show the distribution of roughness 

throughout the section, but it is long enough to avoid local peaks caused by a single slab or joint. 

Figure 69. Graph. Right Roughness Profile for Section 0265. 

Figure 69 demonstrates that in later visits roughness was distributed evenly along the section. 

This is because the magnitude of faulting was relatively consistent. The figure also demonstrates 

that roughness continued to increase throughout the section over the entire experiment. 

In later visits, a patch of short-wavelength chatter appeared in the left-side profile within the slab 

from 314 to 328 ft from the start of the section. Distress surveys recorded scaling over this area 

and indicated “irregular surface characteristics” on the section. Portions of the section were 

diamond ground in an effort to alter the surface texture. 

SECTION 0266 

Section 0266 included a 60-ft-long bump beginning 400 ft from the start of the section. The bump 

was more than 0.6 inches high throughout the monitoring history. On the left side, a narrow dip 

appeared 438 ft from the start of the section and grew in severity over time. The dip appeared at 

50 100 150 200 250 300 350 400 450

Distance (feet)

0

50

100

150

200

250

Right Roughness Profile (in/mi)

25-Jan-2010

08-Nov-2001

25-Jan-1994
86 

a joint where photos in the 2004 distress survey showed a gap in the sealant and some missing 

concrete at the aft side of the joint. PSD plots and filtered elevation profile plots showed that the 

curl on this section was more severe than it was on sections 0267 and 0268. 

Distress surveys indicated “irregular surface characteristics” on the section. Diamond grinding 

was performed on the left wheel path from 405 to 450 ft from the start of the section to adjust the 

texture. In the photos, it appeared the grinding barely submerged the existing texture. As such, 

the grinding did not affect IRI. 

SECTION 0267 

A weigh-in-motion scale was installed in section 0267 between visit 11 (12-Dec-2004) and visit 12 

(13-Aug-2006). The scales appeared 206 ft from the start of the section on the left side and 194 ft 

from the start of the section on the right side. The portion of the section upstream of the scales 

received diamond grinding as part of the installation procedure. Diamond grinding reduced the IRI 

of the first 200 ft of the section by about 20 inches/mi on the right side but had very little effect 

on the left side. Figure 70 shows the profile from visit 12 over a segment that includes the scale. 

In the figure, the scale is about 0.1 inches above the surrounding pavement and contributes some 

roughness to the section. The series of closely spaced peaks from 176 to 192 ft along the plot 

occurs in an area that includes the inductive loop and the approach slab. 

Figure 70. Graph. Weigh-in-Motion Scale on Section 0267. 

SECTION 0268 

No specific observations are listed for section 0268. 

160 170 180 190 200 210 220

Distance (feet)

-.2

-.1

0

.1

.2

Left Elevation (inches)

scale

joint
87 

APPENDIX E. JOINT FINDING 

The slab-by-slab analysis required careful synchronization of repeat profile measurements and 

identification of joint locations within a tight tolerance. The joint-finding strategy depended on 

the following properties of the profile data from each test section: 

 Narrow dips appeared in the profiles at many of the joints. 

 Repeat measurements on a given section were rigorously synchronized, and the repeated 

presence of a narrow dip at a given location and in the left- and right-side profiles 

provided evidence of a potential joint instead of a crack or erroneous sensor reading. 

 Narrow dips (i.e., negative spikes) that corresponded to joints appeared in a regular 

pattern that corresponded to the joint spacing. 

The strategy for assembling a list of joint positions exploited the repeated presence of negative 

spikes at the same location. Each group of five profile measurements from a given visit of a given 

section formed a set, including both the left- and right-side profiles. For each set of 10 profiles, a 

list of joint positions for the entire set was found using the steps described in this chapter. 

STEP 1: FILTER THE PROFILES 

High-pass filter each profile with an anti-smoothing moving average filter using a base length 

of 0.82 ft. 

STEP 2: NORMALIZE 

Normalize each filtered profile by its standard deviation. Figure 71 provides an example trace 

that has been high-pass filtered and normalized. The figure shows the trace produced after 

application of steps 1 and 2 to a profile from visit 15 of section 0215. 

Figure 71. Graph. High-Pass Filtered, Normalized Profile. 

0 50 100 150 200

Distance (feet)

-15

-10

-5

0

5

Normalized Left Elevation (–)

threshold
88 

STEP 3: SEEK THE NEGATIVE SPIKES 

Search the normalized trace. List the longitudinal position of points with a value below -3. This 

criterion produces a list of longitudinal positions with regular spacing for the trace in figure 71, 

with some extraneous locations. Extraneous locations often appeared in the list at transverse 

joints and in multiple locations along distressed slabs. 

The threshold value of -3 was used throughout the experiment. The appropriate threshold value for 

other experiments depends on the length and depth of the gaps at the joints and on the profiler 

height-sensor footprint, low-pass filtering, and recording interval. 

STEP 4: WEED OUT LESSER SPIKES 

Eliminate any spike within 0.82 ft of a deeper spike. 

STEP 5: AGGREGATE ACROSS THE REPEAT MEASUREMENTS 

Assemble the negative spikes for the left and right profiles of all five repeat measurements into a 

single list. For sections with skewed joints, offset values of longitudinal position for the left side 

by 0.919 ft. Sections 0262–0265 included skewed joints. 

STEP 6: SORT THE LIST 

Sort the list of negative spikes in ascending order of longitudinal position. 

STEP 7: CONSOLIDATE GROUPS OF NEARBY SPIKES 

Consolidate any set of closely spaced spike positions into a group. Merge spike positions for 

which no gap larger than 1.97 inches exists between consecutive values. For each group, record 

the range of longitudinal position values and the number of spikes included in the group. To do 

this, apply the following steps: 

 Step 7a: Establish an open group using the first item in the list. 

 Step 7b: Promote the next item on the list to the current item. If the list is complete, close 

the final group. 

 Step 7c: If the current item is no more than 1.97 inches downstream of the previous item, 

add it to the open group and return to step 7b. 

 Step 7d: If the current item is more than 1.97 inches downstream, close out the current 

group. Open a new group with the current item as the first member. Return to step 7b. 

This procedure often produces groups that cover a greater longitudinal distance than 1.97 inches 

but without any gaps within the group greater than that. 

Besides the range, record the average value of longitudinal position within each group. These 

values provide a basis for calculating the actual slab length in subsequent analyses. 

On visit 04 of section 0264, the threshold gap value was adjusted to 3.15 inches. 
89 

STEP 8: TRIM THE LIST 

Eliminate all groups with a count below a given threshold. The threshold value that produced the 

proper results varied from 2 to 6. Because the joint locations were derived using sets of 10 profiles, 

this meant retaining groups for which 20–60 percent of the profiles contributed spikes. The most 

common threshold value was 20 percent. Table 31 provides sample output of step 8 for visit 15 

of section 0215. 

Table 31. Negative Spike Groups from Visit 15 of Section 0215. 

Range (ft) Average 

Position (ft) 

Number of 

Spikes 

Compatibility 

Start End Score 

-21.04 -20.84 -20.90 10 35 

-10.83 -10.70 -10.76 2 2 

-6.08 -5.82 -5.92 10 35 

8.94 9.13 9.07 7 35 

24.02 24.22 24.15 10 35 

38.98 39.18 39.08 10 35 

54.00 54.20 54.11 8 35 

69.02 69.22 69.13 10 35 

82.16 82.16 82.16 2 5 

83.98 84.17 84.10 8 35 

98.93 99.13 99.05 10 35 

104.01 104.07 104.04 2 0 

113.96 114.15 114.08 9 35 

129.04 129.17 129.13 8 35 

144.00 144.13 144.08 10 35 

158.95 159.15 159.08 8 35 

173.98 174.17 174.09 10 35 

189.00 189.19 189.10 10 35 

204.02 204.08 204.06 5 35 

219.04 219.23 219.14 9 36 

233.86 234.06 233.97 10 36 

248.95 249.08 249.01 9 36 

263.78 263.97 263.88 9 36 

278.80 278.99 278.91 10 36 

293.82 294.01 293.93 7 36 

308.77 308.97 308.89 10 36 

323.80 323.93 323.88 9 36 

338.82 339.01 338.93 10 36 

353.84 353.97 353.91 7 36 

368.79 368.99 368.92 10 36 

383.88 383.94 383.91 8 36 

398.84 399.03 398.92 9 36 

413.79 413.92 413.86 10 36 

420.36 420.42 420.38 3 3 

428.81 428.94 428.88 10 36 

436.49 436.62 436.53 3 5 
90 

Table 31. Negative Spike Groups from Visit 15 of Section 0215—Continued. 

Range (ft) Average 

Position (ft) 

Number of 

Spikes 

Compatibility 

Start End Score 

443.77 443.90 443.84 10 35 

458.85 458.99 458.91 10 36 

473.81 473.94 473.86 10 36 

479.79 479.79 479.79 2 5 

488.77 488.90 488.85 8 36 

495.27 495.33 495.29 3 3 

503.79 503.98 503.88 9 36 

505.41 505.41 505.41 2 2 

510.42 510.55 510.49 4 3 

512.05 512.24 512.10 5 3 

515.17 515.43 515.28 5 2 

518.55 518.87 518.74 9 19 

Note: Bold row indicates the group designated as joint location. Italic rows indicate the 

groups left out by steps 11 and 12. 

STEP 9: EVALUATE EACH GROUP ON THE LIST 

Calculate a compatibility score for each surviving group. To do this, seek other groups that appear 

at the expected distances from the group under evaluation within an acceptable tolerance, given 

the expected saw cut spacing. The tolerance for compatibility was set at 2 percent of the average 

expected saw cut spacing. (This was 0.27 or 0.30 ft, depending on the section.) 

The compatibility score is the number of compatible groups found within the rest of the list. For 

example, the expected saw cut spacing on section 0215 was 15 ft. The first group in table 31 

produced a compatibility score of 35, because 35 other groups appeared within the list that were 

an integer multiple of 15 ft away, to within 0.3 ft. 

Sections 0213–0224 included slabs that were all about 15 ft long. However, the saw cuts in 

sections 0262–0265 appeared in intervals of about 12, 14, 13, and 15 ft, and the saw cuts in 

sections 0266–0268 appeared in intervals of 15, 13, 15, and 17 ft. Each group was evaluated 

four times on sections with irregular joint spacing, once for each of the possible starting points 

within the pattern. The algorithm retained the highest of the four scores. 

STEP 10: DESIGNATE ONE OF THE GROUPS AS A JOINT LOCATION 

Designate the group with the highest compatibility score as a joint. If multiple groups share the 

highest compatibility rating, select the joint that is farthest upstream. For visit 15 of section 0215, a 

joint was selected that produced negative spikes from 219.04 to 219.23 ft from the start of the profile. 

STEP 11: SEEK OTHER JOINTS DOWNSTREAM 

Seek the adjacent joint in the forward direction. Designate the adjacent joint as the group with the 

highest compatibility score that appears between the shortest expected joint spacing for the section 

(minus 6 percent of its length) and the longest expected joint spacing for the section (plus 6 percent 
91 

of its length). Each time a joint is found, seek the next joint using the same criteria until the end 

of the section is reached. 

The search for the next joint location covered a range of 14.1–15.9 ft from the current joint 

location on sections 0213–0224; the range was 12.72–15.90 ft on sections 0262–0265; and the 

range was 13.79–18.02 ft on sections 0266–0268. 

STEP 12: SEEK OTHER JOINTS UPSTREAM 

Repeat step 11 in the reverse direction. 

DISCUSSION 

This procedure produced a list of joints for each set of five repeat measurements. However, the 

locations were expressed as a range rather than a precise value. For example, the joint locations 

listed in table 31 include spike groups that cover a range of 0.130–0.325 ft (2 to 5 times the profile 

recording interval). The range for spike groups in this experiment typically covered a distance of 

less than 0.33 ft.2

The range at each joint proved to be important in the subsequent slab-by-slab curve fitting analysis, 

where the profile at each end of the slab was masked over the range where the spikes were detected 

plus a 0.082-ft-long margin of safety. The average position within a group of spikes was used at 

each joint to provide slab end locations for calculating overall slab length. 

The strategy of searching for narrow dips was successful in all of the profiles after visit 02 because 

profile data were recorded at a short interval (0.77 or 0.98 inches) and measured using a height 

sensor with a footprint with a longitudinal dimension equal to or less than the gap at the joint.(17)

The joint-finding strategy described here is not suited for profiles measured with the K.J. Law 

Engineers DNC 690. As a result, the joint locations found for visit 03 of each section were also used 

in the analysis of visit 01 and visit 02. This practice was successful because the synchronization 

was very consistent between visits and because the longer recording interval (6 inches) in 

visits 01 and 02 reduced the requirement on precision of the joint locations.

 2

 Of the 10,539 joints, 10,200 covered a range of 0.33 ft or less. 

93 

APPENDIX F. PSG ESTIMATION 

Analyses were performed to segregate and quantify the portion of roughness caused by slab curl 

and warp within a profile and the portion associated with other sources of roughness such as 

built-in defects and surface distress. 

The level of curl and warp present within each profile was estimated using slab-by-slab analysis 

of local profile segments. The automated procedure described in appendix D isolated the profile 

of each slab by seeking the locations where negative spikes appeared repeatedly in the same 

locations. The procedure described in this chapter quantifies the level of curl and warp on each 

slab using PSG, which is the gross strain gradient required to deform a slab into the shape that 

appears within its measured profile from a flat baseline. 

Using PSG to quantify curl and warp represents an approach similar to the calculation of 

equivalent temperature gradient from measured slab profiles.(19,20) PSG is used rather than 

equivalent temperature gradient because this study sought to relate curl and warp to IRI rather 

than relate content within the profile to the environment in which the pavement functions. 

Other examples of this analytical strategy for processing slab profiles have been documented by 

Sixbey and Vandenbossche.(21,22) Those studies applied curve fitting to profiles of individual slabs 

using appropriately selected polynomials to represent idealized slabs with a strain gradient. The 

specific approach applied in this study uses an idealized profile for a slab with curling and warping 

proposed by Westergaard in the classical literature.(23) With only minor exceptions, the step-by-step 

procedure used in this study follows the analysis methods proposed by Rasmussen and applied 

by Chang.(2,24) Portions of this appendix duplicate the descriptions by Chang, with additional 

specific information pertinent to this study.(2,24)

WESTERGAARD 

The curve fitting procedure for measured slab profiles used an idealized shape proposed by 

Westergaard.(23) The idealized profile is based on the assumption of a linear temperature and 

moisture gradient through the depth of the slab, unrestrained slab ends, and an infinite slab along 

the undeformed axis. Westergaard provided the solution for an infinitely long pavement of finite 

width. This study applies the solution to an infinitely wide slab of finite length. 

The idealized profile relates the slab elevation (z) to position along the slab as shown in figure 72. 

 
94 

z  z0

2cos cosh

sin2 sinh2 (tan  tanh)cos x

l 2

cosh x

l 2





 (tan  tanh)sin x

l 2

sinh x

l 2







z0  (1)(T  sh )

h

l

2   b

l 8

l  Eh3

12(12)k 4

Figure 72. Equation. Relationship of Slab Elevation to Position. 

Where: 

x is the horizontal coordinate along the slab profile, referenced to the slab center (L). 

z0 is the uplift at the slab ends (L).

l is the radius of relative stiffness (L).

b is the slab width (used as slab length here) (L).

E is slab elastic modulus (F/L2).

 is Poisson’s ratio (–).

k is the modulus of subgrade support (F/L2/L). 

Figure 72 is a specialized version of the Westergaard solution that includes both moisture 

gradient ( ) and temperature gradient ( ). 

The four independent pavement properties b, E, , and k are parametric inputs needed to estimate l. 

The curve fitting procedure applied in this study assumes a fixed value for the five aforementioned 

parameters along a pavement section and seeks the optimal value for total strain gradient on each 

slab segment as shown in figure 73. 

PSG  (T  sh )

h

Figure 73. Equation. PSG. 

PSG is given the prefix “pseudo” because it is estimated empirically. 

SLAB-BY-SLAB ANALYSIS 

The PSG associated with each slab profile was estimated using the following procedure. 

Step 1: Crop 

Crop the profile of the slab to exclude the negative spikes at the joints. Appendix E describes 

the procedure for determining the location of the joints. Set the profile starting point to the end 

of the spike group found at the leading joint plus a small offset. Set the profile ending point to 

the start of the spike group found at the trailing joint minus a small offset. This study applied 

an offset of 1 inch. 



sh/h T/h


95 

Step 2: Shift 

Shift the longitudinal scale to place the slab center at a value of 0. Assume that the center of the 

slab is at the midpoint between the two average spike position values, derived as described in 

appendix E. Figure 74 shows an isolated slab profile after offset of the longitudinal scale. 

Figure 74. Graph. Measured Slab Profile for Section 0215. 

Step 3: Detrend 

Detrend the isolated profile. Apply a least-squares linear fit to the profile segment and subtract 

the best-fit line point by point. The resulting signal will have a zero mean. Figure 75 shows the 

detrended profile. 

Figure 75. Graph. Detrended Slab Profile for Section 0215. 

-100 -50 0 50 100

Longitudinal Distance (inches)

-.3

-.2

-.1

0

.1

Measured Profile (inches)

-100 -50 0 50 100

Longitudinal Distance (inches)

-.1

0

.1

.15

Detrended Profile (inches)

.05

-.05
96 

Step 4: Estimate Pavement Properties 

Estimate the pavement properties needed to apply the Westergaard equation for the slab under 

examination. The LTPP database includes measurements of elastic modulus (E), Poisson’s ratio ( ), 

and slab thickness (h) for each section. For this study, these values were held constant for all slabs 

within a given section. Values for modulus of subgrade support (k) were not available, and a value 

of 200 psi/inch was used for the entire experiment. Table 32 lists the values of E, , and h for 

each section, as well as the radius of relative stiffness (l). 

Table 32. Pavement Properties. 

Section 

Elastic 

Modulus (ksi) 

Poisson’s 

Ratio (–) 

Slab Thickness 

(inches) 

Radius of 

Relative Stiffness 

(inches) 

0213 5,100 0.15 7.9 32.2 

0214 4,100 0.13 8.3 31.6 

0215 4,850 0.15 11.0 40.7 

0216 4,300 0.19 11.2 40.2 

0217 5,050 0.16 8.1 32.7 

0218 4,050 0.14 8.3 31.5 

0219 4,900 0.14 10.8 40.2 

0220 4,150 0.15 11.2 39.7 

0221 4,750 0.15 8.1 32.2 

0222 4,075 0.135 8.6 32.4 

0223 5,000 0.14 11.1 41.3 

0224 5,150 0.15 10.6 40.2 

0262 5,150 0.09 8.1 32.7 

0263 5,300 0.12 8.2 33.3 

0264 5,250 0.13 11.5 42.9 

0265 4,300 0.16 10.8 39.0 

0266 4,900 0.15 12.3 44.4 

0267 5,350 0.13 11.3 42.5 

0268 4,850 0.13 8.5 33.5 

The joint-finding procedure provided the length of each slab (b). To obtain slab length, calculate 

the longitudinal distance between the average spike positions at the leading and trailing joint. 

Each slab requires a distinct estimate. 

Step 5: Curve Fit 

Perform a non-linear curve fit of the Westergaard model to the measured slab profile. This 

provides an estimate of the PSG required to optimize the linear fit. In this study, curve fitting 

was performed using functions MRQMIN and MRQCOF provided in Numerical Recipes.

(25)

Figure 76 shows a sample curve fit for a slab on section 0215. For this slab, the routine used a 

slab length of 15.1 ft and radius of relative stiffness of 40.7 inches. For this slab, the routine 

returned a PSG value of 70.57 × 10-6 in units of strain per inch or 70.57 /inch. 






97 

Figure 76. Graph. Curve Fit for Section 0215. 

SUMMARY INDEX 

Summary PSG values for a section were compiled using a weighted average of the absolute 

slab-by-slab PSG values. A weighting factor was applied to the PSG values in proportion to 

their length, relative to the overall section length. For slabs that appeared at the ends of a section, 

a weighting factor was applied to the PSG values in proportion to the length that appeared within 

the section, relative to the overall section length. 

-100 -50 0 50 100

Longitudinal Distance (inches)

-.1

0

.1

.15

Slab Profile (inches)

.05

-.05 model

measurement

99 

ACKNOWLEDGEMENTS 

The authors of this report would like to thank ADOT and FHWA for their support of this work. 

This research was originally instigated by ADOT, who supported the work needed to organize 

the data set, study trends in roughness values, and apply traditional analysis methods to the profile 

data. Subsequently, the FHWA supported a continuation of the work, including detailed analysis 

of the influence of curling, warping, and faulting on the development of roughness.

101 

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