Characterization of Transverse 

Profiles

PUBLICATION NO. FHWA-RD-01-024 APRIL 2001 

Research, Development, and Technology 

Turner-Fairbank Highway Research Center 

6300 Georgetown Pike 

McLean, VA 22101-2296 
FOREWORD 

This report documents a study undertaken to identify and evaluate indices to characterize 

pavement rutting. As a result of this work, several transverse profile indices have been added to 

the Long Term Pavement Performance (LTPP) database to facilitate future analysis. In addition, 

the study has yielded important findings regarding the accuracy and repeatability of three- and 

five-point rut depth measurements commonly collected for pavement management purposes. It 

was found that the three-point rut depth measurement does not provide repeatable and accurate 

measurement of pavement rutting. Also, if a five-sensor rut bar is used for network-level data 

collection, care should be taken to ensure that the transverse location of the rut bar is consistent 

from year to year and that the mean values are adjusted to reflect more realistic rut depth values. 

This report will be of interest to highway agency engineers involved in the collection, 

processing, and interpretation of data collected to characterize pavement rutting. The study 

findings regarding the repeatability and accuracy of three- and five-point rut depth measurements 

have been summarized in Publication No. FHWA-RD-01-027, which may be found at 

http://www.tfhrc.gov/pavement/lttpp/library.htm under “TechBriefs.” 

 T. Paul Teng, P.E. 

 Director, Office of Infrastructure 

 Research and Development 

NOTICE 

This document is disseminated under the sponsorship of the Department of Transportation in the 

interest of information exchange. The United States Government assumes no liability for its 

contents or use thereof. This report does not constitute a standard, specification, or regulation. 

The United States Government does not endorse products or manufacturers. Trade and 

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

object of the document. 
Technical Report Documentation Page

Reproduction of completed page authorized

1. Report No.

FHWA-RD-01-024

2. Government Accession No. 3. Recipi ent's Catalog No.

4. Title and Subtitle 5. Report Date

Characterization of Transverse Profiles

6. Performing Organization Code

7. Author(s)

A.L. Simpson

8. Performing Organization Report No.

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

Fugro-BRE, Inc.

8613 Cross Park Drive

Austin, Texas 78754

11. Contract or Grant No.

DTFH61-96-C-00003

13. Type of Report and Period Covered

Final Report, 1997-2000

12. Sponsoring Agency Name and Address

Office of Infrastructure Research and Development

Federal Highway Administration

6300 Georgetown Pike

McLean, Virginia 22101-2296

14. Sponsoring Agency Code

15. Supplementary Notes

Data used in this study was obtained from NIMS release 8.6. The files are dated October 1998. 

Contracting Officer’s Technical Representative (COTR): Cheryl Richter, HRDI-13

Project Contractor: ERES Consultants, Inc.

Subcontractor: Fugro-BRE, Inc.

16. Abstract

A study of the transverse profile data currently being collected under the Long Term Pavement Performance 

project was undertaken. The data were collected by three processes: (1) Dipstick, (2) a photographic method, 

and (3) straightedge used to collect rut depths.

This study examined several indices for the purposes of quantifying and qualifying the transverse profiles. It is 

recommended that five indices be added to the National Information Management System. These indices include 

the area of the rut below a straight line connecting the end points of the transverse profile, the total area below 

the straight lines connecting the maximum surface elevations, the maximum depth for each wheelpath between a 

1.8-m straightedge placed across the wheelpath and the surface of the pavement, and the width of the rut based 

on a 1.8-m straightedge.

These indices were studied in order to determine typical trends by climate, surface thickness, soil type, and age. 

In addition, the time -series trends for each test section were studied in order to determine whether any anomalies 

existed and the potential causes of these anomalies.

17. Key Words

Transverse profile, permanent deformation, rut depth, 

asphalt pavement.

18. Distribution Statement

No restrictions. This document is available to the 

public through the National Technical Information 

Service, Springfield, Virginia 22161.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

303

22. Price

iii 

TABLE OF CONTENTS 

CHAPTER PAGE

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

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

 OBJECTIVES .................................................................................................................. 2 

 SCOPE OF REPORT....................................................................................................... 2 

CHAPTER 2. DATA USED IN STUDY ................................................................................... 3 

 PASCO RoadRecon 75 .................................................................................................... 3 

 Data Collection Equipment .................................................................................. 3 

 Calibration............................................................................................................ 3 

 Data Collection..................................................................................................... 3 

 Data Processing.................................................................................................... 4 

 FACE Dipstick ............................................................................................................... 4 

 Data Collection Equipment .................................................................................. 4 

 Calibration Process............................................................................................... 4 

 Data Processing.................................................................................................... 7 

 1.2-m STRAIGHTEDGE................................................................................................. 7 

 DATA AVAILABILITY ................................................................................................. 7 

CHAPTER 3. CALCULATION OF INDICES ........................................................................ 11 

 POTENTIAL INDICES ................................................................................................. 11 

 ETG RECOMMENDATIONS ...................................................................................... 12 

 METHOD OF CALCULATION ................................................................................... 12 

 Positive and Negative Areas .............................................................................. 12 

 Area of Fill ......................................................................................................... 14 

 Calculated Rut Depth Based on a 1.8-m Straightedge....................................... 15 

 Calculated Rut Depth Based on a Lane-Width Wire Line................................. 15 

 Radius of Curvature ........................................................................................... 16 

 PASCO Typecasting .......................................................................................... 23 

 RUTCHAR PROGRAM................................................................................................ 23 

 Program Description .......................................................................................... 23 

 Program Verification.......................................................................................... 26 

CHAPTER 4. INDEX COMPARISONS.................................................................................. 27 

 MINIMUM NUMBER OF MEASUREMENTS........................................................... 27 

 INDEX COMPARISONS.............................................................................................. 29 

 Rut Widths.......................................................................................................... 31 

 Rut Depths.......................................................................................................... 31 

 Areas................................................................................................................... 34 

 Summary ............................................................................................................ 34 

 
iv 

TABLE OF CONTENTS (CONTINUED) 

CHAPTER PAGE

CHAPTER 5. INDEX EVALUATION ....................................................................................... 37 

 SECTION COMPARISONS ............................................................................................ 37 

 Pavement Age ....................................................................................................... 39 

 Experiment Comparisons ...................................................................................... 41 

 Thickness of Asphalt Concrete Layers.................................................................. 41 

 Base Stabilization.................................................................................................. 41 

 Climatic/Environmental Zones ............................................................................. 42 

 Summary ............................................................................................................... 42 

 VARIABILITY COMPARISONS.................................................................................... 43 

 TIME-SERIES STABILITY............................................................................................. 45 

 Slope Comparisons................................................................................................ 45 

 Check for Decreasing Ruts.................................................................................... 46 

 SUMMARY ...................................................................................................................... 52 

CHAPTER 6. COMPARISONS OF THREE-POINT AND FIVE-POINT RUT DEPTHS ....... 55 

 METHOD OF CALCULATION ...................................................................................... 55 

 ANALYSES...................................................................................................................... 62 

 Variation................................................................................................................ 62 

 Combined Data Sets.............................................................................................. 62 

 Blocked Data Sets Versus Shape .......................................................................... 67 

 Blocked Data Sets Versus Rut Depth.................................................................... 73 

 SUMMARY ...................................................................................................................... 75 

CHAPTER 7. FIELD STUDY..................................................................................................... 79 

 DATA COLLECTION...................................................................................................... 79 

 ANALYSIS ....................................................................................................................... 80 

 SUMMARY ...................................................................................................................... 83 

CHAPTER 8. CONCLUSIONS AND RECOMMENDATIONS ............................................... 85 

APPENDIX A. RUTCHAR PROGRAM USER’S GUIDE ......................................................... 89 

APPENDIX B. DISTRIBUTION OF THE INDICES.................................................................. 95 

APPENDIX C. COMPARISONS OF SECTION MEANS TO DETERMINE NUMBER OF 

TRANSVERSE PROFILES NECESSARY ............................................................................... 187 

APPENDIX D. t-TESTS COMPARING VARIOUS PAVEMENT PARAMETERS............... 211 

APPENDIX E. COMPARISONS OF TIME-SERIES SLOPES ................................................ 267 

REFERENCES............................................................................................................................ 289 
v

LIST OF FIGURES 

FIGURE PAGE

 1. Transverse profiles obtained on test section 491001 on October 30, 1989 by PASCO...... 5 

 2. Transverse profiles obtained on test section 501002 on April 27, 1993 by PASCO .......... 5 

 3. Transverse profiles obtained on test section 811803 on July 5, 1989 by PASCO.............. 6 

 4. Transverse profiles obtained on test section 124107 on March 9, 1994 by PASCO .......... 6 

 5. Transverse profiles obtained on test section 151003 on February 20, 1991 with 

 a Dipstick ......................................................................................................................... 8 

 6 Transverse profiles obtained on test section 161010 on December 16, 1993 with 

 a Dipstick ......................................................................................................................... 8 

 7. Transverse profiles obtained on test section 201010 on April 22, 1993 with 

 a Dipstick .......................................................................................................................... 9 

 8. Transverse profiles obtained on test section 561007 on September 8, 1995 with 

 a Dipstick .......................................................................................................................... 9 

 9. Illustration of the positive and negative area indices ........................................................ 13 

10. Illustration of the fill area index........................................................................................ 14 

11. Illustration of the 1.8-m rut depth and 1.8-m rut width .................................................... 15 

12. Illustration of the wire line rut depth and the wire line rut width ..................................... 16 

13. Transverse profile for test section 48A506 obtained on March 9, 1995 by PASCO at 

 station 91.5 m .................................................................................................................... 17 

14. Transverse profile for test section 541640 obtained on September 29, 1992 by 

 PASCO at station 152.4 m ................................................................................................ 18 

15. Transverse profile for test section 36B340 obtained on October 9, 1995 by 

 PASCO at station 92.7 m .................................................................................................. 19 

16. Transverse profile for test section 566032 obtained on August 26, 1996 by 

 PASCO at station 61 m ..................................................................................................... 21 

17. Transverse profile for test section 421610 obtained on May 17, 1990 by 

 PASCO at station 91.8 m .................................................................................................. 22 

18. PASCO typecasting shapes (shapes 0-6) .......................................................................... 24 

19. PASCO typecasting shapes (shapes 7-13) ........................................................................ 25 

20. Paired t-test comparing the LWP 1.8-m rut depths versus the LWP wire line rut depths 32 

21. Paired t-test comparing the RWP 1.8-m rut depths versus the RWP wire line rut depths 33 

22. Comparison between the negative area index and the fill area index ............................... 35 

23. Illustration of those States that use a three-point profiling system ................................... 56 

24. Rut bar measurement......................................................................................................... 57 

25. Means and standard deviations of the differences observed for the LWP versus 

 wander ............................................................................................................................... 58 

26. Means and standard deviations of the differences observed for the RWP versus 

 wander ............................................................................................................................... 59 

27. Calculation of rut depth from the rut bar........................................................................... 60 

28. Typical transverse profile providing a negative rut depth from three-point analysis ....... 61 

29. Typical profile providing a negative rut depth from five-point analysis .......................... 61 

30. Graphical comparison of the three-point rut depths versus the wire line rut depths......... 65 

31. Graphical comparison of the five-point rut depths versus the wire line rut depths .......... 66 
vi 

LIST OF FIGURES (CONTINUED) 

FIGURE PAGE

32. Transverse profile shape categories .................................................................................. 68 

33. Number of profiles within each shape category................................................................ 69 

34. Profiles obtained using the straightedge method at station 76.2 m................................... 81 

35. Distribution of the negative area index ............................................................................. 96 

36. Distribution of the positive area index .............................................................................. 97 

37. Distribution of the fill area index ...................................................................................... 98

38. Distribution of the LWP 1.8-m rut depth .......................................................................... 99 

39. Distribution of the LWP 1.8-m rut width........................................................................ 100 

40. Distribution of the LWP 1.8-m rut location .................................................................... 101 

41. Distribution of the RWP 1.8-m rut depth........................................................................ 102 

42. Distribution of the RWP 1.8-m rut width........................................................................ 103 

43. Distribution of the RWP 1.8-m rut location.................................................................... 104 

44. Distribution of the LWP wire line rut depth ................................................................... 105 

45. Distribution of the LWP wire line rut width ................................................................... 106 

46. Distribution of the LWP wire line rut location ............................................................... 107 

47. Distribution of the RWP wire line rut depth ................................................................... 108 

48. Distribution of the RWP wire line rut width................................................................... 109 

49. Distribution of the RWP wire line rut location ............................................................... 110 

50. Distribution of the section means of the negative area index ......................................... 111 

51. Distribution of the section means of the positive area index .......................................... 112 

52. Distribution of the section means of the fill area index .................................................. 113 

53. Distribution of the section means of the LWP 1.8-m rut depths..................................... 114 

54. Distribution of the section means of the LWP 1.8-m rut widths..................................... 115 

55. Distribution of the section means of the LWP 1.8-m rut locations................................. 116 

56. Distribution of the section means of the RWP 1.8-m rut depths..................................... 117 

57. Distribution of the section means of the RWP 1.8- rut widths ....................................... 118 

58. Distribution of the section means of the RWP 1.8-m rut locations................................. 119 

59. Distribution of the section means of the LWP wire line rut depths ................................ 120 

60. Distribution of the section means of the LWP wire line rut widths................................ 121 

61. Distribution of the section means of the LWP wire line rut locations ............................ 122 

62. Distribution of the section means of the RWP wire line rut depths................................ 123 

63. Distribution of the section means of the RWP wire line rut widths................................ 124 

64. Distribution of the section means of the RWP wire line rut locations............................ 125 

65. Distribution of the section means of the negative area index on GPS-1 test sections .... 126 

66. Distribution of the section means of the positive area index on GPS-1 test sections ..... 127 

67. Distribution of the section means of the fill area index on GPS-1 test sections ............. 128 

68. Distribution of the section means of the LWP 1.8-m rut depths on GPS-1 test 

 sections............................................................................................................................ 129 

69. Distribution of the section means of the LWP 1.8-m rut widths on GPS-1 test 

 sections............................................................................................................................ 130 

70. Distribution of the section means of the LWP 1.8-m rut locations on GPS-1 test 

 sections............................................................................................................................ 131 
vii

LIST OF FIGURES (CONTINUED) 

FIGURE PAGE

71. Distribution of the section means of the RWP 1.8-m rut depths on GPS-1 test sections 

 sections............................................................................................................................ 132 

72. Distribution of the section means of the RWP 1.8-m rut widths on GPS-1 test 

 sections............................................................................................................................ 133 

73. Distribution of the section means of the RWP 1.8-m rut locations on GPS-1 test 

 sections............................................................................................................................ 134 

74. Distribution of the section means of the LWP wire line rut depths on GPS-1 test 

 sections............................................................................................................................ 135 

75. Distribution of the section means of the LWP wire line rut widths on GPS-1 test 

 sections............................................................................................................................ 136 

76. Distribution of the section means of the LWP wire line rut locations on GPS-1 test 

 sections............................................................................................................................ 137 

77. Distribution of the section means of the RWP wire line rut depths on GPS-1 test 

 sections............................................................................................................................ 138 

78. Distribution of the section means of the RWP wire line rut widths on GPS-1 test 

 sections............................................................................................................................ 139 

79. Distribution of the section means of the RWP wire line rut locations on GPS-1 test 

 sections............................................................................................................................ 140 

80. Distribution of the section means of the negative area index on GPS-2 test sections .... 141 

81. Distribution of the section means of the positive area index on GPS-2 test sections ..... 142 

82. Distribution of the section means of the fill area index on GPS-2 test sections ............. 143 

83. Distribution of the section means of the LWP 1.8-m rut depths on GPS-2 test 

 sections............................................................................................................................ 144 

84. Distribution of the section means of the LWP 1.8-m rut widths on GPS-2 test 

 sections............................................................................................................................ 145 

85. Distribution of the section means of the LWP 1.8-m rut locations on GPS-2 test 

 sections............................................................................................................................ 146 

86. Distribution of the section means of the RWP 1.8-m rut depths on GPS-2 test 

 sections............................................................................................................................ 147 

87. Distribution of the section means of the RWP 1.8-m rut widths on GPS-2 test 

 sections............................................................................................................................ 148 

88. Distribution of the section means of the RWP 1.8-m rut locations on GPS-2 test 

 sections............................................................................................................................ 149 

89. Distribution of the section means of the LWP wire line rut depths on GPS-2 test 

 sections............................................................................................................................ 150 

90. Distribution of the section means of the LWP wire line rut widths on GPS-2 test 

 sections............................................................................................................................ 151 

91. Distribution of the section means of the LWP wire line rut locations on GPS-2 test 

 sections............................................................................................................................ 152 

92. Distribution of the section means of the RWP wire line rut depths on GPS-2 test 

 sections............................................................................................................................ 153 
viii

LIST OF FIGURES (CONTINUED) 

FIGURE PAGE

93. Distribution of the section means of the RWP wire line rut widths on GPS-2 test 

 sections............................................................................................................................ 154 

94. Distribution of the section means of the RWP wire line rut locations on GPS-2 

 test sections ..................................................................................................................... 155 

95. Distribution of the section means of the negative area index on GPS-6 test sections .... 156 

96. Distribution of the section means of the positive area index on GPS-6 test sections ..... 157 

97. Distribution of the section means of the fill area index on GPS-6 test sections ............. 158 

98. Distribution of the section means of the LWP 1.8-m rut depths on GPS-6 test 

 sections............................................................................................................................ 159 

99. Distribution of the section means of the LWP 1.8-m rut widths on GPS-6 test 

 sections............................................................................................................................ 160 

100. Distribution of the section means of the LWP 1.8-m rut locations on GPS-6 test 

 sections............................................................................................................................ 161 

101. Distribution of the section means of the RWP 1.8-m rut depths on GPS-6 test 

 sections............................................................................................................................ 162 

102. Distribution of the section means of the RWP 1.8-m rut widths on GPS-6 test 

 sections............................................................................................................................ 163 

103. Distribution of the section means of the RWP 1.8-m rut locations on GPS-6 test 

 sections............................................................................................................................ 164 

104. Distribution of the section means of the LWP wire line rut depths on GPS-6 test 

 sections............................................................................................................................ 165 

105. Distribution of the section means of the LWP wire line rut widths on GPS-6 test 

 sections............................................................................................................................ 166 

106. Distributions of the section means of the LWP wire line rut locations on GPS-6 test 

 sections............................................................................................................................ 167 

107. Distribution of the section means of the RWP wire line rut depths on GPS-6 test 

 sections............................................................................................................................ 168 

108. Distribution of the section means of the RWP wire line rut widths on GPS-6 test 

 sections............................................................................................................................ 169 

109. Distribution of the section means of the RWP wire line rut locations on GPS-6 test 

 sections............................................................................................................................ 170 

110. Distribution of the section means of the negative area index on GPS-7 test sections .... 171 

111. Distribution of the section means of the positive area index on GPS-7 test sections ..... 172 

112. Distribution of the section means of the fill area index on GPS-7 test sections ............. 173 

113. Distribution of the section means of the LWP 1.8-m rut depths on GPS-7 test 

 sections............................................................................................................................ 174 

114. Distribution of the section means of the LWP 1.8-m rut widths on GPS-7 test 

 sections............................................................................................................................ 175 

115. Distribution of the section means of the LWP 1.8-m rut locations on GPS-7 test 

 sections............................................................................................................................ 176 

116. Distribution of the section means of the RWP 1.8-m rut depths on GPS-7 test 

 sections............................................................................................................................ 177 
ix

LIST OF FIGURES (CONTINUED) 

FIGURE PAGE

117. Distribution of the section means of the RWP 1.8-m rut widths on GPS-7 test 

 sections............................................................................................................................ 178 

118. Distribution of the section means of the RWP 1.8-m rut locations on GPS-7 test 

 sections............................................................................................................................ 179 

119. Distribution of the section means of the LWP wire line rut depths on GPS-7 test 

 sections............................................................................................................................ 180 

120. Distribution of the section means of the LWP wire line rut widths on GPS-7 test 

 sections............................................................................................................................ 181 

121. Distribution of the section means of the LWP wire line rut locations on GPS-7 test 

 sections............................................................................................................................ 182 

122. Distribution of the section means of the RWP wire line rut depths on GPS-7 test 

 sections............................................................................................................................ 183 

123. Distribution of the section means of the RWP wire line rut widths on GPS-7 test 

 sections............................................................................................................................ 184 

124. Distribution of the section means of the RWP wire line rut locations on GPS-7 test 

 sections............................................................................................................................ 185 

125. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the negative area index ................................................... 188 

126. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the positive area index ..................................................... 189 

127. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the fill area index ............................................................. 190 

128. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the LWP 1.8-m rut depths................................................ 191 

129. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the LWP 1.8-m rut widths ............................................... 192 

130. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the RWP 1.8-m rut depths ............................................... 193 

131. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the RWP 1.8-m rut widths ............................................... 194 

132. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the LWP wire line rut depths........................................... 195 

133. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the LWP wire line rut widths........................................... 196 

134. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the RWP wire line rut depths........................................... 197 

135. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for the RWP wire line rut widths........................................... 198 

136. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the negative area index.. 199 

137. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the positive area index... 200 
x

LIST OF FIGURES (CONTINUED) 

FIGURE PAGE

138. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the fill area index........... 201 

139. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the LWP 1.8-m rut 

 depths ............................................................................................................................. 202 

140. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the LWP 1.8-m rut 

 widths ............................................................................................................................. 203 

141. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the RWP 1.8-m rut 

 depths ............................................................................................................................. 204 

142. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the RWP 1.8-m rut 

 widths ............................................................................................................................. 205 

143. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the LWP wire line rut 

 depths ............................................................................................................................. 206 

144. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the LWP wire line rut 

 widths ............................................................................................................................. 207 

145. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the RWP wire line rut 

 depths ............................................................................................................................. 208 

146. Paired t-test comparing section means from all of the profiles versus those from 

 profiles taken every 30 m for data collected by Dipstick® for the RWP wire line rut 

 widths ............................................................................................................................. 209 

147. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 negative area index.......................................................................................................... 212 

148. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 positive area index........................................................................................................... 213 

149. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the fill 

 area index ........................................................................................................................ 214 

150. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 LWP 1.8-m rut depths ..................................................................................................... 215 

151. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 LWP 1.8-m rut widths..................................................................................................... 216 

152. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 RWP 1.8-m rut depths..................................................................................................... 217 

153. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 RWP 1.8-m rut widths..................................................................................................... 218 

154. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 LWP wire line rut depths ................................................................................................ 219 
xi

LIST OF FIGURES (CONTINUED) 

FIGURE PAGE

155. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 LWP wire line rut widths ................................................................................................ 220 

156. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 RWP wire line rut depths ................................................................................................ 221 

157. Paired t-test comparing GPS-1 section means versus GPS-7 section means for the 

 RWP wire line rut widths................................................................................................ 222 

158. Paired t-test comparing GPS-1 and GPS-2 section means for the negative area index 

 versus surface thickness ................................................................................................. 223 

159. Paired t-test comparing GPS-1 and GPS-2 section means for the positive area index 

 versus surface thickness .................................................................................................. 224 

160. Paired t-test comparing GPS-1 and GPS-2 section means for the fill area index 

 versus surface thickness .................................................................................................. 225 

161. Paired t-test comparing GPS-1 and GPS-2 section means for the LWP 1.8-m rut 

 depths versus surface thickness....................................................................................... 226 

162. Paired t-test comparing GPS-1 and GPS-2 section means for the LWP 1.8-m rut 

 widths versus surface thickness ...................................................................................... 227 

163. Paired t-test comparing GPS-1 and GPS-2 section means for the RWP 1.8-m rut 

 depths versus surface thickness....................................................................................... 228 

164. Paired t-test comparing GPS-1 and GPS-2 section means for the RWP 1.8-m rut 

 widths versus surface thickness ...................................................................................... 229 

165. Paired t-test comparing GPS-1 and GPS-2 section means for the LWP wire line rut 

 depths versus surface thickness....................................................................................... 230 

166. Paired t-test comparing GPS-1 and GPS-2 section means for the LWP wire line rut 

 widths versus surface thickness ...................................................................................... 231 

167. Paired t-test comparing GPS-1 and GPS-2 section means for the RWP wire line rut 

 depths versus surface thickness....................................................................................... 232 

168. Paired t-test comparing GPS-1 and GPS-2 section means for the RWP wire line rut 

 widths versus surface thickness ...................................................................................... 233 

169. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the 

 negative area index versus base type............................................................................... 234 

170. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the 

 positive area index versus base type ............................................................................... 235 

171. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the fill 

 area index versus base type ............................................................................................. 236 

172. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the 

 LWP 1.8-m rut depths versus base type.......................................................................... 237 

173. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the 

 LWP 1.8-m rut widths versus base type.......................................................................... 238 

174. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the 

 RWP 1.8-m rut depths versus base type.......................................................................... 239 

175. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the 

 RWP 1.8-m rut widths versus base type ......................................................................... 240 
xii

LIST OF FIGURES (CONTINUED) 

FIGURE PAGE

176. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the LWP 

 wire line rut depths versus base type............................................................................... 241 

177. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the LWP 

 wire line rut widths versus base type .............................................................................. 242 

178. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the RWP 

 wire line rut depths versus base type............................................................................... 243 

179. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 section means for the RWP 

 wire line rut widths versus base type .............................................................................. 244 

180. Paired t-test comparing thin-surfaced GPS-2 section means for the negative area 

 index versus base type..................................................................................................... 245

181. Paired t-test comparing thin-surfaced GPS-2 section means for the positive area 

 index versus base type..................................................................................................... 246

182. Paired t-test comparing thin-surfaced GPS-2 section means for the fill area index 

 versus base type............................................................................................................... 247 

183. Paired t-test comparing thin-surfaced GPS-2 section means for the LWP 1.8-m 

 rut depths versus base type.............................................................................................. 248 

184. Paired t-test comparing thin-surfaced GPS-2 section means for the LWP 1.8-m 

 rut widths versus base type.............................................................................................. 249 

185. Paired t-test comparing thin-surfaced GPS-2 section means for the RWP 1.8-m 

 rut depths versus base type.............................................................................................. 250 

186. Paired t-test comparing thin-surfaced GPS-2 section means for the RWP 1.8-m 

 rut widths versus base type.............................................................................................. 251 

187. Paired t-test comparing thin-surfaced GPS-2 section means for the LWP wire line 

 rut depths versus base type.............................................................................................. 252 

188. Paired t-test comparing thin-surfaced GPS-2 section means for the LWP wire line 

 rut widths versus base type.............................................................................................. 253 

189. Paired t-test comparing thin-surfaced GPS-2 section means for the RWP wire line 

 rut depths versus base type.............................................................................................. 254 

190. Paired t-test comparing thin-surfaced GPS-2 section means for the RWP wire line 

 rut widths versus base type.............................................................................................. 255 

191. Paired t-test comparing climate for the GPS-7 section means of the negative area 

 index ............................................................................................................................. 256 

192. Paired t-test comparing climate for the GPS-7 section means of the positive area 

 index ............................................................................................................................. 257 

193. Paired t-test comparing climate for the GPS-7 section means of the fill area 

 index ............................................................................................................................. 258 

194. Paired t-test comparing climate for the GPS-7 section means of the LWP 1.8-m 

 rut depths......................................................................................................................... 259 

195. Paired t-test comparing climate for the GPS-7 section means of the LWP 1.8-m 

 rut widths......................................................................................................................... 260 

196. Paired t-test comparing climate for the GPS-7 section means of the RWP 1.8-m 

 rut depths......................................................................................................................... 261 
xiii

LIST OF FIGURES (CONTINUED) 

FIGURE PAGE

197. Paired t-test comparing climate for the GPS-7 section means of the RWP 1.8-m 

 rut widths......................................................................................................................... 262 

198. Paired t-test comparing climate for the GPS-7 section means of the LWP wire 

 line rut depths.................................................................................................................. 263 

199. Paired t-test comparing climate for the GPS-7 section means of the LWP wire 

 line rut widths.................................................................................................................. 264 

200. Paired t-test comparing climate for the GPS-7 section means of the RWP wire 

 line rut depths.................................................................................................................. 265 

201. Paired t-test comparing climate for the GPS-7 section means of the RWP wire line 

 rut widths......................................................................................................................... 266 

202. Distribution of the time-series slopes for the negative area index .................................. 268 

203. Distribution of the time-series slopes on the positive area index.................................... 269 

204. Distribution of the time-series slopes on the fill area index............................................ 270 

205. Distribution of the time-series slopes on the LWP 1.8-m rut depths .............................. 271 

206. Distribution of the time-series slopes on the LWP 1.8-m rut widths.............................. 272 

207. Distribution of the time-series slopes on the RWP 1.8-m rut depths.............................. 273 

208. Distribution of the time-series slopes on the RWP 1.8-m rut widths.............................. 274 

209. Distribution of the time-series slopes on the LWP wire line rut depths ......................... 275 

210. Distribution of the time-series slopes on the LWP wire line rut widths ......................... 276 

211. Distribution of the time-series slopes on the RWP wire line rut depths ......................... 277 

212. Distribution of the time-series slopes on the RWP wire line rut widths......................... 278 

213. Comparison of the signs of the slopes for the negative area index versus those for the 

 LWP 1.8-m rut depths ..................................................................................................... 279 

214. Comparison of the signs of the slopes for the positive area index versus those for the 

 LWP 1.8-m rut depths ..................................................................................................... 280 

215. Comparison of the signs of the slopes for the fill area index versus those for the LWP 

 1.8-m rut depths............................................................................................................... 281 

216. Comparison of the signs of the slopes for the LWP 1.8-m rut widths versus those for 

 the LWP 1.8-m rut depths .............................................................................................. 282 

217. Comparison of the signs of the slopes for the RWP 1.8-m rut depths versus those for 

 the LWP 1.8-m rut depths ............................................................................................... 283 

218. Comparison of the signs of the slopes for the RWP 1.8-m rut widths versus those for 

 the LWP 1.8-m rut depths ............................................................................................... 284 

219. Comparison of the signs of the slopes for the LWP wire line rut depths versus those 

 for the LWP 1.8-m rut depths.......................................................................................... 285 

220. Comparison of the signs of the slopes for the LWP wire line rut widths versus those 

 for the LWP 1.8-m rut depths.......................................................................................... 286 

221. Comparison of the signs of the slopes for the RWP wire line rut depths versus those 

 for the LWP 1.8-m rut depths.......................................................................................... 287 

222. Comparison of the signs of the slopes for the RWP wire line rut widths versus those 

 for the LWP 1.8-m rut depths.......................................................................................... 288 
xiv 

LIST OF TABLES 

TABLE PAGE

1. Comparison of section means of all versus six measurements for all indices .................. 28 

2. Results of sample size analysis, 11 versus 6 measurements ............................................. 29 

3. Correlation matrix for indices ........................................................................................... 30 

4. Range of standard deviations for each index .................................................................... 38 

5. Range of COVs for each index ......................................................................................... 38 

6. Results from comparisons with age for the GPS-1 section means.................................... 40 

7. Results from comparisons with age for the GPS-2 section means.................................... 40 

8. Distribution of within-section COVs for GPS-1 and GPS-2 experiments........................ 43 

9. Distribution of within-section COVs for thin and thick test sections ............................... 44 

10. Distribution of within-section COVs for weak and strong structures............................... 44 

11. Time-series stability trends ............................................................................................... 47 

12. Summary of comparisons.................................................................................................. 53 

13. Correlation of three-point and five-point rut depths versus the wire line rut depths ........ 63 

14. Correlation of average three-point and five-point rut depths versus the wire line rut 

 depths ............................................................................................................................... 67 

15. Correlation of the three-point and five-point rut depths versus the wire line rut depths 

 by category ........................................................................................................................ 71 

16. Correlation of three-point and five-point rut depths versus the wire line rut depths for 

 profiles with less than 4.5 mm of rutting .......................................................................... 74 

17. Correlation of three-point and five-point rut depths versus the wire line rut depths for 

 profiles with from 4.5 mm to 7 mm of rutting .................................................................. 76 

18. Correlation of three-point and five-point rut depths versus the wire line rut depths for 

 profiles with more than 7 mm of rutting ........................................................................... 77 

19. Within-operator precision for each index.......................................................................... 82 

20. Between-operator precision for each index....................................................................... 82 

21. Minimum and maximum levels of bias............................................................................. 84 

22. File format for the UR##YYYY.RIP file.......................................................................... 91 

23. File format for the UR##YYYY.RIS file.......................................................................... 92 
1 

CHAPTER 1. INTRODUCTION 

BACKGROUND 

Rutting is not just a common mode of distress on asphalt pavements, but also a safety hazard 

because it allows water to pool on the roadway. Many studies have attempted to predict the 

progression of rutting in asphalt concrete and composite pavements. In some of the studies, 

rutting or rut depth is referred to as “permanent deformation.” However, permanent deformation 

is layer- or material-dependent, while rutting measured at the surface is the accumulation of 

permanent deformation in each pavement layer and the subgrade. The terms “rutting” and “rut 

depth” will be used exclusively within this report. 

Rutting measured on the pavement’s surface is caused by three different mechanisms. These are: 

• One-dimensional vertical permanent or plastic deformation in the asphalt concrete layers 

(typically referred to as localized densification). 

• Lateral flow in the asphalt concrete mixtures (sometimes referred to as accelerated 

deformation, tertiary or shear flow). 

• Mechanical deformation of subsurface layers. 

Unfortunately, rut depths measured with a 1.2-m or 1.8-m straightedge (the two lengths most 

commonly used) do not identify the mechanism of the rutting observed at the surface. 

Identification of the cause is critical to the development of an accurate rutting prediction model; 

however, more importantly, it would be highly beneficial for managing pavements and selecting 

appropriate rehabilitation options. 

Within the Long Term Pavement Performance (LTPP) program, transverse profiles have been 

used to quantify wheelpath rutting and other types of surface distortion. Currently, these 

profiles exist within the National Information Management System (NIMS) as a series of x-y 

points defining the pavement surface. Rut depths measured using a 1.2-m straightedge are 

available in the NIMS, but no indices representing the transverse profile measurements were 

available when the work reported herein was undertaken. 

Different agencies have used different measurement techniques for quantifying the surface rut 

depths along a roadway for use in managing and evaluating their pavements. The American 

Society for Testing and Materials (ASTM) has a specification (ASTM E1703-95) for measuring 

the rut depth of a pavement using a straightedge. ASTM E1656-94 covers the collection of 

automated transverse profile data. Currently, Texas uses a five-point system in which x-y 

coordinates are collected adjacent to the lane edge, in each wheelpath, and mid-lane. The rut 

depth is defined as the vertical distance between a line connecting the points at the edges of the 

lane and the point in each wheelpath. Many States, such as Kansas and Florida, use a three-point 

system in which data are collected in each wheelpath and mid-lane. In this case, the rut depth is 
2 

defined as the difference in elevation between the mid-lane measurement and the wheelpath 

measurements. 

The use of these various systems (the straightedge, 3.7-m string line, five-point system, threepoint system, and the transverse profile) is not conducive to the standardized system that is 

required for the development of a mechanistic-empirical rutting prediction model. More 

importantly, a one-parameter index (i.e., rut depth) does not allow one to identify the mechanism 

or mechanisms that cause the surface distortions. 

OBJECTIVES 

The objectives for this research were as follows: 

• Identify and characterize representative cross-profiles. 

• Quantify bias and precision in time-series measurements. 

• Select methodology and compute rut indices. 

SCOPE OF REPORT 

This report is divided into eight chapters. The second chapter provides an overview of how 

transverse profile data have been collected for LTPP. The third chapter provides the definitions 

of the indices that were considered in this study and how these indices are calculated. The fourth 

chapter presents comparisons of the indices. The fifth chapter examines the variability of the 

indices. It also compares the indices to common materials characteristics and pavement 

parameters to relate the behavior of the indices to commonly accepted theories of rutting. The 

sixth chapter evaluates the methods of data collection that are most commonly used by the 

States. The seventh chapter provides the field-determined bias and precision values that may be 

expected from each index. The eighth chapter summarizes the investigations and provides 

recommendations for future research. 
3

CHAPTER 2. DATA USED IN STUDY 

Transverse profile measurements are made within the LTPP program using three different 

procedures. These three procedures are listed below and each of these procedures is described in 

this chapter. 

• PASCO RoadRecon 75 

• FACE Dipstick

• 1.2-m Straightedge 

Dipstick is used whenever a manual distress survey is conducted. These measurements are 

intended as a backup for the transverse profile measurements collected by RoadRecon 75. The 

1.2-m straightedge measurements are required for the SPS-3 projects only, but were obtained on 

some sections in other experiments. 

PASCO RoadRecon 75 

Data Collection Equipment 

The PASCO RoadRecon system incorporates a van driven across the test section at night. A 

boom, on which a 35-mm camera has been mounted, extends from the rear of the van at the top 

of the unit. A strobe projector, mounted on the bumper, contains a glass plate that has a hairline 

etched onto it. The strobe and the camera are synchronized so that when the camera is triggered 

to take a picture, the strobe projects a shadow of the hairline onto the pavement surface at a 

specific angle in relationship to the van (and thus at an approximate angle to the pavement 

surface). The coordinates along the hairline image for each picture are later digitized and stored 

on a computer. Photographs are taken approximately every 15.2 m. 

Calibration 

PASCO follows a rigorous process for calibration, data processing, and data review to ensure 

data quality for the LTPP database. A more detailed description of these steps may be found in 

reference 1. 

Data Collection 

The driver films each General Pavement Study (GPS) test section several times in an attempt to 

obtain two or three good, complete passes of the section. For the Specific Pavement Study (SPS) 

projects with multiple test sections, the entire project is filmed several times to obtain two or 

three good, complete passes of the project. The film is reviewed in the office for the purpose of 

selecting the best “pass” for entry into the database. For the SPS projects, the best two sets of 

film are chosen and the project is pieced together by choosing one section from one film and the 
4

next section from the other film. All of the film, whether it is used or not, is retained as a backup 

by the contractor. 

Data Processing 

The film is used to create a digital profile, which is a series of x-y points defining the location of 

the surface of the pavement in a plane. All of the digitizing is performed using the negatives of 

the film. The point (0, 0) is the outside edge of the lane. A mouse with cross hairs is moved 

across the line on the film. The technician selects from 24 to 30 points on the line that include the 

peak highs and lows on the profile. The resulting profile is stored in a computer file that can be 

loaded directly into the database. 

As of October 1998, there were five rounds of PASCO data in the NIMS. This means that for 

some sections, there may be as many as five or six observations. Figures 1 through 4 illustrate 

some common sets of PASCO transverse profile data. The legend for these figures provides the 

longitudinal location along the test section of the profile. 

FACE Dipstick

Data Collection Equipment 

The FACE Dipstick is used as part of a manual distress survey. This equipment is described in 

the Distress Identification Manual as follows:(2)

“The body of the Dipstick houses an inclinometer (pendulum), LCD panels and a 

battery for power supply. The sensor of the Dipstick is mounted in such a manner that 

its axis and the line passing through the contact points of the footpads are coplanar. The 

sensor becomes unbalanced as the Dipstick is pivoted from one leg to the other as it is 

moved down the pavement, causing the display to become blank. After the sensor 

achieves equilibrium, the difference in elevation between the two points is displayed. 

The Dipstick is equipped with a choice of hardened steel spike feet or ball-and-swivel 

footpads. The swivel pads should be used on textured pavements.” 

Calibration Process 

A series of calibration and zero checks are performed prior to data collection.(2) When these 

checks are completed, the operator may begin transverse profile measurements. The operator 

“pops” a chalk line to establish a transverse line on the pavement surface every 15.2 m, carefully 

avoiding any raised pavement markings. Readings are taken every 0.3 m across the lane and 

back to the starting point so that a closed loop is used at each station. The perfect closed loop 

results in a difference of 0 between the first reading and the last reading. The difference in the 

first reading and the last reading is used as a quality control check. The maximum allowable 

error is 0.076 mm per reading, or 1.8 mm total difference in the first reading and last reading for 

a transverse run 7.32 m long (3.66 m up and 3.66 m back). When all profile measurements for a 
5

Figure 1. Transverse profiles obtained on test section 491001 

on October 30, 1989 by PASCO. 

Figure 2. Transverse profiles obtained on test section 501002 

on April 27, 1993 by PASCO. 

-20

-15

-10

-5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000

Transverse Distance, mm

Relative Elevation, mm

-0.6

14.6

29.6

44.8

60.1

75.3

90.2

105.5

120.7

136

151.2

-20

-15

-10

-5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000

Transverse Distance, mm

Relative Elevation, mm

0.6

15.9

31.1

46.3

61.9

76.8

92.1

107.6

123.2

138.1

153.4
6

Figure 3. Transverse profiles obtained on test section 811803 

on July 5, 1989 by PASCO. 

Figure 4. Transverse profiles obtained on test section 124107 

on March 9, 1994 by PASCO. 

-20

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-10

-5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000

Transverse Profile, mm

Relative Elevation, m

m

1.5

16.8

32

47.3

62.5

77.7

93

108.2

123.8

139

154.3

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-10

-5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000

Transverse Distance, mm

Relative Elevation, mm

0

15.5

31.1

46

61.3

76.2

91.5

106.7

122.3

137.5

152.7
7

given section have been taken, the operator performs a second set of “zero” and calibration 

checks to validate the measurements.(2) 

Data Processing 

The Dipstick data are entered manually into the PROQUAL software for quality assurance 

checks.(3) The checks performed by PROQUAL include a user review of a graph of the 

transverse profile and a check to ensure that the transverse loop falls within acceptable tolerance 

levels. PROQUAL also calculates a rut depth using the string line method for each wheelpath 

for each transverse profile entered; however, the rut depth data are not stored in the NIMS. 

These rut depths are easily recalculated from the data that are stored in the database. 

Figures 5 through 8 illustrate typical transverse profiles collected with the Dipstick. The 

legends on these figures provide the longitudinal location along the test section of the profile. 

Prior to February 1997, measuring transverse profiles using the Dipstick during manual distress 

surveys was encouraged, but not required, and a limited number of measurements were made. 

As of February 1997, all manual distress surveys conducted on asphalt-surfaced test sections are 

required to include transverse profile measurements taken with the Dipstick. A comparison of 

the Dipstick method and the PASCO method is discussed in chapter 3. 

1.2-m STRAIGHTEDGE 

In the past, lateral distortion differentials generally have been limited to measurements of rut 

depths using a straightedge (usually 1.2 m in length). The straightedge is placed across a 

wheelpath so that the vertical distance between the bottom of the straightedge and the pavement 

surface is maximized. This vertical distance is called the “rut depth.” One measurement is taken 

for each wheelpath every 15.2 m along the test sections. Straightedge measurements are required 

only on the SPS-3 sections.(2)

DATA AVAILABILITY 

All analyses completed for this study are based on data contained in Release 8.6 of the NIMS, 

dated October 1998. There were 4,127 sets of profiles in this data set, with 45,370 total 

transverse profiles. A set of profiles includes one profile measurement every 15.2 m. Of the 

4,127 sets of observations, 806 were collected by Dipstick and 3,321 were collected by 

PASCO. 

Usually, 11 profiles are taken per test section. The quality control checks performed on the 

NIMS do not require that all transverse profiles taken on the same day for a single test section 

pass the quality control checks at the same time. Therefore, some sets do not include the typical 

11 profiles. In addition, throughout the analysis, it was noted that a few of the sets of profiles 

taken with the Dipstick only included profiles for every 30.5 m, i.e., these sets of profiles only 

contained six profiles.
8

Figure 5. Transverse profiles obtained on test section 151003 on 

February 20, 1991 with a Dipstick. 

Figure 6. Transverse profiles obtained on test section 161010 on 

December 16, 1993 with a Dipstick. 

-20

-15

-10

-5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000

Transverse Distance, mm

Relative Elevation, mm

0

15.2

30.5

45.7

61

76.2

91.5

106.7

122

137.2

152.4

-20

-15

-10

-5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Transverse Distance, mm

Relative Elevation, mm

0

15.2

30.5

45.7

61

76.2

91.5

106.7

122

137.2

152.4
9

Figure 7. Transverse profiles obtained on test section 201010 on 

April 22, 1993 with a Dipstick. 

Figure 8. Transverse profiles obtained on test section 561007 on 

September 8, 1995 with a Dipstick.

-20

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-10

-5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000

Transverse Distance, mm

Relative Elevation, mm

0

15.2

30.5

45.7

61

76.2

91.5

106.7

122

137.2

152.4

-20

-15

-10

-5

0

5

10

15

20

0 500 1000 1500 2000 2500 3000 3500 4000

Transverse Distance, mm

Relative Elevation, mm

0

15.2

30.5

45.7

61

76.2

91.5

106.7

122

137.2

152.4

 11

CHAPTER 3. CALCULATION OF INDICES 

POTENTIAL INDICES 

Ten characterizations or indices of the transverse profile were chosen for study. Figures for 

these indices are provided in a later section of this chapter, which includes a more thorough 

description. These indices were selected from discussions with various experts and include the 

following: 

• Area of rut below and area of pavement above a straight line connecting the end points of 

the transverse profile. 

• Area between straight lines connecting the maximum surface elevations and the 

pavement surface. 

• Maximum depth for each wheelpath between a 1.2-m straightedge placed across a 

wheelpath and the surface of the pavement below the straightedge. 

• Maximum depth for each wheelpath between a 1.8-m straightedge placed across a 

wheelpath and the surface of the pavement below the straightedge. 

• Maximum depth for the outside wheelpath between a horizontal line from the edge of the 

pavement and the pavement surface (i.e., the depth of water that may accumulate before 

drainage onto the shoulder). 

• Maximum depth for the inside wheelpath between a horizontal line from the maximum 

elevation between the wheelpaths and the pavement surface (i.e., the maximum depth of 

water that may accumulate before drainage into the outer wheelpath, assuming elevations 

in an adjacent lane greater than the maximum depth between wheelpaths). 

• Maximum depth for each wheelpath between a wire line extended across the entire lane 

width and the pavement surface. 

• Width of rut. 

• Radius of curvature of deformation. 

• PASCO typecasting as described below. 

This list of characterizations includes the ideas of the research team, as well as those obtained 

during a literature review; discussions with the LTPP Distress Expert Task Group (ETG) at a 

meeting held in September 1997; discussions with PASCO, USA; and discussions with the Data 

Analysis ETG. The ETGs are part of an advisory structure operated by the Transportation 

Research Board (TRB), which advises the Federal Highway Administration (FHWA) on the 
 12

conduct of LTPP. As the name implies, the Data Analysis ETG provides guidance and support 

on issues concerning data analysis. The Distress ETG provides guidance and support on issues 

concerning the collection and interpretation of distress information. 

At the American Association of State Highway Officials (AASHO) Road Test, the rut depth was 

defined as the maximum depth for each wheelpath between a 1.2-m straightedge and the surface 

of the pavement below the straightedge.(4) Recent studies of rutting in hot-mix asphalt (HMA) 

pavements have defined rut depth as the maximum depth for each wheelpath between a 1.8-m 

straightedge and the surface of the pavement below the straightedge.(5-6) One shortcoming of the 

straightedge method is that it provides no indication as to the type of surface distortion that is 

occurring. 

ETG RECOMMENDATIONS 

Based on the recommendations of the Distress and Data Analysis ETGs, the rut depth and rut 

width based on a 1.2-m straightedge and the depth of water in each wheelpath were not 

considered in any further analyses. The positive and negative areas, the fill area, the rut depth 

and rut width from the 1.8-m straightedge, the rut depth and rut width from the lane-width wire 

line, and the radius of curvature were considered the most beneficial. The location of the rut 

depth based on the distance from the edge of the lane was added to serve as a diagnostic tool. 

For the remainder of the report, the terms “1.8-m rut depth” and “1.8-m rut width” refer to the rut 

depth or width of the rut based on a 1.8-m straightedge, respectively. In addition, the terms 

“wire line rut depth” and “wire line rut width” refer to the rut depth and width of the rut based on 

a lane-width wire line, respectively. 

METHOD OF CALCULATION 

The physical description of each index was examined with relationship to the transverse profile 

being collected for the purpose of determining how each index would be calculated. These 

methods of calculation were incorporated into a VisualBasic program entitled RUTCHAR. The 

RUTCHAR program, which was used to calculate each index from the transverse profile data, is 

discussed later in this chapter. 

Positive and Negative Areas 

As shown in figure 9, positive and negative areas are the areas of deviation between the 

pavement surface and a straight line connecting the end points of the transverse profile. The 

outcome from this calculation will be a positive area for the area below the pavement surface and 

above the straight line, and a negative area for the area above the pavement surface and below 

the straight line. These areas were easily determined, because the straight line is the x-axis. 
 13

A finite integral technique is employed. The best method to use is the trapezoidal rule since the 

distances between the points on the x-axis are not necessarily equal. This method assumes that a 

pair of x-y coordinates provides the four corners of a trapezoid. The area of the trapezoid is: 

Area = 1⁄2 (yi+1 + yi) (xi+1 – xi) (1) 

This value is calculated for each x-y pair where both y's have the same sign. If the y's change 

their sign, it is necessary to find the slope between the two points. The x coordinate (x0), where 

the line connecting the two points cross the x-axis, can be found by the following equation: 

 0

i

i

y x x

slope

= + (2) 

Figure 9. Illustration of the positive and negative area indices. 

-25

-20

-15

-10

-5

0

5

10

15

0 500 1000 1500 2000 2500 3000 3500 4000

X, mm

Y, mm

+

- -

+
 14

The area of the triangle between (xi, yi) and (x0, 0) can be determined, and the area of the triangle 

between (x0, 0) and (xi+1, yi+1) can be determined. 

Finally, the positive area is the sum total area where yi and yi+1 are greater than or equal to 0. 

The negative area is the sum total area where yi and yi+1 are less than or equal to 0. These two 

values can be used in conjunction as a sum (positive minus negative) or a ratio to indicate the 

amount of rutting affecting the pavement. 

Area of Fill 

The area of fill is the area in millimeters squared below the straight lines connecting the 

maximum surface elevations and above the pavement surface as shown in figure 10. This value 

describes the material required to “fill in” the ruts for a unit length of pavement. 

Figure 10. Illustration of the fill area index. 

The first step is to stretch an imaginary wire line across the pavement surface (i.e., the lane 

width). The fill area is defined as the area between the wire line and the pavement surface, and 

is calculated using the trapezoidal rule previously described. 

X, mm 

Fill Area Fill Area 

Pavement 

Surface 

Y, mm 
 15

Calculated Rut Depth Based on a 1.8-m Straightedge 

This rut depth is the maximum distance in millimeters in each wheelpath between a 1.8-m 

straightedge and the surface of the pavement, as shown in figure 11. The procedure described 

below provides the rut depth, width, and location for the left wheelpath (LWP) and is repeated 

for the other half of the lane to obtain the values for the right wheelpath (RWP). 

An iterative process was used to place the straightedge on each half of the lane. The distance 

between the points on which the straightedge sat never exceeded 1.8 m. When the maximum rut 

depth was determined for one-half of the lane, the exact distance between the points on which 

the straightedge sat and the location at which the maximum rut depth occurred was recorded. 

The same process was used for determining rut depth in each half of the lane. 

Figure 11. Illustration of the 1.8-m rut depth and 1.8-m rut width. 

Calculated Rut Depth Based on a Lane-Width Wire Line 

This rut depth, reported in millimeters, is the maximum distance for each wheelpath between a 

lane-width wire line placed across the lane and the pavement surface, as shown in figure 12. 

This value can best be visualized by imagining a wire stretched across the pavement surface so 

that it touches only the maximum elevation, or peaks, of the pavement surface. The rut depth is 

the distance between that wire and the pavement surface. 

The wire line is defined as a series of straight lines. When the wire line is established, the next 

step is to determine the distance of each x-y coordinate from the wire line. The lane is then 

divided into half. The rut depth in each wheelpath is the maximum distance between the wire 

line and the x-y coordinates in each half-lane. 

-6

-5

-4

-3

-2

-1

0

1

2

3

0 1000 2000 3000 4000

X, mm

Y, mm

1.8-m Rut Width

1.8-m Rut Depth
 16

The rut width is the difference in the x’s of the two peak points surrounding the rut depth in each 

wheelpath. The rut location is the value of x at which the maximum rut depth in each wheelpath 

occurred. 

Figure 12. Illustration of the wire line rut depth and the wire line rut width. 

Radius of Curvature 

The radius of curvature is the minimum radius of curvature of the surface profile in each 

wheelpath. Three points are required to uniquely define a circle. Initially, the radius of 

curvature was found by determining the radius of the circle defined by each set of three 

consecutive points. The radius of curvature reported in each wheelpath was the minimum radius 

for that half of the lane where the center of the circle was still above the surface of the pavement. 

Figures 13, 14, and 15 show examples of the circles circumscribed by this method. While these 

circles are geometrically correct, they do not provide any meaningful measure of the wheelpath. 

-6

-5

-4

-3

-2

-1

0

1

2

3

0 1000 2000 3000 4000

X, mm

Y, mm

3.7-m Rut Width

3.7-m Rut Depth
Figure 13. Transverse profile for test section 48A506 obtained on

March 9, 1995 by PASCO at station 91.5 m.

-1-2-3-4-5

6543210

0 500 1000 1500 2000 2500 3000 3500 4000

X, mm

Y, mm

17 
Figure 14. Transverse profile for test section 541640 obtained on 

September 29, 1992 by PASCO at station 152.4 m.

-2-4

86420

0 500 1000 1500 2000 2500 3000 3500 4000

X, mm

Y, mm

18 
Figure 15. Transverse profile for test section 36B340 obtained on 

October 9, 1995 by PASCO at station 92.7 m.

86420

1210

0 500 1000 1500 2000 2500 3000 3500 4000

X, mm

Y, mm

19 
 20

A second approach was considered in which a circle would be circumscribed for each wheelpath. 

If the pavement did not exhibit a definable depression in the wheelpaths, then a circle would be 

fitted to the mid-lane hump as shown in figure 16. However, in attempting to apply this concept, 

the profile shown in figure 17 was encountered. The question then became how to apply a circle 

to the wheelpaths or the mid-lane of this profile. From this evaluation, a decision was made to 

apply a parabola to each wheelpath rather than a circle. A parabola is defined as follows: 

(3) 

where: 

(h, k) = vertex of the parabola. 

p = distance between the focus and the vertex. 

Alternatively, one may say that “a parabola is the set of points in a plane that are equidistant 

from a given fixed point and a fixed line in the plane.”(7) The fixed point is the focus and the 

fixed line is the directrix. The value p is directly related to the width of the opening of the 

parabola. 

Each profile was examined to determine if any of the y values were negative. If at least four 

consecutive y-coordinates were negative, a parabola was fitted through those negative points. A 

least-squares regression was used to fit a quadratic equation to the x-y points. The equation fit 

was of the form: 

(4) 

and 

(5) 

The values reported from the regression were the p-value, the F-statistic, and R2

. The F and the 

R2

 were reported so that some judgment could be made as to the significance of the fit. This 

method was applied to the available data, but only 35 percent of the profiles had a statistically 

significant fit. 

The radius of curvature is not commonly used to measure rutting. Hence, to establish a 

minimum radius would be problematic. If the radius was too small, the value obtained would not 

necessarily be representative of what was occurring in the wheelpath. If the radius was too large, 

then some wheelpaths with very narrow rutting would be totally overlooked. Figure 16 does not 

show any definable wheelpaths; therefore, the proposal was to fit a parabola to the surface of the 

pavement with the opening of the parabola facing down rather than facing up as it would in a 

wheelpath. Figure 17 does not have a definable hump in the middle of the lane as seen in figure 

16. Neither a parabola nor a circle could be fit to the middle of the lane or the wheelpaths. Due 

to the difficulties in appropriately defining and calculating this index, no additional analyses 

were attempted. It is not recommended for inclusion in the database. 

( ) 4 ( ) 2x − h = p y − k

2 4

1

B p =

2

0 1 2 y = B + B x + B x
Figure 16. Transverse profile obtained for test section 566032 

obtained on August 26, 1996by PASCO at station 61 m. 

76543210

0 500 1000 1500 2000 2500 3000 3500 4000

X, mm

Y, mm

21 
Figure 17. Transverse profile for tests section 421610 obtained 

 on May 17, 1990 by PASCO at station 91.8 m. 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 500 1000 1500 2000 2500 3000 3500 4000

X, mm

Y, mm

22 
23 

PASCO Typecasting 

The typecasting method groups the individual profiles into one of 14 shape categories. Each 

profile in the database fits into one of the 14 categories illustrated in figures 18 and 19. The 

shape factor is the number shown at the left of each profile category. 

The shapes are based on the location of the rut in each half of the lane and the number of ruts 

present in each half of the lane. These shapes may provide a clue as to the rutting mechanism. 

However, the number of shapes that have been specified make it difficult to determine the 

category to which the profile belongs. Figure 17 is a good example of the problems encountered 

in determining shape factors. The middle of the section is the lowest point on the profile. The 

difficulty with this profile is deciding whether or not this is dual wheel-track rutting and how to 

automate this decision. For these reasons, it is recommended that this factor be excluded from 

the Information Management System (IMS). 

RUTCHAR PROGRAM 

Program Description 

Since there were in excess of 45,000 profiles, a VisualBasic program was written to automate the 

calculations of the rutting indices noted previously. It also calculates the means and standard 

deviations of each index. The user’s guide is provided in appendix A. 

The program provides two output files. The first file includes the indices for each transverse 

profile contained in the input file. This file also includes the lane width provided by the 

transverse profile, a flag indicating whether or not the profile was taken within the 152-m section 

limits, and flags on the individual indices. The second input file contains the mean, standard 

deviation, minimum, and maximum for each index for each transverse profile survey. 

Transverse profile measurements are to be taken every 15 m along the test section. Though the 

RoadRecon unit generally meets this requirement, it may record a measurement anywhere from 

0.2 m prior to the station or 0.1 m after the station. Since some of these profiles fall outside of 

the 152-m test section, these profiles are flagged and excluded from the section averages. 

The flags on the individual indices indicate a potential outlier. The values are flagged if they lie 

more than two standard deviations away from the mean. These values are still included in the 

mean and standard deviation calculations. The flag is provided as a tool for analysts. 
24 

Figure 18. PASCO typecasting shapes (shapes 0-6). 

X X

0

1

2

3

4

5

6

X X

Center Shoulder 
25 

Figure 19. PASCO typecasting shapes (shapes 7-13). 

7 

8 

9 

10 

11 

12 

13 

X X 

X 

X 

X 

X X 

X X 
26 

In addition to the output files, the program creates another file, DATCHK.OUT. This file 

contains the results of checks on the data. In the process of calculating the indices from the data 

extraction, two discontinuities were noted in the data. These discontinuities were encountered 

with the PASCO data only and are probably a result of the data processing. The first is a 

duplicate x-y point. In this case, the duplicate point was removed and all calculations were 

performed without the duplicate point. A message is written to DATCHK.OUT, which contains 

the State code, Strategic Highway Research Program (SHRP) ID, construction number, survey 

date, station, x, and “IS A DUPLICATE POINT.” 

The second discontinuity occurs when two y-values are shown for the same x-coordinate. In this 

case, the x-value is reduced by 1 mm, so the first x-y point is moved back by 1 mm. In this case, 

the same fields are written to DATCHK.OUT except that the message is changed to read “IS A 

DUPLICATE X”. A list of the profiles with these discontinuities was provided to FHWA. 

Program Verification 

The purpose of the verification process was to ensure that the program accurately calculated the 

indices, not to validate the physical representation of the indices. One hundred profiles were 

randomly selected from the data set for program verification. Each of the indices was calculated 

manually for each of the profiles. This program was used for calculating all of the indices for 

these profiles. The algorithm for each index was written and the program was run using the test 

set as the input file. The output was compared to the hand calculations and, if the data were not 

the same, the algorithm was reviewed. The process was reiterated using the test set until the 

program was found to accurately calculate each index. Appendix B provides the overall 

distribution of the indices calculated by the RUTCHAR program for the individual profiles and 

the section means. 

The complete data set was used to provide a final check of the program. Some relationships 

were known to exist between the indices prior to their calculations (for example, the rut depth 

calculated based on a lane-width wire line should be greater than the rut depth based on a 1.8-m 

straightedge). These relationships were used to confirm that the algorithms had been accurately 

programmed. 
 27

CHAPTER 4. INDEX COMPARISONS 

In order to identify the index or set of indices that would be most useful to practicing engineers, 

a set of comparisons were made. First, the indices were examined to determine the number of 

measurements required along each test section to get an accurate representation of the rutting on 

each section. Second, the indices were compared to each other. These comparisons allow for 

the determination of which indices provide the same general information about the transverse 

profile. Two indices are thought to be providing the same information if they are highly 

correlated. 

MINIMUM NUMBER OF MEASUREMENTS 

As previously stated, profiles are collected every 15.2 m. The question arose as to whether the 

number of profiles taken on each section could be reduced from 11 total observations (one 

profile every 15 m) to 6 total observations (one every 30 m) without sacrificing the accuracy. An 

analysis was conducted to determine the consequences of reducing the number of surveys. 

Specifically, the averages of the indices were determined, but only using the data measured every 

30 m. These values were then compared to the averages of all of the stations in a series of 

pairwise t-tests,(8) using a significance level of 0.05. 

The results from these tests are provided in appendix C. As can be seen in table 1, there is little 

difference between the two data sets. The 1.8-m RWP rut depth, 1.8-m RWP rut width, the wire 

line RWP rut depth, and the wire line rut width were the only indices for which the t-test was not 

significant. All of the results for the other indices showed a statistically significant difference. 

The mean differences for the indices were so small that they were within the capability of the 

equipment. For example, the difference in the LWP 1.8-m rut depths was 0.02 mm. Finally, the 

spread around the line of equality, as shown in the figures in appendix C, was quite narrow. The 

largest spread seen was in the rut widths. 

The first set of comparisons noted above included all of the available data. However, the 

question of the number of measurements necessary to accurately determine the amount of rutting 

on a test section originally arose with respect to the Dipstick data. If this reduction is 

appropriate, then the time required to collect the Dipstick transverse profiles would be reduced 

by almost half. Thus, a second set of comparisons was made that included only the Dipstick

data. These results are also shown in appendix C. This reduced data set exhibits exactly the 

same trends as the complete data set. 

The pairwise t-tests showed that using 6 observations (rather than 11) produced no overall bias in 

the estimate of the average rut depth. The standard deviation of an arithmetic average of n

observations is σ/ n. Hence, the curve y= n provides the relationship between the precision (y) 

and the number of observations (n). In this case, the relative precision is σ/ 6. Reducing the 

sample size from 11 to 6 increases σ/ n by 25 percent. 
 28

Table 1. Comparison of section means of all versus six measurements for all indices. 

Index p-Value Mean Difference 

Negative Area, mm2 0.0002 51 

Positive Area, mm2 0.0147 42 

Fill Area, mm2 0.0045 36 

1.8-m Rut Depth, LWP, mm 0.0046 0.02 

1.8-m Rut Width, LWP, mm 0.0465 2.3 

1.8-m Rut Depth, RWP, mm 0.7940 0.00 

1.8-m Rut Width, RWP, mm 0.9858 0.00 

Wire Line Rut Depth, LWP, mm 0.0019 0.02 

Wire Line Rut Width, LWP, mm 0.2825 2.6 

Wire Line Rut Depth, RWP, mm 0.1312 0.01 

Wire Line Rut Width, RWP, mm 0.6749 1.0 

Another approach for examining this question, which addresses sample size, was also 

investigated. In this approach, one determines the number of observations required to detect the 

difference in means μ2 and μ1. In this case, it is possible to determine the minimum number of 

samples required to detect, with 95 percent confidence, a specific level of bias.(8) The calculation 

is as follows: 

(6) 

where: 

n = sample size. 

σ

2

 = within-section variance of index. 

z = normal distribution statistic associated with α and β.

μ2-μ1 = bias or difference in means to be detected. 

α = level of significance, 5 percent. 

β = probability of false acceptance, 20 percent. 

Table 2 presents the results of these calculations for each index. The level of bias used to 

develop these numbers is provided in the (μ2 - μ1) column. 

2 2 1 /2 1

2 2 1

( )

( )

z z

n

σ α β

μ μ

− − +

− =
 29

Table 2. Results of sample size analysis, 11 versus 6 measurements. 

Index (μ2 - μ1) n 

Positive Area, mm2

Negative Area, mm2

Fill Area, mm2

LWP 1.8-m Rut Depth, mm 

RWP 1.8-m Rut Depth, mm 

LWP 1.8-m Rut Width, mm 

LWP 1.8-m Rut Location, mm 

RWP 1.8-m Rut Width, mm 

RWP 1.8-m Rut Location, mm 

LWP Wire Line Rut Depth, mm 

RWP Wire Line Rut Depth, mm 

LWP Wire Line Rut Width, mm 

LWP Wire Line Rut Location, mm 

RWP Wire Line Rut Width, mm 

RWP Wire Line Rut Location, mm 

3000 

3000 

3000 

2 

2 

100 

100 

100 

100 

2 

2 

100 

100 

100 

100 

9 

8 

8 

4 

5 

17 

29 

16 

35 

6 

6 

184 

26 

182 

35 

The data in this table illustrate that the only indices for which six profiles are acceptable are the 

rut depths. All other indices require at least 11. 

INDEX COMPARISONS 

The indices were compared to determine which were most likely to provide consistent 

information for a specific profile. If two indices provide consistent information, it will not be 

necessary to consider both indices in future analyses. Correlation between the indices indicates 

the strength of the relationship between two indices. For example, the 1.8-m rut depth and the 

wire line rut depth should be highly correlated because these values should be measuring the 

same information about the surface. Table 3 contains the correlation matrix for the indices.(8) As 

shown, some of the correlations are much stronger than others. Note that data from the 

individual profiles were used to generate the correlation matrix and other comparisons shown 

later in this section. A more detailed discussion of these results follows. 

The rut locations were not included in the correlation matrix. These values will be useful to 

analysts in examining trends in rut depths for individual profiles and sections. However, the 

location is of little value without the rut depth. It describes nothing about the severity or quality 

of the rut and it only provides the location of the wheelpath. For this reason, rut location was not 

included in the correlation matrix. 
Table 3. Correlation matrix for indices. 

 Negative 

Area, 

mm2 

Positive 

Area, 

mm2

Fill 

Area, 

mm2

1.8-m Rut 

Depth, 

LWP, mm 

1.8-m Rut 

Width, 

LWP, mm 

1.8-m Rut 

Depth, 

 RWP, mm 

1.8-m Rut 

Width, 

RWP, mm 

Wire Line 

 Rut Depth, 

LWP, mm 

Wire Line 

Rut Width, 

LWP, mm 

Wire Line 

Rut Depth, 

RWP, mm 

Wire Line 

Rut Width, 

RWP, mm 

Negative Area 1.0000 0.4967 -0.9098 -0.6443 -0.3239 -0.6757 -0.3691 -0.7748 -0.5633 -0.7904 -0.5846 Positive Area 0.4967 1.0000 -0.4225 -0.2694 -0.3971 -0.2640 -0.4067 -0.3428 -0.5247 -0.3269 -0.5311 Fill Area -0.9098 -0.4225 1.0000 0.8045 0.3906 0.8372 0.4355 0.8985 0.4956 0.9186 0.5220 1.8-m Rut Depth, LWP 

-0.6443 -0.2694 0.8045 1.0000 0.3851 0.7392 0.2843 0.9555 0.2339 0.7191 0.2127 

1.8-m Rut Width, LWP 

-0.3239 -0.3971 0.3906 0.3851 1.0000 0.2390 0.2677 0.4293 0.5707 0.2710 0.3224 

1.8-m Rut Depth, RWP 

-0.6757 -0.2640 0.8372 0.7392 0.2390 1.0000 0.4070 0.7249 0.1955 0.9639 0.2691 

1.8-m Rut Width, RWP 

-0.3691 -0.4067 0.4355 0.2843 0.2677 0.4070 1.0000 0.3228 0.3218 0.4420 0.5994 

Wire Line Rut Depth, LWP 

-0.7748 -0.3428 0.8985 0.9555 0.4293 0.7249 0.3228 1.0000 0.4011 0.7683 0.3697 

Wire Line Rut Width, LWP 

-0.5633 -0.5247 0.4956 0.2339 0.5707 0.1955 0.3218 0.4011 1.0000 0.3320 0.8541 

Wire Line Rut Depth, RWP 

-0.7904 -0.3269 0.9186 0.7191 0.2710 0.9639 0.4420 0.7683 0.3320 1.0000 0.4089 

Wire Line Rut Width, RWP 

-0.5846 -0.5311 0.5220 0.2127 0.3224 0.2691 0.5994 0.3697 0.8541 0.4089 1.0000 

30 
31

Rut Widths 

In general, the correlation matrix shows that the 1.8-m rut widths are not very highly correlated 

with any of the other indices. A paired t-test was performed to compare the values in the two 

wheelpaths. The results indicate that there is a significant statistical difference between the 

wheelpaths. The dispersion of the data was so large that it appears that almost any line could be 

fitted. This shows that there is virtually no relationship between the rut widths of the LWP and 

RWP. One potential cause of the differences observed in the rut widths between the two 

wheelpaths is the varying distances between wheels from one vehicle to another. If the drivers 

of the various vehicles tend to follow a particular path, the rut width for a particular wheelpath 

could be fairly narrow, while the other is fairly wide. 

The 1.8-m rut widths had the highest correlation with the wire line rut widths. Paired t-tests 

were performed to compare the 1.8-m rut widths to the wire line rut widths. The 1.8-m rut width 

cannot exceed 1,800 mm as defined by the straightedge length. Generally, where the rut width 

for the lane-width wire line was less than 1,800 mm, the 1.8-m rut width was the same value. In 

most cases, the rut width was greater than 1,800 mm as determined by the wire line. Therefore, 

the 1.8-m rut width is not recommended for widespread use in the analysis of rutting. 

A second boundary was observed at approximately 3,700 mm. For computational purposes, the 

imaginary wire stretched across the pavement surface is the same width as the lane. Most of the 

sections included in the LTPP program are 3.7 m wide, which is the location of the upper 

boundary. However, a few of the sections are almost 4.3 m wide, which accounts for data points 

above the 3,700-mm boundary. 

The highest correlation for the wire line rut width was between the wheelpaths. A paired t-test 

comparing the values for each wheelpath also was conducted. The test was statistically 

significant. The graph shows a large amount of scatter in the bottom left corner of the graph, 

though there appears to be a clear upper boundary as shown by the diagonal line. Those points 

not falling on the line of equality have different rut widths for each wheelpath. The boundary 

occurs when the sum of the rut widths in each wheelpath equals the lane width. Beyond that 

point, the rut widths fall exactly on the line of equality. If the sum of the rut widths is greater 

than the lane width, and the rut widths for the two wheelpaths fall on the line of equality, then 

the middle portion of the transverse profile is lower than the outside edges. 

The 1.8-m rut widths and the wire line rut widths should provide the same general measure of the 

transverse profile. However, these two indices are not correlated. When the wire line rut width 

is used, data from either wheelpath may be sufficient to accurately describe the profile. 

Rut Depths 

The highest correlations shown are between the 1.8-m rut depths and the wire line rut depths. 

Figures 20 and 21 show the results from a paired t-test for the LWP and RWP, respectively. The 

figures show that the 1.8-m rut depths are never more than the wire line rut depths. In general, 

the values are not the same, but they are closely related. The correlation between the wheelpaths 
32

for each rut depth is moderate. The rut depth in one wheelpath is a reasonable indicator of the 

rut depth in the other wheelpath. 

Figure 20. Paired t-test comparing LWP 1.8-m rut 

depths versus the LWP wire line rut depths. 

LWP 3.7 By LWP 1.8

0

10

20

30

40

0 10 20 30 40

LWP 1.8

Paired t-Test

Paired t-Test

LWP 1.8 - LWP 3.7

Mean Difference

Std Error

t-Ratio

DF

-0.65493

0.006047

-108.312

 45369

 Prob > |t|

Prob > t

Prob < t

0.0000

1.0000

0.0000
33

Figure 21. Paired t-test comparing the RWP 1.8-m rut 

depths versus the RWP wire line rut depths. 

RWP 3.7 By RWP 1.8

0

10

20

30

40

50

60

0 10 20 30 40 50 60

RWP 1.8

Paired t-Test

Paired t-Test

RWP 1.8 - RWP 3.7

Mean Difference

Std Error

t-Ratio

DF

-0.65246

0.006054

-107.764

 45369

 Prob > |t|

Prob > t

Prob < t

0.0000

1.0000

0.0000
34

Areas 

The fill area was fairly highly correlated to the rut depths. As noted previously, fill area is the 

volume of material required to “fill in” the ruts for a unit length of pavement. This value is 

essentially a two-dimensional representation of the rut or the rut width multiplied by the rut 

depth. By definition, it must show good correlation with the rut depths. However, for this 

reason, it was expected that the wire line rut width would also have a relatively large correlation 

with the fill area. However, just the opposite was observed when the correlations were 

examined. 

The fill area also had a good correlation with the negative area. Figure 22 illustrates the 

relationship between these two indices. The fill area can be more than the absolute value of the 

negative area, but it can never be less. A fairly strong relationship was found between the fill 

area and the negative area. This is expected, because if the positive area is 0, the fill area and the 

negative area should be the same. Comparing the fill area to the negative area can be used as a 

quality control check on the data. 

Summary 

In general, the 1.8-m rut depth and the wire line rut depths provide the same measure of the 

rutting. The negative area and the fill area may indicate the same causes of the rutting. The 1.8-

m and wire line rut widths generally provide the same type of information, though not highly 

correlated. The positive area does not provide the same information as any of the other indices. 

Each index recommended for inclusion in the IMS has advantages and disadvantages. Rut depth 

is the most widely used index and many engineers have a good understanding of the range of rut 

depths typically encountered. However, this value alone provides only a one-dimensional 

measure of rutting. 

The rut width provides data on the second dimension of rutting. Without using the rut depth in 

addition to the rut width, the severity of rutting is difficult to quantify. Since this parameter is 

not typically measured, most people may not have a feel for the range of rut widths that they may 

encounter. 

The areas provide a two-dimensional characterization of the rutting. Because none of the area 

indices have been used widely in the past as with the rut widths, it may take some time to 

develop a good understanding of the range of values that may be encountered. The fill area 

could be useful to the State Highway Agencies (SHAs) for determining initial estimates of 

volumes of material to be used in a leveling course. Because this index is two-dimensional, a 

deep narrow rut will have the same value as a wide shallow rut. Finally, it is hypothesized that 

the combined use of the positive and negative areas may be indicative of the cause of the rutting. 

Trenching would be required to test this hypothesis. 
35

Figure 22. Comparison between the negative area index and the fill area index. 

Area Fill By Area Neg

0

10000

20000

30000

40000

50000

60000

70000

80000

-80000 -60000 -40000 -20000 0

Area Neg

Linear Fit

Linear Fit

Area Fill = 5331.75 û 0.91453 Area Neg

Summary of Fit

RSquare

RSquare Adj

Root Mean Square Error

Mean of Response

Observations (or Sum Wgts)

0.811252

0.811248

3741.927

10813.19

 43841

Analysis of Variance

Source

Model

Error

C Total

DF

 1

43839

43840

Sum of Squares

2.6383e+12

6.13835e11

3.25214e12

Mean Square

2.638e12

14002020

F Ratio

188422.9

Prob>F

 0.0000

Parameter Estimates

Term

Intercept

Area Neg

Estimate

5331.7545

-0.914532

Std Error

21.88248

0.002107

t Ratio

243.65

-434.1

Prob>|t|

0.0000

0.0000

37

CHAPTER 5. INDEX EVALUATION 

This chapter examines the relationship of each index to the other pavement parameters. These 

parameters include such items as age, base type, and HMA thickness. This analysis examines 

how the indices behave with respect to the wire line depth. In this way, the reader may gain 

more familiarity with these unfamiliar values. Furthermore, this analysis begins the process of 

discerning which indices may be useful in determining the mechanism causing the rutting. Any 

index that is affected by subgrade type provides information about how the surface rutting is 

affected by the subgrade. 

A preliminary study was conducted to assess the variability of each index since most of the 

analyses conducted in this chapter use the section mean. Table 4 presents the ranges of the 

within-section standard deviations. As is evident, the ranges are quite broad. Each index, except 

the fill area, has some surveys for which the standard deviation is 0. Note that a standard 

deviation of 0 for the rut depths is the result of rounding off the data. The difference between the 

minimum and maximum rut depths for the cases where a standard deviation of 0 was found was 

typically 1 or 2 mm. The rut widths and rut locations that have a standard deviation of 0 were 

obtained from data that were collected by the Dipstick. In these cases, the data for that survey 

were fairly uniform, such that even with the variations in the y-values collected, no variation was 

seen in the calculated indices. Finally, the surveys for which the negative area or the positive 

area has a 0 standard deviation merely indicates that all 11 profiles for each survey were either 

all above the horizontal datum or all below the horizontal datum. 

Some of the test sections are extremely uniform, as shown by the minimum standard deviation of 

0, while other test sections are quite variable. In general, the larger variabilities were seen in test 

sections with larger amounts of permanent deformation. This is illustrated by the range of the 

coefficient of variation (COV) shown in table 5. For the positive and negative areas where the 

standard deviation was 0, the mean was also 0. Because the COV was incalculable, the 

minimum shown in table 5 for these indices was not 0. 

SECTION COMPARISONS 

The section means were compared to determine how each index varied with some of the basic 

pavement parameters, such as surface thickness, climatic zone, subgrade type, and age. While 

many researchers and State highway personnel are familiar with rut depth (how it develops and 

the general magnitude of the value), it is anticipated that not nearly as many are familiar with the 

area indices or rut widths. 
38

Table 4. Range of standard deviations for each index. 

Standard Deviation Index 

Minimum Mean Maximum 

Negative Area 

Positive Area 

Fill Area 

1.8-m Rut Depth, LWP 

1.8-m Rut Location, LWP 

1.8-m Rut Width, LWP 

1.8-m Rut Depth, RWP 

1.8-m Rut Location, RWP 

1.8-m Rut Width, RWP 

Wire Line Rut Depth, LWP 

Wire Line Rut Location, LWP 

Wire Line Rut Width, LWP 

Wire Line Rut Depth, RWP 

Wire Line Rut Location, RWP 

Wire Line Rut Width, RWP

0 

0 

206 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0

3,128 

3,552 

3,096 

2 

213 

181 

2 

227 

184 

2 

210 

457 

2 

229 

459 

19,164 

27,616 

18,373 

11 

700 

796 

18 

737 

774 

11 

685 

1,915 

18 

755 

1,915 

Table 5. Range of COVs for each index. 

Coefficient of Variation, % Index 

Minimum Maximum 

Negative Area 

Positive Area 

Fill Area 

1.8-m Rut Depth, LWP 

1.8-m Rut Width, LWP 

1.8-m Rut Location, LWP 

1.8-m Rut Depth, RWP 

1.8-m Rut Location, RWP 

1.8-m Rut Width, RWP 

Wire Line Rut Depth, LWP 

Wire Line Rut Location, LWP 

Wire Line Rut Width, LWP 

Wire Line Rut Depth, RWP 

Wire Line Rut Location, RWP 

Wire Line Rut Width, RWP

-7 

5 

5 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

-350 

367 

329 

100 

124 

28 

200 

146 

123 

100 

26 

135 

200 

146 

123 
39

 

The comparisons in this section were used to examine the relationship between each index and 

standard materials characteristics and pavement parameters. These analyses were limited to 

simple comparisons of the indices between various groups. In all likelihood, the rutting observed 

on the surface is not due to just one factor, but rather to a combination of factors. In each case 

examined, the statements made are broad, sweeping claims that are only true if all the other 

conditions are equivalent. These supplemental analyses were conducted to determine whether 

the other indices behave in the same manner as the rut depth, which is better understood. 

The test sections were divided into groups based on the parameter of interest, such as the age of 

the pavement or the thickness of the HMA layer. The group means were then compared using a 

Student’s t-test with an α-level of 0.05. This provides a 95 percent level of confidence that the 

means are different. A test also was performed to determine whether the variances for each 

group were the same. All of these results are provided in appendix E. The distributions by GPS 

and SPS experiments are provided in appendix B. 

Pavement Age 

A linear regression was performed to determine how each index varied by age. Table 6 provides 

the results from each of the regressions for the GPS-1 experiment, HMA over granular base. A 

simple linear regression of the form y = mx + b was used. In this case, y was the rutting index of 

interest. The coefficient (or slope), m, is provided in table 6. The age was x and the y-intercept 

was b or the value of the index at time 0. The F-statistic and the “Prob>F” provide the level of 

significance. The “Prob>F” is the probability of finding a larger F by pure chance. The 

regression is considered significant for a probability of less than 0.05.(8) The last value in the 

table is the coefficient of age from the linear regression or the slope of the line fit through the 

data. 

These analyses show that the only indices that do not change significantly with age are the 1.8-m 

and wire line rut widths. At first, it appears that the negative area improves with age. However, 

the negative area is a negative number; therefore, a negative coefficient simply indicates that the 

negative area gets more negative (increases) with age. The sign of the coefficients for all of the 

other indices with significant regressions is positive. Because these are all positive numbers, 

these indices increase with time. Note that the coefficients for the 1.8-m and the wire line rut 

depths are the same and corroborate the fairly large correlation shown between these indices in 

chapter 4. In summary, the area and rut depth indices all increase with age, as expected. 

Table 7 provides the results for the GPS-2 experiment, HMA over stabilized base. These results 

are similar to those for HMA over granular base. The 1.8-m and wire line rut widths did not 

have significant results except for the RWP 1.8-m rut width, which had a negative slope. This 

indicates that the RWP 1.8-m rut width decreases (the width gets narrower) with time. The 

results for the negative area also were insignificant. The other indices with significant results 

increased with time. While the coefficients for the 1.8-m and wire line rut depths are not as 

similar to each other as those for the HMA sections on granular base, these values lie within a 

narrow range. 
40

Table 6. Results from comparisons with age for the GPS-1 section means. 

Index F Prob>F Coefficient 

Negative Area 

Positive Area 

Fill Area 

1.8-m LWP Rut Depth 

1.8-m LWP Rut Width 

1.8-m RWP Rut Depth 

1.8-m RWP Rut Width 

Wire Line LWP Rut Depth 

Wire Line LWP Rut Width 

Wire Line RWP Rut Depth 

Wire Line RWP Rut Width 

5.5967 

8.7846 

13.4480 

22.3839 

0.0537 

12.8283 

0.1082 

22.6285 

1.8210 

11.9857 

1.7074 

0.0182 

0.0031 

0.0003 

<0.0001 

0.8168 

0.0004 

0.7423 

<0.0001 

0.1775 

0.0006 

0.1916 

-105 

142 

162 

0.10 

-0.2 

0.08 

-0.4 

0.10 

-4.7 

0.09 

-4.7 

Table 7. Results from comparisons with age for the GPS-2 section means. 

Index F Prob>F Coefficient 

Negative Area 

Positive Area 

Fill Area 

1.8-m LWP Rut Depth 

1.8-m LWP Rut Width 

1.8-m RWP Rut Depth 

1.8-m RWP Rut Width 

Wire Line LWP Rut Depth 

Wire Line LWP Rut Width 

Wire Line RWP Rut Depth 

Wire Line RWP Rut Width 

0.7411 

7.6285 

7.0746 

10.5178 

1.8177 

5.8403 

5.5479 

11.3622 

1.6629 

6.9163 

3.0783 

0.3897 

0.0059 

0.0080 

0.0012 

0.1788 

0.0160 

0.0188 

0.0008 

0.1977 

0.0088 

0.0799 

-43 

194 

127 

0.07 

-2.3 

0.05 

-4.5 

0.08 

-6.4 

0.07 

-8.9 
41

Experiment Comparisons 

Next, the indices for the HMA over granular base experiment were compared to those observed 

on test sections in the GPS-7 experiment, HMA overlay of portland cement concrete (PCC). 

These results are provided in appendix E. No significant difference was seen between the two 

experiments for the positive area and the LWP wire line rut width. For all of the other indices, 

the test sections with HMA over granular base had greater amounts of rutting than the HMA 

overlay of PCC sections. It is anticipated that the HMA overlay of PCC sections would have less 

rutting than the GPS-1 sections. Rutting potentially could occur in any layer of the structure in 

the HMA over granular base sections. However, since no rutting is expected to occur in the PCC 

layer, rutting should be limited to the HMA overlay in the GPS-7 sections. This should limit the 

total amount of rutting that does occur. In this comparison, the positive area does not behave in 

the same manner as the other indices. This index probably does not provide the same information about the transverse profile as the other indices. 

Thickness of Asphalt Concrete Layers 

The test sections in the GPS-1 (HMA over granular base) and GPS-2 (HMA over stabilized base) 

experiments were grouped by the thickness of the HMA surface. If the section had less than 76 

mm of HMA surface, it was placed in the thin group. If a section had between 76 mm and 178 

mm of HMA, it was placed in the moderate group. If the section had more than 178 mm of 

HMA, it was placed in the thick group. The thick sections had significantly more negative area 

and less positive area than the other two groups. The thick sections had larger RWP 1.8-m rut 

widths than the thin or moderate sections. The thin sections had smaller LWP 1.8-m rut widths 

than the moderate or thick sections. The thin sections had smaller LWP 1.8-m rut depths and 

LWP wire line rut widths. In general, the thicker asphalt sections had wider ruts. 

Base Stabilization 

The sections in the GPS-1 (HMA over granular base) and GPS-2 (HMA over stabilized base) 

experiments with less than 127 mm of HMA were selected for further study. In general, the 

rutting of thin asphalt pavements is expected to be governed by base and subgrade properties. 

Therefore, the set of sections used were limited to those that would be considered thin-surfaced. 

These sections were divided into two groups based on whether or not the base had been 

stabilized, and comparisons were made between the two groups. The results are provided in 

appendix E. 

All of the indices, except positive area, were larger for the sections with granular bases than for 

those with stabilized bases. The test sections with granular bases exhibited smaller positive area 

than the sections with stabilized bases. In theory, and all else being equal, the stabilized bases 

will do a better job of distributing the load on the subgrade. The improved load distribution 

should prevent some of the accumulation of rutting (or permanent deformation) in the lower 

portion of the structure, such as the base and subgrade. Therefore, the sections with stabilized 

bases should perform better than those with granular bases. 
42

The sections with stabilized bases subsequently were divided into two groups based on whether 

the base was portland cement-stabilized (cement) or asphalt-stabilized (asphalt). The test 

sections in the cement group had larger positive areas, on average, than the sections in the 

asphalt group. Otherwise, all of the indices were larger, on average, for the sections in the 

asphalt group than for the sections in the cement group. In general, a cement-stabilized material 

is expected to be stiffer than an asphalt-stabilized material. The stiffer material should prevent 

rutting in the underlying layers. Therefore, the sections with a cement-stabilized base should 

accumulate less rutting than those with an asphalt-stabilized base, assuming that all other 

conditions are equal. It was expected that the indices would be larger for the sections with an 

asphalt-stabilized base than for those with a cement-stabilized base. 

Climatic/Environmental Zones 

For the last set of comparisons, the GPS-7 (HMA overlay of PCC) sections were used to 

examine the trends of the indices by environmental zones. These test sections 

 were divided into freeze (F) and no-freeze (NF) based on the freeze index. If the freeze index 

was greater than 56°C-days, the section was considered to be in a freeze zone. If the freeze 

index was less than 56°C-days, the section was considered to be in a no-freeze zone. These 

results are also provided in appendix E. 

The no-freeze zone had more negative area, more fill area, larger 1.8-m rut depths, larger wire 

line rut depths, and larger wire line rut widths in the LWP than the freeze zone. There were no 

significant differences observed in the positive area, 1.8-m rut widths, and RWP wire line rut 

widths. The rut widths in this case were not larger for the sections in the warmer climate. The 

positive area is not just a measure of rutting, but also may be a measure of heave. The lack of a 

significant difference for the positive area and the rut widths should not be a cause for concern as 

these indices are providing new information about the transverse profile. 

Theoretically, larger rutting should occur in the overlay in a warm climate. Those indices most 

closely related to the severity of rutting increase in the no-freeze environment. 

Summary 

For most of the groups described above, the indices performed in a manner that is consistent with 

theory. Sections with a stiff structure exhibited less rutting. The GPS-7 (HMA overlay of PCC) 

sections had larger indices than the GPS-1 (HMA over granular base) sections. Stiff base types 

had smaller indices than the less stiff base types. In addition, GPS-7 sections in warm climates 

had more rutting, or larger indices, than those in cool climates. However, the rut width and 

positive areas were the least likely to conform to generally accepted, albeit simplistic, theory on 

how rutting progresses. This indicates that as a rut gets deeper, it does not necessarily get wider. 
43

VARIABILITY COMPARISONS 

Table 5 listed the minimum and maximum within-section COV. A check was made to determine 

how the COVs varied with changes in structure and environment. Table 5 provided the range of 

COVs for all of the data in the database. Table 8 provides the minimum, mean, and maximum 

within-section COV for the test sections in the GPS-1 and GPS-2 experiments. 

Table 8. Distribution of within-section COVs for GPS-1 and GPS-2 experiments. 

Index Minimum Mean Maximum 

Negative Area 

Positive Area 

Fill Area 

1.8-m LWP Rut Depth 

1.8-m RWP Rut Depth 

1.8-m LWP Rut Width 

1.8-m RWP Rut Width 

Wire Line LWP Rut Depth 

Wire Line RWP Rut Depth 

Wire Line LWP Rut Width 

Wire Line RWP Rut Width 

-7 

6 

6 

0 

0 

0 

0 

0 

0 

0 

0 

-87 

82 

28 

28 

29 

14 

14 

28 

29 

25 

26 

-350 

367 

329 

100 

200 

124 

123 

100 

200 

135 

123 

Table 8 illustrates that the distribution of the within-section variation is similar for the indices. 

The mean COV for the negative and positive areas are larger than the other means, but the rest of 

the values are close. The sections were then divided into a “thin” group if the HMA surface was 

less than 127 mm or a “thick” group if the HMA surface was greater than 127 mm. Table 9 

provides the ranges of COVs for these two groups. 

Not much difference is observed between the two groups. The number of observations in the 

thin group is 716 and the number of observations in the thick group is 711. 

Further examination of the indices variability with structure is based on a comparison between 

those sections with a thin surface and a granular base and those sections with a thick surface and 

a stabilized base. Table 10 includes these results. In this table, “weak” refers to a pavement that 

has less than 76 mm of HMA and a granular base, while “strong” refers to a pavement that has 

more than 76 mm of HMA and a stabilized base. 
44

Table 9. Distribution of within-section COVs for thin and thick test sections. 

Thin Thick Index 

Min. Mean Max. Min. Mean Max. 

Negative Area 

Positive Area 

Fill Area 

1.8-m LWP Rut Depth 

1.8-m RWP Rut Depth 

1.8-m LWP Rut Width 

1.8-m RWP Rut Width 

Wire Line LWP Rut Depth 

Wire Line RWP Rut Depth 

Wire Line LWP Rut Width 

Wire Line RWP Rut Width 

-8 

7 

6 

0 

0 

0 

0 

0 

0 

0 

0 

-87 

82 

29 

29 

29 

14 

15 

29 

29 

25 

26 

-350 

367 

329 

100 

200 

124 

123 

100 

200 

135 

123 

-7 

7 

7 

0 

0 

0 

0 

0 

0 

0 

0 

-83 

85 

26 

27 

29 

12 

12 

27 

28 

24 

25 

-350 

333 

115 

100 

100 

96 

102 

100 

100 

96 

102 

Table 10. Distribution of within-section COVs for weak and strong structures. 

Weak Strong Index 

Min. Mean Max. Min. Mean Max. 

Negative Area 

Positive Area 

Fill Area 

1.8-m LWP Rut Depth 

1.8-m RWP Rut Depth 

1.8-m LWP Rut Width 

1.8-m RWP Rut Width 

Wire Line LWP Rut Depth 

Wire Line RWP Rut Depth 

Wire Line LWP Rut Width 

Wire Line RWP Rut Width 

-8 

8 

7 

0 

0 

0 

0 

0 

0 

0 

0 

-81 

86 

29 

28 

30 

13 

12 

29 

30 

25 

25 

-341 

367 

171 

100 

100 

124 

123 

100 

100 

135 

123 

-13 

8 

9 

0 

0 

0 

0 

0 

0 

0 

3 

-93 

75 

27 

30 

29 

14 

15 

30 

29 

24 

25 

-340 

277 

84 

100 

100 

54 

102 

100 

100 

80 

102 
45

There were 401 sections in the weak group and 173 sections in the strong group. The maximum 

COV is lower for the strong group than for the weak group; however, the difference may be due 

to the number of test sections. No conclusions can be drawn from these data. 

TIME-SERIES STABILITY 

Each index from each section was plotted by survey date. In this analysis, the section means of 

the indices were used. A line was fitted through the points. In some cases, only two points in 

time were available. If more than two points were available, least-squares regression was used to 

fit the line to the data.(8) Generally, even if the data do not follow a linear trend, if they increase 

with time, a line fit to the data will have a positive slope. The plots and regressions were used to 

examine the time-series trends exhibited by the indices. 

Slope Comparisons 

The slopes of the lines fitted to the data were placed in a separate database. The sign of the slope 

for each index was compared to the sign on the RWP 1.8-m rut depth. The 1.8-m rut depth is a 

quantity that has been used on many occasions and its response to various conditions is fairly 

well documented. The expectation is that the rut depth will usually increase with time. 

Occasionally, a section of roadway may experience frost heave or swelling soil and, in this case, 

the rut depth could decrease. The results for these analyses, as well as the distributions of the 

slopes, are provided in appendix F. 

The cross tabs, or contingency tables, provide a count for each of the cells.(8) The –1 indicates a 

negative slope, 0 indicates a zero slope, and +1 indicates a positive slope. In the first figure in 

appendix F, the slopes for the negative area are compared to those for the RWP 1.8-m rut depth. 

Only 20 percent of the test sections had the same slope. The negative area is a negative number. 

For the size of the negative area to increase over time, the slope of the line has to be negative. 

This means that for the negative area to exhibit the same trend as the 1.8-m rut depth (i.e., 

increasing in size when the rut depth increases in size), its slope must be opposite in sign. A 

second review of the table illustrates that the slopes for the negative area are opposite in sign 

from the slopes for the RWP 1.8-m rut depth 64 percent of the time. The negative area index 

should not be expected to behave the same way over time as the RWP 1.8-m rut depth. 

The positive area was examined in comparison to the RWP 1.8-m rut depth. For one section of 

793 total sections, the positive area exhibited a 0 slope where the RWP 1.8-m rut depth exhibited 

a positive slope. The slope for the rut depth on this section was 0.0003. In all other instances, if 

the RWP 1.8-m rut depth exhibited a zero slope, the positive area exhibited a zero slope, and if 

the positive area exhibited a zero slope, the RWP 1.8-m rut depth exhibited a zero slope. For 39 

percent of the sections, the slopes for the two indices had the same sign. For the amount of 

rutting to increase significantly, the amount of positive area will probably decrease. In this case, 

the sign of the positive area over time would be the opposite of the sign of the RWP 1.8-m rut 

depth. A second review of the contingency table shows that 44 percent of the sections are the 

opposite in sign. Based on this review, the positive area may not exhibit consistent trends with 

the RWP 1.8-m rut depth. 
46

The fill area, LWP 1.8-m rut depth, and the wire line rut depths were all fairly highly correlated 

with the RWP 1.8-m rut depth, so the slopes were expected to be similar. In addition, if the rut 

depth increases, the fill area and other rut depths should increase. The contingency tables for 

each of these indices reveal that if the RWP 1.8-m rut depth exhibited a zero slope, then the other 

indices also exhibited a zero slope and vice versa. In addition, the slopes had the same sign for 

85 percent of the sections for the fill area, 82 percent of the sections for the LWP 1.8-m rut 

depth, 95 percent of the sections for the RWP wire line rut depth, and 82 percent of the sections 

for the LWP wire line rut depth. This analysis indicates that these indices will follow the same 

general trends as the RWP 1.8-m rut depth. 

The 1.8-m rut widths and the wire line rut widths were the last set of indices to be examined. 

The slopes for these indices were all zero when the slope for the RWP 1.8-m rut depth was zero. 

The slopes had the same sign for 67 percent of the sections for the RWP 1.8-m rut width, 63 

percent of the sections for the LWP 1.8-m rut width, 69 percent of the sections for the RWP wire 

line rut width, and 66 percent of the sections for the LWP wire line rut width. These values 

indicate that these indices may not follow the same trend as the RWP 1.8-m rut depth. 

Check for Decreasing Ruts 

The next step in examining the time-series trends was to review the plots to determine if there 

were significant decreases or increases on any of the test sections. Again, the section means 

were used rather than the individual index. A threshold value was set for this examination. The 

decrease had to be larger than these values before it was reported. An estimate of error of 2 mm 

was used in the examination of rut depths. An error in the rut widths was allowed to be as high 

as 100 mm before it was reported. The area indices were all allowed to have an error of 1,000 

mm

2

. Initially, 4,133 sections were reviewed to obtain the list provided in table 11. 

These decreases may be due to a number of causes, such as frost heave or swelling soils. 

Alternatively, they may be due to maintenance or rehabilitation of the test section. These trends 

were noted on test sections where both the PASCO RoadRecon unit and the Dipstick had been 

used to collect data; however, not all sections where both equipment had been used to collect 

data exhibited this type of trend. Another factor that might contribute to this trend is the fact that 

the measurements are never taken at exactly the same station in consecutive surveys. While 

Dipstick surveys generally repeat the same stations on each survey, the PASCO RoadRecon 

unit will not be able to achieve such accuracy. Table 11 includes a list of test sections that 

exhibited these decreases and possible explanations. 

The trends reviewed were of the section averages. When all of the sections with decreasing 

trends were identified, the trends for the individual stations within each test section were 

reviewed. With the exception of one or two stations in any given section, the individual stations 

followed the same trends as the section averages. Next, the longitudinal profile and distress data 

were identified to determine whether these exhibited a similar decrease. A decrease in the 

International Roughness Index (IRI) or other distress would have been indicative of a 

maintenance or rehabilitation event. As seen in the table, many of the trends can be attributed to 
47

Table 11. Time-series stability trends. 

Section 

ID 

Index Potential Explanation 

021001 Pos Area No explanation 

041001 All Areas Use of both PASCO and Dipstick for measurement 

041002 All Use of both PASCO and Dipstick for measurement 

041003 All Distress decreased from May 1993 to Jan. 1994, suggesting 

rehabilitation or maintenance 

041006 All Distress decreased from May 1993 to Jan. 1994, suggesting 

rehabilitation or maintenance 

041007 All Distress decreased from Sept. 1994 to Feb. 1995, 

suggesting rehabilitation or maintenance 

041015 Fill, Neg Areas; Widths Use of both PASCO and Dipstick for measurement 

041017 Widths Use of both PASCO and Dipstick for measurement 

041022 Neg, Fill Areas, Depths, 

Widths 

Appears to be maintenance or rehabilitation, but not 

enough distress or longitudinal profile data available to 

verify 

041034 Depths Use of both PASCO and Dipstick for measurement 

068153 Pos, Neg Areas; Depths Use of both PASCO and Dipstick for measurement 

081029 Depths, Widths IRI decreased from Nov. 1993 to Sept. 1997, suggesting 

rehabilitation or maintenance 

081047 All Areas, Depths Decrease is due to use of both PASCO and Dipstick for 

measurement 

087780 Depths Appears to be maintenance or rehabilitation, but not 

enough distress or longitudinal profile data available to 

verify 

161005 Neg, Fill Areas No explanation 

161009 All Areas, Depths Decrease in IRI from Aug. 14, 1991 to Oct. 24, 1992, 

suggesting an unrecorded maintenance or rehabilitation 

event 

161010 Pos Area Use of both PASCO and Dipstick for measurement 

161020 All No explanation 

161021 Pos Area, Widths Use of both PASCO and Dipstick for measurement 

231001 Depths No explanation 

307066 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

341003 RWP Depths No explanation 

341011 Pos, Neg Areas No explanation 

341030 Depths No explanation 

371006 Depths Use of both PASCO and Dipstick for measurement 

371024 All Database shows overlaid on Nov. 10, 1992; however, data 

trend indicates that construction probably took place prior 

to Oct. 14, 1992 

371817 Depths No explanation 

371992 All Use of both PASCO and Dipstick for measurement 
48

Table 11. Time-series stability trends (continued). 

Section 

ID 

Index Potential Explanation 

421597 Pos Area, Depths Use of both PASCO and Dipstick for measurement 

421605 Neg, Fill Areas; Depths Decrease in distress from May 5, 1993 to Oct. 20, 1993, 

suggesting an unrecorded maintenance or rehabilitation 

event 

491001 Depths, Widths Use of both PASCO and Dipstick for measurement 

491008 Neg, Fill Areas; Depths Distress and IRI data suggest that the drop is not due to a 

maintenance or rehabilitation event 

491017 Depths Use of both PASCO and Dipstick for measurement 

501002 Widths No explanation available 

501004 Depths No explanation 

511002 Depths IRI data suggest that the drop is not due to a maintenance 

or rehabilitation event 

531008 All Areas, Depths Decrease in distress from June 16, 1994 to Aug. 31, 1994, 

suggesting an unrecorded maintenance or rehabilitation 

event 

531801 All Areas No explanation 

811805 Neg, Fill Areas; Depths, 

Widths 

Decrease in distress from May 24, 1995 to Aug. 25, 1995, 

suggesting an unrecorded maintenance or rehabilitation 

event 

041062 Pos Area, Depths Use of both PASCO and Dipstick for measurement 

062041 Neg Area, Depths Use of both PASCO and Dipstick for measurement 

062647 Pos Area Use of both PASCO and Dipstick for measurement 

087781 Depths Appears to be maintenance or rehabilitation, but not 

enough distress or longitudinal profile data to verify 

322027 All Use of both PASCO and Dipstick for measurement 

341638 All Areas, Depths No explanation 

361643 Neg Area, Depths, 

Widths 

Decrease in IRI from May 1996 to Oct. 1997, suggesting 

rehabilitation or maintenance 

361644 Depths No explanation 

371645 Depths, Widths Use of both PASCO and Dipstick for measurement 

372825 Depths Use of both PASCO and Dipstick for measurement 

412002 Neg, Fill Areas; Depths, 

Widths 

Decrease in distress from May 5, 1993 to Oct. 20, 1993, 

suggesting an unrecorded maintenance or rehabilitation 

event 

501681 All No explanation 

541640 All Decrease in IRI from Sept. 1990 to Nov. 1991, suggesting 

rehabilitation or maintenance 

562015 Depths IRI data suggest that the drop is not due to maintenance or 

rehabilitation 

562037 Pos, Neg Areas No explanation 

567772 All Use of both PASCO and Dipstick for measurement 

567773 All Areas No explanation 
49

Table 11. Time-series stability trends (continued). 

Section 

ID 

Index Potential Explanation 

818529 Neg, Fill Areas; Depths Use of both PASCO and Dipstick for measurement 

871680 Pos Area, Widths No explanation 

881647 Pos Area No explanation 

892011 Pos Area No explanation 

046055 Pos Area, Widths No explanation 

046060 All Areas Use of both PASCO and Dipstick for measurement 

066044 Depths Use of both PASCO and Dipstick for measurement 

086002 Neg, Fill Areas; Depths Use of both PASCO and Dipstick for measurement 

306004 Pos, Neg Areas; Depths No explanation 

416011 Pos Area Use of both PASCO and Dipstick for measurement 

491005 Depths No explanation 

491006 All Areas No explanation 

536048 All Areas No explanation 

566029 Neg, Fill Areas No explanation 

566031 All Areas, Widths Decrease in IRI from July 1994 to July 1997, suggesting 

rehabilitation or maintenance 

566032 All Areas Use of both PASCO and Dipstick for measurement 

826007 Depths Use of both PASCO and Dipstick for measurement 

846804 Neg, Fill Areas; Depths, 

Widths 

IRI data suggest that the drop is not due to maintenance 

or rehabilitation 

361008 Pos Area No explanation 

371803 Depths Use of both PASCO and Dipstick for measurement 

511423 Pos Area No explanation 

811804 Fill Area Use of both PASCO and Dipstick for measurement 

371352 Pos Area Use of both PASCO and Dipstick for measurement 

826007 Fill Area, Depths, 

Widths 

Use of both PASCO and Dipstick for measurement 

871620 Pos Area, Widths No explanation 

087035 Neg, Fill Areas; Depths, 

Widths 

Appears to be maintenance or rehabilitation, but not 

enough distress or longitudinal profile data to verify 

417018 Neg, Fill Areas; Depths Use of both PASCO and Dipstick for measurement 

421610 Pos Area No explanation 

547008 All Decrease in IRI from April 29, 1992 to Nov. 5, 1993, 

suggesting an unrecorded maintenance or rehabilitation 

event 

872811 Pos Area No explanation 

872812 Pos Area, Depths No explanation 

421614 Depths No explanation 

320103 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 
50

Table 11. Time-series stability trends (continued). 

Section 

ID 

Index Potential Explanation 

320104 Pos Area Use of both PASCO and Dipstick for measurement 

320105 Pos Area Use of both PASCO and Dipstick for measurement 

320107 Pos Area Use of both PASCO and Dipstick for measurement 

320108 Neg Area Use of both PASCO and Dipstick for measurement 

320109 Neg, Fill Areas Use of both PASCO and Dipstick for measurement 

320110 Neg Area Use of both PASCO and Dipstick for measurement 

320112 Pos Area Use of both PASCO and Dipstick for measurement 

510114 Pos Area No explanation 

04C340 Depths, Widths Use of both PASCO and Dipstick for measurement 

04C350 Neg, Fill Areas; Depths, 

Widths 

EXPERIMENT_SECTION table shows Out of Study on 

Feb. 1, 1997; however, data indicate that the 

construction probably took place prior to Sept. 26, 1996 

04D310 Widths Use of both PASCO and Dipstick for measurement 

08A320 All Areas Use of both PASCO and Dipstick for measurement 

08A350 Neg, Fill Areas Use of both PASCO and Dipstick for measurement 

16A310 Pos Area Use of both PASCO and Dipstick for measurement 

16A320 All Areas Use of both PASCO and Dipstick for measurement 

16A330 Pos Area Use of both PASCO and Dipstick for measurement 

16A350 Pos Area Use of both PASCO and Dipstick for measurement 

16B320 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

16B330 Pos Area Use of both PASCO and Dipstick for measurement 

16B350 Pos Area Use of both PASCO and Dipstick for measurement 

24A310 Pos, Fill Areas Use of both PASCO and Dipstick for measurement 

24A311 Pos Area Use of both PASCO and Dipstick for measurement 

24A331 Pos Area Use of both PASCO and Dipstick for measurement 

24A350 Pos Area Use of both PASCO and Dipstick for measurement 

30A310 Pos, Neg Areas; Depths Use of both PASCO and Dipstick for measurement 

30A330 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

32B310 Pos Area Use of both PASCO and Dipstick for measurement 

32B330 Neg Area Use of both PASCO and Dipstick for measurement 

32B340 All Areas Use of both PASCO and Dipstick for measurement 

32B350 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

36A310 Depths No explanation 

36A320 All No explanation 

36A321 Neg Area, Depths No explanation 

36A331 Pos, Neg Areas; Depths Use of both PASCO and Dipstick for measurement 

36A340 Neg Area, Depths Use of both PASCO and Dipstick for measurement 

36B320 Depths Use of both PASCO and Dipstick for measurement 

36B350 Pos Area No explanation 
51

Table 11. Time-series stability trends (continued). 

Section 

ID 

Index Potential Explanation 

36B351 Pos Area, Depths, 

Widths 

EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

36B353 Pos Area No explanation 

42B330 Pos Area No explanation 

42B340 Pos Area, Depths No explanation 

42B350 Pos Area No explanation 

42B351 Pos, Neg Areas, Depths Use of both PASCO and Dipstick for measurement 

49A320 Pos Area, Depths; 

Widths 

Use of both PASCO and Dipstick for measurement 

49A330 Pos Area Use of both PASCO and Dipstick for measurement 

49B350 Pos Area Use of both PASCO and Dipstick for measurement 

49B390 Pos Area Use of both PASCO and Dipstick for measurement 

49C320 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

49C330 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

49C350 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

51A321 Pos Area Use of both PASCO and Dipstick for measurement 

53C350 Pos, Fill Areas Use of both PASCO and Dipstick for measurement 

87A311 Widths No explanation 

87B360 Pos Area, Depths EXPERIMENT_SECTION table shows no change in 

construction number 

87B361 Depths Use of both PASCO and Dipstick for measurement 

040503 Depths Use of both PASCO and Dipstick for measurement 

040505 Depths Use of both PASCO and Dipstick for measurement 

040506 Depths Use of both PASCO and Dipstick for measurement 

230503 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

230504 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

230505 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

230506 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

230507 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

230508 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

230509 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

230559 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 
52

Table 11. Time-series stability trends (continued). 

240559 Pos Area Use of both PASCO and Dipstick for measurement 

240563 Pos Area Use of both PASCO and Dipstick for measurement 

240560 All EXPERIMENT_SECTION table has not been updated 

to include construction event number 2 

300561 Pos Area Use of both PASCO and Dipstick for measurement 

060603 Pos Area Use of both PASCO and Dipstick for measurement 

060604 Pos Area Use of both PASCO and Dipstick for measurement 

060606 Pos Area Use of both PASCO and Dipstick for measurement 

060607 Pos Area Use of both PASCO and Dipstick for measurement 

060608 Pos, Fill Areas Use of both PASCO and Dipstick for measurement 

420603 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

420604 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

420606 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

420607 Pos, Neg Areas Use of both PASCO and Dipstick for measurement 

420608 Depths Use of both PASCO and Dipstick for measurement 

300805 Pos Area Use of both PASCO and Dipstick for measurement 

340801 Neg, Fill Areas Use of both PASCO and Dipstick for measurement 

340802 Fill Area, Depths, 

Widths 

Use of both PASCO and Dipstickfor measurement 

360801 Pos Area Use of both PASCO and Dipstickfor measurement 

the change in devices (i.e., PASCO and Dipstick) between surveys. Some of the trends, 

however, cannot be explained by a change in device or by a maintenance or rehabilitation event. 

SUMMARY 

The comparisons in this chapter are provided in table 12. This summary shows that the positive 

area, negative area, and LWP rut depths are the most consistently affected of all of the pavement 

parameters. The 1.8-m rut widths were the least affected indices. The positive and negative 

areas should be examined further for their potential for identifying the rutting mechanism. 
Table 12. Summary of comparisons. 

GPS-1 and GPS-2 

Surface Thickness Rutting Index Age HMA/Granular Base vs. HMA 

Overlay of PCC < 76 

vs. 76-118 

76-118 

vs. > 118 

HMA < 127 mm 

Stabilized vs. 

Non-Stabilized 

HMA < 127 mm 

Asphalt Stabilized 

vs. Cement 

Stabilized 

GPS-7 

Freeze vs. 

No-Freeze 

Negative Area I S S S S S 

Positive Area I S S S 

Fill Area I S S S S 

1.8-m LWP Rut Depth I S S S S S 

1.8-m LWP Rut Width S S S S 1.8-m RWP Rut Depth I S S S S 

1.8-m RWP Rut Width S S S S 

Wire Line LWP Rut Depth I S S S 

Wire Line LWP Rut Width S S S S S Wire Line RWP Rut Depth I S S S S 

Wire Line RWP Rut Width S S S S 

I = Increase, S = Significant at 95 percent level of confidence 

53 

55

CHAPTER 6. COMPARISONS OF THREE-POINT AND FIVE-POINT RUT DEPTHS 

The three-point and five-point systems are used by many SHAs for collecting project- and 

network-level rut depths. Most of these agencies use a “Rut Bar” mounted on a vehicle with 

either three or five acoustic sensors. A survey of SHAs on equipment used for transverse profile 

data collection indicated that among the 39 SHAs responding, 22 SHAs use a three-point system. 

These data are shown graphically in figure 23. 

The acoustic sensors measure the distance, or height, from the sensor to the pavement surface at 

the locations defined below. 

• The three-point systems have one sensor located above each wheelpath and one sensor in 

the middle. Hence, a rut depth is obtained for each wheelpath by calculating the 

difference between the height at the center of the pavement and the height over each 

wheelpath. 

• The five-point systems have two extra sensors, usually located approximately 0.30 m 

from the outside of the two wheelpath sensors. 

An analysis was undertaken to determine how measurements from the three- and five-point 

systems compare and how the measurements compare with rut depths calculated based on a lanewidth wire line. 

METHOD OF CALCULATION 

A software program was written to calculate the three-point and five-point rut depths from the 

transverse profiles collected by the RoadRecon unit and the Dipstick®. In this program, it is 

assumed that the data collected by these two methods are connected by straight lines. This is 

considered to yield a reasonably accurate representation of the transverse profile. 

The software used two approaches in generating the data, as illustrated in figure 24. In the “best 

case” scenario, the transverse placement of the rut bar is identical at each station along the test 

section at which transverse profiles are collected. This scenario assumes that there is no lateral 

vehicle movement in the lane within the test section. In the “worst case” scenario, the transverse 

placement of the rut bar is random for all stations. This scenario assumes that there is variable 

lateral vehicle movement in the lane within the test section. 

Regardless of the scenario, 30 rut depth calculations are made at each station along the highway 

at a randomly selected transverse location. The left sensor is placed assuming a normal 

distribution, with an average placement of 914 mm. 
Figure 23. Illustration of those States that use a three-point profiling system. 

3-point system other system 

56 
57

Figure 24. Rut bar measurement. 

The lateral standard deviation or “wander” of the survey vehicle used in the computations was 

127 mm. This value for the vehicle wander was determined from field data collected at a limited 

number of sites. On these sites, a five-sensor rut bar was used to obtain five repeat 

measurements. Elevation measurements were also obtained on these sites. The program was 

used to generate rut bar data, with the wander ranging from 50 mm to 250 mm. The standard 

deviation of the five-sensor rut bar results at each level of wander was compared to the standard 

deviation of the actual measurements. These results are provided for the LWP and the RWP in 

figures 25 and 26, respectively. Based on these results, a wander of 127 mm is the most suitable 

value. 

The sensors on the three-sensor rut bar are assumed to have a standard spacing of 914 mm. The 

rut depth is calculated as the difference between the elevation of the pavement in the center of 

the lane and the elevation of the pavement in each wheelpath, as shown in the lower portion of 

figure 27. 

N

.

.

.

3

2

1

N

.

.

.

3

2

1

(a) “best case” (b) “worst case”

D

ata

C

olle

ctio

n

P

oints

N

.

.

.

3

2

1

N

.

.

.

3

2

1

(a) “best case” (b) “worst case”

D

ata

C

olle

ctio

n

P

oints

N

.

.

.

3

2

1

N

.

.

.

3

2

1

N

.

.

.

3

2

1

(a) “best case” (b) “worst case”

D

ata

C

olle

ctio

n

P

oints
58

Figure 25. Means and standard deviations of the differences observed for 

the LWP versus wander. 

Left Diff By Wander

0

5

10

15

20

25

30

2 3 4 5 6 7 8 9 10

Wander

Means and Std Deviations

Level

2

3

4

5

6

7

8

9

10

Number

 29

 29

 29

 29

 29

 29

 29

 29

 29

Mean

 6.66975

 6.53182

 6.11803

 6.28286

 5.33951

 5.09694

 4.64694

 4.31728

 4.30567

Std Dev

 6.86628

 6.80275

 6.61878

 6.34861

 5.95524

 5.58873

 5.64195

 5.29818

 5.04997

Std Err Mean

 1.2750

 1.2632

 1.2291

 1.1789

 1.1059

 1.0378

 1.0477

 0.9838

 0.9378
59

Figure 26. Means and standard deviations of the differences observed for 

the RWP versus wander. 

Right Diff By Wander

0

5

10

15

20

25

2 3 4 5 6 7 8 9 10

Wander

Means and Std Deviations

Level

2

3

4

5

6

7

8

9

10

Number

 29

 29

 29

 29

 29

 29

 29

 29

 29

Mean

 7.58147

 7.05976

 6.93029

 6.33562

 5.79595

 5.54251

 5.06599

 4.67769

 4.25476

Std Dev

 6.14350

 5.81465

 5.67262

 5.75870

 5.29036

 5.09489

 5.21097

 4.47739

 4.04032

Std Err Mean

 1.1408

 1.0798

 1.0534

 1.0694

 0.9824

 0.9461

 0.9677

 0.8314

 0.7503
60

Figure 27. Calculation of rut depth from the rut bar. 

The three center sensors of the five-sensor rut bar have the same spacing as the sensors on the 

three-sensor rut bar. The two outside sensors are located 305 mm from the sensors placed over 

the wheelpath. The rut depth is obtained by drawing a line from sensors 1 to 3 and sensors 3 to 

5. The difference between the line and the pavement elevation at sensors 2 and 4 is the rut depth 

for the LWP and RWP, respectively. This calculation is illustrated in the upper portion of figure 

27. 

Both the three- and the five-point calculations can yield a negative rut depth. The three-point 

system will provide a negative rut depth for transverse profiles, such as that shown in figure 28. 

The five-point system will provide a negative rut depth for transverse profiles, such as that 

shown in figure 29. However, other shapes may also yield a negative rut depth. 

-12

-10

-8

-6

-4

-2

0

0 500 1000 1500 2000 2500 3000 3500 4000

Rut Depth

Sensor 1 Sensor 2 Sensor 3 Sensor 4 Sensor 5

-12

-10

-8

-6

-4

-2

0

0 500 1000 1500 2000 2500 3000 3500 4000

Rut Depth

Sensor 1 Sensor 2 Sensor 3

Transverse Location, mm

Relative Elevation, mm Relative Elevation, mm

Transverse Location, mm
61

Figure 28. Typical transverse profile providing a negative rut depth 

from three-point analysis. 

Figure 29. Typical profile providing a negative rut depth 

from five-point analysis. 

0

5

10

15

20

25

30

0 500 1000 1500 2000 2500 3000 3500 4000 4500

X, mm

Y, m

m

-8

-7

-6

-5

-4

-3

-2

-1

0

0 500 1000 1500 2000 2500 3000 3500 4000

X, mm

Y, mm
62

ANALYSES 

To examine the rut depths for the three-point and five-point profiles, a histogram was created for 

the three-point rut depths, the five-point rut depths, and the wire line rut depths. As a minimum, 

these histograms illustrate that both the three-point and five-point calculations can provide 

negative rut depths. The mean, standard deviation, and minimum and maximum values for the 

three-point rut depths, the five-point rut depths, and the wire line rut depths are all provided in 

table 13. 

Variation 

The standard deviations of the simulation runs were pooled across stations to obtain a value for 

each survey date. The standard deviations provide some indication of the effect of vehicle 

wander on the calculated rut depth. PASCO corrects for this phenomenon by taking a picture 

that is slightly larger than the width of the lane. The standard deviation for each wheelpath 

provides an indication of the range of values (maximum and minimum rut depths) that may be 

observed for a given transverse profile. These standard deviations were found to be correlated to 

the mean rut depth for the section. Therefore, it is more appropriate to discuss the variability in 

terms of COV. 

The pooled standard deviation and section mean were used to calculate the COV. These values 

were used to examine the variability associated with each profile for both the best-case and 

worst-case scenarios. The values of COV were within round-off error between the two 

scenarios. For the three-point rut bars, the average COV was 104 percent, while the average for 

the five-point rut bars was 239 percent. These values indicate that the transverse placement of 

the rut bar dramatically influences the measurement and, hence, the rut depth calculation. 

Combined Data Sets 

The correlation matrix for these rut depths shows that the five-point rut depths have a higher 

correlation with the wire line rut depths (0.8 and 0.6 for the LWP and RWP, respectively) than 

the three-point rut depths (0.5 and 0.4 for the LWP and RWP, respectively). In addition, the 

correlations of the LWP for all three rut depths were higher than those for the RWP (table 13). 

This higher correlation with the LWP rut depth may be partially attributed to the fact that there is 

typically greater consistency/uniformity in the LWP over time. 

Comparisons were then made among the three-point rut depth, the five-point rut depth, and the 

wire line rut depth by wheelpath. Paired t-tests indicated that there were statistically significant 

differences, indicating that the different measurement techniques do not provide the same 

estimate of rutting. 
Table 13. Correlation of three-point and five-point rut depths versus the wire line rut depths. 

LWP = Leftt Wheelpath, RWP = Right Wheelpath, RMSE = Root Mean Square Error, Se/Sy = Standard error of the regression divided by the standard deviation of the y-value 

3-Point, Worst Case 5-Point, Worst Case Wire Line 3-Point, Best Case 5-Point, Best Case 

LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. 

Number of Observations 

79,616 79,616 79,616 79,616 79,616 79,616 79,616 79,616 79,616 79,616 79,616 79,616 79,616 79,616 79,616 

Mean 3.2 3.1 3.2 1.0 -0.1 0.4 5.9 5.9 5.9 3.2 3.1 3.2 1.0 -0.1 0.4 Standard Deviation 4.28 4.68 3.93 2.24 1.91 1.67 4.4 4.6 4.2 4.28 4.68 3.93 2.24 1.91 1.67 Minimum -37.0 -25.0 -21.5 -14.0 -13.0 -10.0 0 0 -36.0 -25.0 -21.0 -14.0 -13.0 -10.0 Maximum 73.0 64.0 65.5 36.0 22.0 19.0 77 63 70 74.0 65.0 66.0 36.0 22.0 17.5 Correlation to wire line rut depth 

0.5363 0.4188 0.4381 0.7761 0.5350 0.7541 --- --- --- 0.5364 0.4193 0.4385 0.7754 0.5356 0.7546 

R2 0.288 0.175 0.192 0.602 0.286 0.569 --- --- --- 0.288 0.176 0.192 0.601 0.287 0.569 RMSE 3.68 4.18 3.78 2.75 3.89 2.76 --- --- --- 3.68 4.18 3.78 2.75 3.89 2.76 Se/Sy 0.84 0.91 0.90 0.62 0.85 0.66 --- --- --- 0.84 0.91 0.90 0.62 0.85 0.66 p-value from paired ttest 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 --- --- --- 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 

63 
64

These data indicate that the five-point rut depth never exceeds the wire line rut depth. However, 

the three-point rut depth may be larger or smaller than the wire line rut depth. The average 

difference between the wire line rut depth and the five-point rut depth was 5 mm for the LWP 

and 6 mm for the RWP. On average, the three-point rut depth was 4 mm smaller than the wire 

line rut depth in both wheelpaths. These values indicate that the differences are significant, both 

statistically and from an engineering perspective. 

Paired t-tests for the three-point rut depths versus the five-point rut depths yielded statistically 

significant differences. On average, the three-point rut depths were 2 mm larger than the fivepoint rut depths; however, some differences were as large as 40 mm. 

Finally, a series of linear regressions were used to examine the potential correlation between the 

rut depths. The results from these regressions are shown in table 13. Figures 30 and 31 show a 

graphical comparison of the three- and five-point rut depths versus those determined from the 

lane-width wire line. As is evident, the correlations are weak. 

The relationship between the wire line rut depth and the five-point rut depth was stronger than 

that between the wire line rut depth and the three-point rut depth (i.e., R2

 of 0.38 versus 0.65 and 

0.15 versus 0.22, respectively). In all cases, the data included a large amount of scatter. 

The relationships between the five-point rut depths and the three-point rut depths were very 

different between the wheelpaths. The R2 for the LWP was 0.44 and the R2 for the RWP was 

0.003. 

Some States that use these systems use the average rut depth from a given length of pavement. 

Therefore, the analyses were repeated, examining the average rut depth for the section for both 

scenarios of the three-point and five-point systems. Table 14 includes the mean, standard 

deviation, and minimum and maximum values for these rut depths. The table shows that 

negative values for average rut depths, though smaller than for the individual rut depths, may 

still be computed. 

The correlation coefficients are also provided in table 14. The values are slightly lower than 

those shown for the five-point rut depth in table 13, but are slightly higher than those for the 

RWP three-point rut depth. Naturally, the same is true for the coefficients of determination (R2

) 

also shown in table 14. 

The results of the paired t-tests reflect a statistically significant difference between the average 

three-point versus the wire line rut depths and the average five-point versus the wire line rut 

depths. The mean difference for the average three-point comparison was 3 mm. The mean 

difference for the average five-point comparison was 5 mm. Both values are of some concern 

from an engineering standpoint. 

In summary, the average three-point and five-point rut depths did not show a stronger 

relationship with the wire line rut depth than did rut depths calculated for the individual 

wheelpaths. 
65

Figure 30. Graphical comparison of the three-point rut depths versus 

the wire line rut depths. 

Left Wheelpath

0

5

10

15

20

25

30

35

40

45

-50 -40 -30 -20 -10 0 10 20 30 40

3-point Rut Depth, mm

3.7-m Rut Depth, mm

Right Wheelpath

0

10

20

30

40

50

60

70

-30 -20 -10 0 10 20 30 40

3-point Rut Depth, mm

3.7-m Rut Depth, mm
66

Figure 31. Graphical comparison of the five-point rut depths versus 

the wire line rut depths. 

Left Wheelpath

0

5

10

15

20

25

30

35

40

45

-15 -10 -5 0 5 10 15 20

5-point Rut Depth, mm

3.7-m Rut Depth, mm

Right Wheelpath

0

10

20

30

40

50

60

70

-15 -10 -5 0 5 10 15 20

5-point Rut Depth, mm

3.7-m Rut Depth, mm
67

Table 14. Correlation of average three-point and five-point rut depths versus 

the wire line rut depths.

 3-Point, 

Worst 

Case 

5-Point, 

Worst 

Case 

Wire 

Line 

3-Point, 

Best Case 

5-Point, 

Best Case 

Number of Observations 7,229 7,229 7,229 7,229 7,229 

Mean 3.2 0.5 5.9 3.2 0.5 

Standard Deviation 3.60 1.48 3.93 3.61 1.49 

Minimum -15.2 -6.9 0.0 -15.7 -6.8 

Maximum 52.6 12.4 54.6 54.4 11.9 

Correlation to wire line 

rut depth 

0.4636 0.8224 --- 0.4623 0.8197 

R2 0.215 0.676 --- 0.214 0.672 

RMSE 3.48 2.23 --- 3.48 2.25 

Se/Sy 0.89 0.57 --- 0.89 0.57 

p-value from paired ttest 0.0000 0.0000 --- 0.0000 0.0000 

 RMSE = Root Mean Square Error 

 Se/Sy = Standard error of the regression divided by the standard deviation of the y-value 

Blocked Data Sets Versus Shape 

The shape of the transverse profile may affect the correlation between the rut depths. To test for 

this possibility, the data were divided into categories based on the transverse profile shape using 

the complete profile information available from the original PASCO and Dipstick profiles. 

Four categories were used for this analysis: 

• Category 1 - Profiles for which the two outside edges were lower than the rest of the 

entire profile. 

• Category 2 - Profiles that were bowl-shaped. 

• Category 3 - Profiles that were all negative, but with a “hump” in the middle. 

• Category 4 - Profiles for which the middle portion of the profile was larger than the two 

outside edges and the portions of the profile in the wheelpaths were lower than the two 

outside edges. 

Examples of each are shown in figure 32. Figure 33 reflects the number of profiles within each 

category. Category 4, which contained the most data, is considered to be a typical profile. 

Category 2 included the fewest number of profiles. 
68

Figure 32. Transverse profile shape categories. 

0

5

10

15

20

25

0 500 1000 1500 2000 2500 3000 3500 4000

X, m m

Y, m m

Category 1

-20

-15

-10

-5

0

5

0 500 1000 1500 2000 2500 3000 3500 4000

X, m m

Y, m m

Category 2

-25

-20

-15

-10

-5

0

0 500 1000 1500 2000 2500 3000 3500 4000

X, m m

Y, m m

Category 3

-20

-15

-10

-5

0

5

0 500 1000 1500 2000 2500 3000 3500 4000

X, m m

Y, m m

Category 4
69

Figure 33. Number of profiles within each shape category. 

Category

1

2

3

4

1

2

3

4

Frequencies

Level

1

2

3

4

Total

Count

 10937

 3074

 7834

 23524

 45369

Probability

0.24107

0.06776

0.17267

0.51850

Cum Prob

0.24107

0.30882

0.48150

1.00000

 4 Levels
70

Table 15 lists the means and standard deviations for each of the profile categories. The 

differences between the best-case and worst-case scenarios were within round-off error; 

therefore, only one value is presented. The differences between the means were all significantly 

different from each other, with the exception of categories 2 and 4 for the RWP five-point rut 

depth. Considerable overlap existed between the distributions of each category for each rut 

depth. 

Statistical tests conducted on each category were identical to those conducted on the combined 

data set. These steps included the examination of the histograms, the development of the 

correlation matrix, a paired t-test between each of the rut depths, and a linear regression between 

each of the rut depth indices. Table 15 summarizes the comparisons with the wire line rut 

depths. 

Category 1 Profiles 

The correlation matrix for category 1 exhibited much weaker correlations than those observed 

for the combined data set. As with the combined data set, the correlations for the five-point rut 

depths versus the wire line rut depths (0.57 and 0.42 percent for the LWP and RWP, 

respectively) were stronger than those for the three-point rut depths versus the wire line rut 

depths (0.54 and 0.24 for the LWP and RWP, respectively). It is interesting to note that the 

correlation between the three-point rut depth and the five-point rut depth for the RWP is 

negative. This means that as the three-point rut depth increases, the five-point rut depth 

decreases, which is contrary to the expectation. 

The results of the paired t-tests for category 1 were all statistically significant. The mean 

differences between the five-point rut depths and the wire line rut depths (3 mm for the LWP and 

4 mm for the RWP) were smaller than those observed for the combined data set. These values 

are considered significant from an engineering perspective. 

The mean differences between the three-point rut depths and the wire line rut depths were also 

smaller than those for the combined data set. The mean difference for both wheelpaths was 1 

mm, suggesting that the significance between the three-point rut depth and the wire line rut depth 

is questionable. 

The differences between the three-point rut depths and the five-point rut depths are also 

considered significant. These differences averaged 3 mm, but some were as large as 24 mm. 

The three-point rut depths were generally, but not always, larger than the five-point rut depths. 

The regression analyses were all statistically significant. The regressions for the five-point rut 

depths had higher R2

 values than the regressions for the three-point rut depths. However, the 

data scatter was extensive. Like the combined data set, the explained variation (i.e., R2

 values) 

for the LWP three-point rut depth versus the five-point rut depth was higher than for the RWP. 
Table 15. Correlation of three-point and five-point rut depths versus the wire line rut depths by category. 

Category 1 Category 2 Category 3 Category 4 

3-point 5-point 3-point 5-point 3-point 5-point 3-point 5-point 

LWP RWP LWP RWP LWP RWP LWP RWP LWP RWP LWP RWP LWP RWP LWP RWP 

Number of Observations 

10,937 10,937 10,937 10,937 3,074 3,074 3,074 3,074 7,834 7,834 7,834 7,834 23,524 23,524 23,524 23,524 

Mean 2.4 2.3 -0.4 -0.6 -1.1 -1.8 0.2 0.0 2.7 2.2 2.2 0.7 3.8 4.1 1.4 0.2 Standard Deviation 

3.25 3.88 1.29 1.26 3.02 2.76 1.26 1.36 3.75 4.15 2.32 1.88 4.61 5.05 2.32 2.07 

Minimum -14.0 -14.0 -9.0 -10.0 -37.0 -14.0 -7.0 -9.0 -17.0 -23.0 -6.0 -8.0 -28.0 -20.0 -11.0 -13.0 Maximum 25.0 24.0 6.0 9.0 10.0 11.0 8.0 22.0 29.0 26.0 17.0 13.0 34.0 64.0 21.0 22.0 R2 0.294 0.059 0.328 0.174 0.00 0.01 0.179 0.283 0.367 0.199 0.603 0.215 0.521 0.433 0.696 0.283 RMSE 1.42 1.76 1.42 1.65 3.52 4.23 3.19 3.60 3.81 4.50 3.01 4.45 2.94 3.57 2.34 4.02 Se/Sy 0.82 0.97 0.82 0.91 1.00 1.00 0.91 0.85 0.80 0.90 0.63 0.89 0.69 0.75 0.55 0.85 p-value from paired t-test 

<0.0001 <0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 

 LWP = Left Wheelpath, RWP = Right Wheelpath, RMSE = Root Mean Square Error, Se/Sy = Standard error of the regression divided by the standard deviation of the y-value 

71 
72

Category 2 Profiles 

The correlation coefficients for the five-point rut depths versus the wire line rut depths were 

lower than those computed for the combined data set (0.42 and 0.53 for the LWP and RWP, 

respectively). However, the correlations for the three-point rut depths versus the wire line rut 

depths were much lower (0.01 and 0.08 for the LWP and RWP, respectively). The correlation 

coefficients for the three-point rut depths versus five-point rut depths were higher for the LWP 

than for the RWP. 

Results from the paired t-tests were all significant. For this shape category, the three-point rut 

depths, like the five-point rut depths, were never larger than the wire line rut depths. This 

yielded greater mean differences than those observed for the combined data set. The five-point 

rut depths were 6 mm smaller than the wire line rut depths in the LWP and 7 mm smaller in the 

RWP, on average. The three-point rut depths were 8 mm smaller than the wire line rut depths in 

the LWP and 9 mm smaller in the RWP, on average. 

The regressions for category 2 data were not all significant. The regression for the LWP threepoint rut depths versus the wire line rut depths was not significant. The amount of scatter in the 

data indicates that, although some of the regressions were moderate, i.e., R2

 less than 0.50, there 

is not a strong relationship between the measurement methods for this category. 

Category 3 Profiles 

The correlations for these data were generally better than those observed for the combined data 

set. In fact, the LWP five-point rut depths versus the wire line rut depths had a correlation 

coefficient of 0.8, which is large. 

Results from the paired t-tests were all significant. For this shape category, the three-point rut 

depths were always less than the wire line rut depths. The mean differences were similar to 

those observed for the category 2 data. The mean differences observed for the comparison of the 

three-point versus the five-point rut depths were so small that they should not be considered 

significant from an engineering perspective. 

The linear regressions for these data were all significant. Though the data show considerable 

scatter, graphical presentation of these data reveals a slight, but identifiable, trend, except for the 

RWP three-point rut depths versus the five-point rut depths. 

Category 4 Profiles 

The correlation coefficients for this category were higher than those computed for the combined 

data set. The correlation coefficients for the five-point rut depths versus the wire line rut depths 

were 0.83 and 0.53 for the LWP and RWP, respectively. The correlation coefficients for the 

three-point rut depths versus the wire line rut depths were 0.72 and 0.66 for the LWP and RWP, 

respectively. 
73

Results of the paired t-tests indicate that the measurements obtained from the different methods 

were significantly different rut depths, although the mean differences were not as large as those 

observed for the category 2 and 3 data. The three-point rut depths were generally, but not 

always, smaller than those obtained using the wire line method. 

The linear regressions were all statistically significant. The data showed quite a bit of scatter, 

but a general trend was detectable from all of the graphs except one. The graph for the RWP 

three-point rut depth versus the five-point rut depth did not show any trend, even though the 

regression was significant. The correlations noted here were similar to those observed for the 

category 3 data set. 

Blocked Data Sets Versus Rut Depth 

In addition to shape, the data were categorized based on the amount of rutting, since the amount 

of rutting may affect the correlation between the rut depths. The data for the individual profiles 

were sorted by mean rut depth for the profile. These data were divided roughly into thirds. The 

“low rutting” group consisted of profiles with an average rut depth of less than 4.5 mm. The 

“moderate rutting” groups consisted of profiles with rutting from 4.5 mm to 7.2 mm. The “high 

rutting” group consisted of profiles with more than 7.2 mm of rutting. 

Low Rutting 

The results from these comparisons are provided in table 16. The correlation coefficients were 

less than those observed from the combined data set. The correlation coefficients for the fivepoint rut depths versus the wire line rut depths were 0.49 and 0.31 for the LWP and RWP, 

respectively. The correlation coefficients for the three-point rut depths versus the wire line rut 

depths were 0.41 and 0.15 for the LWP and RWP, respectively. 

The paired t-test results indicate that the measurements obtained from the different techniques 

were significantly different rut depths. The mean differences observed for the five-point rut 

depths were greater than 2 mm and large enough to be considered significant. The mean 

differences observed for the three-point rut depths were small enough to be considered 

insignificant, but the amount of scatter in the data was large enough to be of concern. 

The linear regressions were all statistically significant. The data showed quite a bit of scatter, 

but a general trend was detectable. Even though these regressions were significant, the 

relationships between the rut depths were limited at best. 
Abstract

Characterization of Transverse Profiles, April 2001 (FHWA-RD-01-024)

A study of the transverse profile data currently being collected under the Long Term Pavement

Performance project was undertaken. The data were collected by three processes: (1) Dipstick, (2)

a photographic method, and (3) straightedge used to collect rut depths.

This study examined several indices for the purposes of quantifying and qualifying the transverse

profiles. It is recommended that five indices be added to the National Information Management

System. These indices include the area of the rut below a straight line connecting the end points of

the transverse profile, the total area below the straight lines connecting the maximum surface

elevations, the maximum depth for each wheelpath between a 1.8-m straightedge placed across the

wheelpath and the surface of the pavement, and the width of the rut based on a 1.8-m straightedge.

These indices were studied in order to determine typical trends by climate, surface thickness, soil

type, and age. In addition, the time-series trends for each test section were studied in order to

determine whether any anomalies existed and the potential causes of these anomalies.

FHWA-RD-01-024

http://www.tfhrc.gov/pavement/ltpp/abstracts/01-024.htm [5/29/2001 1:47:16 PM]
Table 16. Correlation of three-point and five-point rut depths versus the wire line rut depths 

for profiles with less than 4.5 mm of rutting. 

3-Point, Worst Case 5-Point, Worst Case 3-Point, Best Case 5-Point, Best Case Wire Line 

LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. 

Number of Observations 

34,781 34,781 34,781 34,781 34,781 34,781 34,781 34,781 34,781 34,781 34,781 34,781 34,781 34,781 34,781 

Mean 1.9 1.9 1.9 -0.3 -0.7 -0.5 1.9 1.9 1.9 -0.3 -0.7 -0.5 2.7 2.7 2.7 Standard Deviation 2.67 3.06 2.26 1.10 1.03 0.78 2.66 3.06 2.26 1.10 1.03 0.78 1.29 1.26 0.95 Minimum -9.0 -14.0 -5.0 -7.0 -12.0 -6.5 -9.0 -14.0 -5.0 -7.0 -11.0 -6.0 0.0 0.0 0.0 Maximum 14.0 17.0 13.0 4.0 3.0 2.0 14.0 17.0 13.0 4.0 3.0 2.0 8.0 7.0 4.0 Correlation to Wire Line Rut Depths 

0.4110 0.1484 0.0829 0.4886 0.3106 0.3481 0.4090 0.1481 0.0817 0.4872 0.3114 0.3466 --- --- --- 

R2 0.169 0.022 0.007 0.239 0.096 0.121 0.167 0.022 0.007 0.237 0.097 0.120 --- --- --- RMSE 1.17 1.25 0.95 1.12 1.20 0.89 1.18 1.25 0.95 1.12 1.20 0.89 --- --- --- Se/Sy 0.91 0.99 1.00 0.87 0.95 0.94 0.91 0.99 1.00 0.87 0.95 0.94 --- --- --- p-value from paired ttest 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 --- --- --- 

LWP = Left Wheelpath, RWP = Right Wheelpath, RMSE = Root Mean Square Error, Se/Sy = Standard error of the regression divided by the standard deviation of the y-value 

74 
75

Moderate Rutting 

The results from the comparisons of the profiles in the moderate rutting category are provided in 

table 17. The correlation coefficients were lower than those for the combined data set. These 

values were larger than those for the low rutting data set. 

Results from the paired t-test indicate that the measurement techniques do not provide the same 

value of rut depth. The differences ranged from 2.6 mm to 5.7 mm. These values are large 

enough to consider the observed differences to be significant from an engineering perspective, as 

well as a statistical perspective. 

The linear regressions were also statistically significant. Although these results were not as good 

as those for the combined data set, they were better than those for the low rutting data set. The 

data showed considerable scatter and the value of these regressions have little meaning from the 

engineering point of view. 

High Rutting 

The results of the comparisons of the high rutting data set are provided in table 18. The 

correlation coefficients were smaller than those observed for either the combined data set or the 

moderate rutting data set. 

Results from the paired t-tests indicate that the measurements obtained from the different 

measurement techniques were not the same. The mean differences were all greater than 5 mm. 

These differences were greater than those observed for the profiles with moderate rutting. 

The linear regressions were statistically significant. However, the R2

 and error terms associated 

with these regressions indicate that the fit of the lines to the data are very poor. 

SUMMARY 

In summary, the following conclusions were drawn from these analyses: 

• The transverse location of the rut bar dramatically affects the measurement and, hence, 

the rut depth computation. Thus, consistent lateral placement of the survey vehicle is 

essential to repeatable rut depth measurements using the three- or five-point rut bars. 

• The paired t-tests illustrate that the three rut depth measurement systems (three-point, 

five-point, and wire line) do not provide the same values (i.e., there are statistically 

significant differences among them). 

• The three-point rut depths underestimate the wire line rut depths for transverse profiles 

where the middle of the profile is lower than the outside edges of the lane (categories 2 

and 3). 
Table 17. Correlation of three-point and five-point rut depths versus the wire line rut depths 

for profiles with from 4.5 mm to 7 mm of rutting. 

3-Point, Worst Case 5-Point, Worst Case 3-Point, Best Case 5-Point, Best Case Wire Line 

LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. 

Number of Observations 

23,565 23,565 23,565 23,565 23,565 23,565 23,565 23,565 23,565 23,565 23,565 23,565 23,565 23,565 23,565 

Mean 3.0 2.7 2.9 0.9 -0.2 0.4 3.0 2.7 2.9 0.9 -0.2 0.4 5.6 5.5 5.6 Standard Deviation 

3.60 4.11 3.22 1.42 1.47 1.01 3.56 4.12 3.22 1.42 1.46 1.01 1.67 1.70 0.84 

Minimum -14.0 -13.0 -8.0 -9.0 -11.0 -6.5 -15.0 -13.0 -7.0 -9.0 -10.0 -6.0 0.0 0.0 4.5 Maximum 19.0 20.0 17.5 6.0 7.0 3.5 18.0 20.0 17.5 6.0 6.0 3.5 13.0 12.0 7.0 Correlation to Wire Line Rut Depths 

0.5013 0.2762 0.1270 0.4900 0.2961 0.2203 0.4997 0.2768 0.1260 0.4901 0.2949 0.2205 --- --- --- 

R2 0.251 0.076 0.016 0.24 0.088 0.049 0.250 0.077 0.016 0.24 0.087 0.049 --- --- --- RMSE 1.44 1.63 0.84 1.45 1.62 0.82 1.44 1.63 0.84 1.45 1.62 0.82 --- --- --- Se/Sy 0.86 0.96 1.00 0.87 0.95 0.98 0.86 0.96 1.00 0.87 0.95 0.98 --- --- --- p-value from paired t-test 

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 --- --- --- 

LWP = Left Wheelpath, RWP = Right Wheelpath, RMSE = Root Mean Square Error, Se/Sy = Standard error of the regression divided by the standard deviation of the y-value 

76 
Table 18. Correlation of three-point and five-point rut depths versus the wire line rut depths 

for profiles with more than 7 mm of rutting. 

3-Point, Worst Case 5-Point, Worst Case 3-Point, Best Case 5-Point, Best Case Wire Line 

LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. LWP RWP Avg. 

Number of Observations 

21,270 21,270 21,270 21,270 21,270 21,270 21,270 21,270 21,270 21,270 21,270 21,270 21,270 21,270 21,270 

Mean 5.5 5.6 5.6 3.2 1.1 2.1 5.5 5.6 5.5 3.2 1.1 2.1 11.2 11.6 11.4 Standard Deviation 5.86 6.25 5.43 2.69 2.73 2.00 5.86 6.25 5.43 2.70 2.73 2.00 4.64 4.94 4.18 Minimum -37.0 -25.0 -21.5 -14.0 -13.0 -10.0 -36.0 -25.0 -21.0 -14.0 -13.0 -10.0 1.0 1.0 7.5 Maximum 73.0 64.0 65.5 36.0 22.0 19.0 74.0 65.0 66.0 36.0 22.0 17.5 77.0 63.0 70.0 Correlation to Wire Line Rut Depths 

0.4711 0.3282 0.2941 0.6427 0.4532 0.6066 0.4724 0.3294 0.2955 0.6407 0.4537 0.6074 --- --- --- 

R2 0.222 0.108 0.086 0.413 0.205 0.368 0.223 0.109 0.087 0.411 0.206 0.369 --- --- --- RMSE 4.10 4.66 3.99 3.56 4.40 3.32 4.09 4.66 3.99 3.56 4.40 3.32 --- --- --- Se/Sy 0.88 0.94 0.95 0.77 0.89 0.79 0.88 0.94 0.95 0.77 0.89 0.79 --- --- --- p-value from paired t-test 

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 --- --- --- 

LWP = Left Wheelpath, RWP = Right Wheelpath, RMSE = Root Mean Square Error, Se/Sy = Standard error of the regression divided by the standard deviation of the y-value 

77 
78

• Although a better correlation (but still considered poor) existed between the five-point rut 

depths and the wire line rut depths than between the three-point rut depths and the wire 

line rut depths, they consistently underestimated the wire line rut depths. 

• A better correlation was found between the rut depths for those transverse profile shapes 

with a “hump” in the middle (categories 3 and 4). 

• Generally, the larger the wire line rut depths, the bigger the difference that will be 

observed between the wire line rut depths and the three-point and five-point rut bars. 

As a result of these analyses and comparisons, the analysts concluded that neither the three-point 

nor the five-point rut depth measurement systems provide reliable and accurate estimates of rut 

depths as measured with a wire line. 
79

CHAPTER 7. FIELD STUDY 

To determine the bias and precision of the PASCO and Dipstick data collection methods, it was 

necessary to conduct a field study. The data set housed in NIMS contains several sets of surveys 

in which the PASCO method and a Dipstick method were used to collect data for a 1-year time 

frame. While these data allowed for comparisons between these two methods, they did not allow 

for a direct computation of the bias and precision of these two measurement methods. 

The field study presented here utilized data from only one roadway. The mechanism causing the 

rutting could potentially affect the bias and precision of the transverse profile and, subsequently, 

the bias and precision for the indices. This field study provides a good initial estimate of the bias 

and precision; however, as additional data become available, the data should be used to verify 

the bias and precision values presented here. 

DATA COLLECTION 

A site with varying rut depths was selected outside of Thompsontown, Pennsylvania, on the 

frontage road of U.S. 322. Two 152.5-m test sections were selected along this roadway for use 

with the field study. The site had minimal traffic because the frontage road was a dead-end road. 

Profile measurements were made along each section every 15 m. All data were collected within 

a 2-week time frame. 

Four methods were used to collect the data. The first was a straightedge survey. A 3.9-m 

straightedge was placed on blocks. The distance between the straightedge and the surface of the 

pavement was measured every 152 mm. Three operators used this method to collect profile data 

on each profile with eleven profiles measured on each section. Each operator made three 

replicate measurements, for a total of nine sets of profiles collected. The data collected by this 

method were considered the benchmark for the bias computation. 

The second method used to collect data was the FACE Dipstick. The Dipstick collects data 

every 305 mm across the profile. As with the straightedge method, each operator made three 

replicate measurements of each profile. 

The RoadRecon unit was then used to collect data along each section. These measurements were 

made using the standard method of taking a picture approximately every 15 m. The images 

collected of each profile were digitized five times by five different operators. Due to the speed at 

which the RoadRecon unit is normally operated, the spacing between the images is rarely exactly 

15 m. Therefore, a second set of measurements was taken using the RoadRecon unit in a static 

mode. The unit was driven to the appropriate station and the image was collected. These 

measurements were taken every 15 m and at the same stations where the dynamic images were 

obtained. Therefore, twice as many profiles were collected using this method than for any other 

method. These images were also digitized five times by each of the five operators. All the data 

were processed to ensure uniformity. The y-values were expressed in terms of elevation relative 
80

to a horizontal datum drawn through the end points of the profiles. The x-values were expressed 

in terms of distance from the outside lane edge. 

ANALYSIS 

The first step of the analysis was to compute each index using the data collected. All the 

analyses were conducted by examining differences between the indices. The indices were 

calculated using the RUTCHAR program. An analysis of variance (ANOVA) was completed to 

examine the differences by operator, section, and station.(8) Differences were expected to occur 

between each of the profiles; however, differences between operators may prove to be important 

in later data collection. 

For the straightedge data collection method, the ANOVA results did not show a statistically 

significant difference between operators for any of the indices. A t-test showed a significant 

difference of 79 mm for the location of the LWP 1.8-m rut depth. This difference is considered 

to be fairly small. No differences were observed for the data collected using the Dipstick. 

The dynamic RoadRecon measurements reflect statistically significant differences between 

operators for the negative area, fill area, LWP 1.8-m rut depth, RWP 1.8-m rut width, and the 

LWP wire line rut depth. The largest difference observed between operators for the fill area was 

3200 mm2

. The largest difference for the LWP 1.8-m rut depth was 2 mm. The difference 

observed for the LWP 1.8-m rut depth is within the precision limits. The differences observed 

for both the fill area and the RWP 1.8-m rut width are quite large. Most of the indices obtained 

from the static RoadRecon unit were significantly different, with the exception of the positive 

area. The differences observed in the data collected by the RoadRecon unit indicate the 

importance of trained operators to process the data. 

Even though these differences were noted, the remainder of the analyses were conducted using 

the pooled data set. The precision values noted may be a little larger than are actually seen in 

practice. Only experienced personnel should process the data. This study incorporated at least 

one set of data processed by inexperienced personnel. On the other hand, at least one set of data 

used was processed by very experienced personnel. The data were pooled by operator to provide 

a between- and within-operator variance, a total variance, and an average for each measurement 

type. The distributions of each of these values were examined by measurement type. 

The first set examined was the measurements collected using the straightedge method. In 

particular, the within-operator variance for the negative area showed one value to be much larger 

than the others. A single profile was found to cause the much larger within-operator variance for 

that one station. Figure 34 shows each of the profiles collected by the straightedge method for 

all of the operators. One profile in particular does not follow the trend of the other profiles. 

Tables 19 and 20 provide the precision for each of the indices by measurement method. These 

are presented by COVs in conjunction with ASTM C670.(9)
81

Figure 34. Profiles obtained using the straightedge method at station 76.2 m. 

A further investigation was undertaken to determine whether the influential profile was errant or 

discrepant. The original data were examined and the profile was processed correctly. This 

profile affects 6 of the 15 indices being examined. No record was made of problems 

encountered while collecting the profile. Even though the profile may be influential, it was 

deemed inappropriate to remove it from the analysis simply because it was different from the 

other observations. 

The other measurement methods were examined for similar influential observations. No profiles 

were found that were significantly different from the other measurements of the same profile. 

The within- and between-operator variances were examined to determine whether they were 

correlated to the average of the index. The within- and between-operator precisions are given in 

tables 19 and 20, respectively. These are given in terms of COV (as directed by ASTM C670-

96) and provide an indication of the repeatability of the data processing by an individual operator 

and the reproducibility of the data processing between two operators. Only a limited number of 

the variances for the indices for any of the measurement types were correlated to the average of 

the index. 

The data were reviewed to determine the effect of longitudinal variation on the profile collected. 

The dynamic measurements were not taken at exactly the same locations as the straightedge and 

Dipstick measurements. (It is not possible for the driver to trigger the system to take a 

measurement at an exact location while the van is moving.) The static RoadRecon 

measurements were taken at twice as many stations as the other systems. In this case, the unit 

was driven to the location of interest, stopped, and triggered to take a measurement. This 

method was used to obtain the data at the stations where the Dipstick and straightedge methods 

were used and the stations where the dynamic measurements were taken. 

P rofile at S tation 76.2 m

-20

-15

-10

-5

0

5

0 500 1000 1500 2000 2500 3000 3500

X, m m

Y, mm
Table 19. Within-operator precision for each index. 

Measurement Type 

Negative Area 

Positive Area 

Fill Area 

1.8-m LWP Depth 

1.8-m LWP Loc. 

1.8-m LWP Width 

1.8-m RWP Depth 

1.8-m RWP Loc. 

1.8-m RWP Width 

Wire Line LWP Depth 

Wire Line LWP Loc. 

Wire Line LWP Width 

Wire Line RWP Depth 

Wire Line RWP Loc. 

Wire Line RWP Width 

Straightedge -14 30 6 8 4 5 7 9 4 8 4 11 7 9 10 Dipstick -6 12 3 6 1 2 2 2 1 7 1 7 2 2 4 Static PASCO -17 64 9 11 6 7 11 14 6 11 19 16 11 14 16 Dynamic PASCO 

-18 71 9 10 5 7 9 12 6 10 5 14 9 12 13 

Table 20. Between-operator precision for each index. 

Measurement Type 

Negative Area 

Positive Area 

Fill Area 

1.8-m LWP Depth 

1.8-m LWP Loc. 

1.8-m LWP Width 

1.8-m RWP Depth 

1.8-m RWP Loc. 

1.8-m RWP Width 

Wire Line LWP Depth 

Wire Line LWP Loc. 

Wire Line LWP Width 

Wire Line RWP Depth 

Wire Line RWP Loc. 

Wire Line RWP Width 

Straightedge -13 18 3 5 3 3 4 4 2 5 2 5 4 4 5 Dipstick -5 12 2 4 1 1 1 1 1 4 1 4 2 1 2 Static PASCO -16 41 9 10 3 4 9 9 3 10 3 9 9 9 9 Dynamic PASCO 

-12 45 6 9 3 3 6 1 4 9 3 7 6 5 6 

82 
83

The offset stations were compared to the stations that were exactly 15.2 m apart. First, a set of 

paired t-tests were conducted. The only index for which a significant difference was found was 

the LWP wire line rut depth, indicating that profiles within a limited distance were very similar. 

The data were examined to determine whether the difference in the values of an index increased 

with increasing distance between the stations where those profiles were observed. The absolute 

value of the differences at the stations and the indices were checked for a correlation, but none 

was noted. A correlation between the difference in the index and the difference at the station 

would provide a means for establishing a limit on the distance from the station the measurement 

can be taken and still be representative of that location. 

A t-test was performed to compare the dynamic PASCO readings to the static PASCO data. In 

all cases, there were no statistically significant differences. The mean differences shown as part 

of the results of the test were well within the COV ranges shown in tables 19 and 20. Therefore, 

the static data were used to assess the bias of the PASCO method of data collection. 

A series of paired t-tests were used to determine the bias of the various measurement methods. 

The straightedge method was used as the benchmark for this analysis. Table 21 presents the 

minimum and maximum levels of bias found for each index where a statistically significant 

difference was found by the t-tests. These values are based on the ASTM procedure of providing 

a 95 percent confidence interval for bias.(9)

The indices calculated from the Dipstick data versus those from the straightedge show 

considerable scatter. This scatter presents itself in the bias values determined for the indices that 

were found to be significantly different from the straightedge indices because the straightedge 

measurements were taken every 152 mm and the Dipstick measurements were taken every 305 

mm. Therefore, the actual measurements for the Dipstick could be compared to those taken at 

the same location. A graph of these data also showed considerable scatter. The bias for these 

relative elevation measurements lies between –4 and –2. 

A direct comparison was made between the indices calculated from the static PASCO data and 

the indices calculated from the Dipstick data. The only indices that were significantly different 

between the two methods were the 1.8-m rut depths, 1.8-m rut widths, wire line rut depths, and 

wire line rut widths. All of the plots showed a large amount of scatter. For analysis purposes, 

the data collected by the RoadRecon unit and the Dipstick may be used interchangeably when 

the area indices are being considered. However, if the researcher is examining either rut depths 

or rut widths, only the data from one of the collection methods should be used. 

SUMMARY 

The precision and bias values for both the Dipstick and the RoadRecon unit were determined 

from five repeat runs. These values are presented in tables 19, 20, and 21. Based on these data, 

the Dipstick data were more precise, but less accurate than the RoadRecon unit. The Dipstick

and RoadRecon unit provide the same results for the area indices, but the results are different for 

the rut depths and rut widths. 
84

Table 21. Minimum and maximum levels of bias. 

Index Minimum Maximum 

RoadRecon 

Negative Area -2135 -5043 

Positive Area -941 -2711 

Fill Area 1135 2629 

LWP 1.8-m Rut Width 20 85 

RWP 1.8-m Rut Depth 0.3 1.3 

RWP 1.8-m Rut Location -20 -75 

RWP 1.8-m Rut Width 49 103 

RWP Wire Line Rut Depth 0.3 1.3 

RWP Wire Line Rut Location -18 -71 

Dipstick 

Negative Area 2592 -10852 

Positive Area 1283 -4775 

LWP 1.8-m Rut Depth -6 -2 

LWP 1.8-m Rut Location -284 132 

LWP 1.8-m Rut Width -222 -40 

LWP Wire Line Rut Depth -6 -2 

LWP Wire Line Rut Location -272 140 

RWP Wire Line Rut Depth 0.1 6 

RWP Wire Line Rut Width -37 820 
85

CHAPTER 8. CONCLUSIONS AND RECOMMENDATIONS 

The following conclusions can be drawn from these analyses. 

• The 1.8-m and wire line rut depths are fairly highly correlated (R2 ≈ 0.95) and 

provide the same type of information, namely the severity of the rutting. 

• It was anticipated that the 1.8-m and wire line rut widths would be related. The data 

do not substantiate this. 

• The fill area provides a two-dimensional rut depth. This index exhibited a fairly high 

correlation with the rut depths (R2 ≈ 0.85) and the negative area (R2 ≈ 0.91). 

• The positive area did not behave in the same manner as any of the other indices; 

therefore, it may provide additional information about the profile. 

• The mean rut depth for a section can be accurately obtained with only six profiles. 

However, the other indices considered in this study require the 11 measurements that 

were originally included in the data collection plan. 

• Results of the paired t-tests indicate that there are statistically significant differences 

between three rut depth measurement systems – three-point, five-point, and wire line. 

• The transverse location of the rut bar dramatically affects the measurement and, 

hence, the rut depth computation. Thus, consistent lateral placement of the survey 

vehicle is essential to repeatable rut depth measurements using the three or five-point 

procedures. 

• Although a better correlation (R2 ≈ 0.5), but still considered poor, existed between the 

five-point rut depths and the wire line rut depths than between the three-point rut 

depths and the wire line rut depths (R2 ≈ 0.2), the five-point rut depths consistently 

underestimated the wire line rut depths. 

• The three-point rut depths underestimate the rut depths for transverse profiles where 

the middle of the profile is lower than the outside edges of the lane (categories 2 and 

3). 

• A better correlation was found between the three-point, five-point, and wire line rut 

depths for those transverse profile shapes with a “hump” in the middle (R2 ≈ 0.35 for 

the three-point and R2 ≈ 0.6 for the five-point) (categories 3 and 4). 

• These data indicate that the five-point rut depth never exceeds the wire line rut depth. 

However, the three-point rut depth may be larger or smaller than the wire line rut 

depth. 
86

• The average three-point and five-point rut depths did not show a stronger relationship 

with the wire line rut depths calculated for the individual wheelpaths. 

• Generally, the size of the difference observed between the wire line rut depths and the 

rut depths from the three-point and five-point rut bars increases with an increase in 

the wire line rut depth. 

• Neither the three-point nor the five-point rut depth measurement system provides 

reliable and accurate estimates of rut depths as measured with a wire line. 

• The Dipstick relative elevation measurements are very precise, but not very 

accurate. The RoadRecon unit relative elevation measurements are not very precise, 

but are relatively accurate. For example, the coefficient of variation of the rut depth 

for the RoadRecon unit was approximately three times that of the Dipstick (11 

percent versus 4 percent, respectively). Also, the bias for the LWP rut depth is much 

larger for the Dipstick than for the RoadRecon unit (4 mm versus 0 mm, 

respectively). These trends, as shown in tables 19, 20, and 21, are consistent for all 

the indices. 

• Analysis performed using rut widths or rut depths should be performed using only 

one method of data collection. Analysis involving any of the other indices could be 

performed using the combined data set. 

The recommendations from this study are as follows: 

• Two tables should be added to NIMS. The first table should contain the values of the 

indices studied for each individual profile. These indices include the positive area, 

negative area, fill area, LWP and RWP 1.8-m rut depths, LWP and RWP 1.8-m rut 

locations, LWP and RWP wire line rut depths, LWP and RWP wire line rut widths, 

and LWP and RWP wire line rut locations. The second table should contain the 

mean, standard deviation, and minimum and maximum values for each index for each 

survey. The rut depths are the most commonly used and most widely understood 

measure of rutting. The rut widths and positive area indices appear to provide 

additional information about the profile. Until it is proven that this additional 

information is not useful, these indices should be kept in NIMS. The fill area and 

negative area are both highly correlated to the rut depths. However, the fill area is a 

very easily understood index and provides the user an opportunity to segue into 

viewing the transverse profile from different perspectives. 

• Further review needs to be undertaken to determine the cause of the negative trends 

for the sections provided in table 11. 

• The three-sensor rut bar does not provide repeatable and accurate rut depth 

measurements and, therefore, would not provide adequate network-level rut depths 
87

for pavement management systems. Inconsistent rut depths obtained over time from 

the highway network would be problematic for determining rehabilitation needs. 

 

• If a five-sensor rut bar is used for network-level data collection, care should be taken 

to ensure that the transverse location of the rut bar is consistent from year to year and 

that the mean values are adjusted to reflect more realistic rut depth values. 

• A second field study should be undertaken. This field study should examine the 

relationship between the indices studied and the mechanism causing the rutting. This 

study should also provide additional information to verify the bias and precision 

values presented here. 

• Indices not recommended for inclusion in the database are: PASCO typecasting, 

radius of curvature, and maximum water depth in each wheelpath. 

• To limit the variability of the area and rut width indices, a transverse profile 

measurement should be made every 15.2 m on each test section. 

89

APPENDIX A. 

RUTCHAR PROGRAM USER’S GUIDE 

INTRODUCTION 

The purpose of the User’s Guide for the RUTCHAR program, developed under the Transverse 

Profile Data Study by Fugro-BRE, Inc. in Austin, Texas, is: (1) to describe the system so that 

potential users can determine its applicability, and (2) to provide users with all the information 

necessary to operate and use the system efficiently and effectively. 

One of the objectives of the Transverse Profile Data Study was to provide a method for 

characterizing the transverse profiles collected on the test sections included in the LTPP project. 

The characterizations were then to be determined for all of the data that had passed through the 

Quality Control (QC) process in the NIMS. At that time, 45,370 transverse profiles resided in 

NIMS for which the rutting characterizations needed to be determined. The RUTCHAR 

program was written to perform these calculations and to provide a method by which these 

calculations could be easily performed for all of the transverse profile data to be collected. 

This program was intended for the sole purpose of calculating the rutting indices of data 

collected for LTPP. The output of the program should then be filtered into a table in NIMS. 

The program was written in VisualBasic and requires an IBM 486-compatible system or later 

with Windows 95 or later. 

APPLICATION DESCRIPTION 

As previously stated, the program was written to calculate the indices used to characterize the 

transverse profile data for NIMS. 

The first step in the program is a check of the input data. This data should be a series of x-y

coordinates that define the transverse profile. Each of the x-y coordinates is reviewed to 

determine whether there are any duplicates. If a duplicate set of x-y coordinates is encountered, 

one of the duplicates is removed from the data set for all further calculations. A message is 

written to a file named DATCHK.OUT, which provides the section ID, construction event 

number, survey data, the x-coordinate, and the statement “IS A DUPLICATE POINT.” 

Next, a check is performed to find duplicate x-values. It was found that not all of the problems 

encountered were due to duplicate x-y coordinates in the data being used to perform these 

calculations. In some cases, the x-values were the same, but the y-values were different. In this 

case, the first of the duplicate x-values is reduced by 1. Furthermore, the section ID, construction 

event number, survey data, the x-coordinate, and the statement “IS A DUPLICATE X” are 

written to the DATCHK.OUT file. 
90

The input file containing the original data set is not overwritten, but the data being used for the 

calculation are slightly altered. Once the check has been completed, the computation of the 

indices is initiated. The following discusses the computation of each index. 

SYSTEM OPERATION 

In order to run the software, double-click on the RUTCHAR icon. The system will prompt the 

user for four file names. The first file should be a data extraction of the 

MON_T_PROF_PROFILE table. The last file should be a data extraction of the 

MON_T_PROF_MASTER table. Both files should be in a fixed-width format. 

The other two file names are the output file names. The first file being created will contain the 

calculated indices for each profile contained in the MON_T_PROF_PROFILE extraction. This 

file name should be formatted UR##YYYY.RIP. In this case “##” refers to the number of times 

these calculations have been performed in the year. “YYYY” is the year. The second file being 

created will contain the mean, standard deviation, and minimum and maximum values for each 

index for each survey. This filename should be formatted UR##YYYY.RIS. The format of 

these files is provided in tables 22 and 23. 

While the data is being processed, a message will appear on the screen, “Please wait, your data is 

being processed.” 

The second output file is the DATCHK.OUT file, which has been previously discussed. This file 

will automatically be written in the directory from which the program was run. This file will be 

written if neither of the two discontinuities discussed are encountered; however, it will be 0-

bytes long. If this file already exists in the directory from which the program is run, it will not be 

overwritten. The program will append information to the DATCHK.OUT file, but will never 

overwrite it. The user should rename or delete the previously written DATCHK.OUT file if 

he/she wants to work with a new file. 
91

Table 22. File format output for the UR##YYYY.RIP file.

Item Format Units IMS Field Name Comments 

1 Character(4) SHRP_ID 1 - 6 

2 Numeric STATE_CODE 8 - 10 

3 DD-MMMYYYY  SURVEY_DATE 12 - 22 

4 Numeric m POINT_LOC 24 - 29 

5 Numeric mm2 NEGATIVE_AREA 31 - 39 

6 Character(1) NEGATIVE_AREA_FLAG 41 - 43 

7 Numeric mm2 POSITIVE AREA 45 - 51 

8 Character(1) POSITIVE_AREA_FLAG 53 - 55 

9 Numeric mm2 FILL_AREA 57 - 63 

10 Character(1) FILL_AREA_FLAG 65 - 67 

11 Numeric mm LLH_DEPTH_1_8 69 - 73 

12 Character(1) LLH_DEPTH_1_8_FLAG 75 - 77 

13 Numeric mm LLH_WIDTH_1_8 79 - 83 

14 Character(1) LLH_WIDTH_1_8_FLAG 85 - 87 

15 Numeric mm LLH_OFFSET_1_8 89 - 93 

16 Character(1) LLH_OFFSET_1_8_FLAG 95 - 97 

17 Numeric mm RLH_DEPTH_1_8 99 - 103 

18 Character(1) RLH_DEPTH_1_8_FLAG 105 - 107 

19 Numeric mm RLH_WIDTH_1_8 109 - 113 

20 Character(1) RLH_WIDTH_1_8_FLAG 115 - 117 

21 Numeric mm RLH_OFFSET_1_8 119 - 123 

22 Character(1) RLH_OFFSET_1_8_FLAG 125 - 127 

23 Numeric mm LLH_DEPTH_WIRE_REF 129 - 133 

24 Character(1) LLH_DEPTH_WIRE_REF_FLAG 135 - 137 

25 Numeric mm LLH_WIDTH_WIRE_REF 139 - 143 

26 Character(1) LLH_WIDTH_WIRE_REF_FLAG 145 - 147 

27 Numeric mm LLH_OFFSET_WIRE_REF 149 - 153 

28 Character(1) LLH_OFFSET_WIRE_REF_FLAG 155 - 157 

29 Numeric mm RLH_DEPTH_WIRE_REF 159 - 163 

30 Character(1) RLH_DEPTH_WIRE_REF_FLAG 165 - 167 

31 Numeric mm RLH_WIDTH_WIRE_REF 169 - 173 

32 Character(1) RLH_WIDTH_WIRE_REF_FLAG 175 - 177 

33 Numeric mm RLH_OFFSET_WIRE_REF 179 - 183 

34 Character(1) RLH_OFFSET_WIRE_REF_FLAG 185 - 187 

35 Numeric mm TRANS_PROFILE_MEASURE_LENGTH 189 - 193 

36 Character(1) SECTION_STAT_INCLUDE_FLAG 195 - 197 

37 DD-MMMYYYY  DATA_PROCESS_EXTRACT_DATE 199 - 209 
92

Table 23. File format for the UR##YYYY.RIS file. 

Item Format Units IMS Field Name Comments 

1 Character(4) SHRP_ID 1 - 6 

2 Numeric STATE_CODE 8 - 10 

3 DD-MMM-YYYY SURVEY_DATE 12 - 24 

4 Numeric NO_PROFILES 26 - 27 

5 Numeric mm2 POSITIVE_AREA_MEAN 29 - 35 

6 Numeric mm2 POSITIVE_AREA_STD 37 - 43 

7 Numeric mm2 POSITIVE_AREA_MIN 45 - 51 

8 Numeric mm2 POSITIVE_AREA_MAX 53 - 59 

9 Numeric mm2 NEGATIVE_AREA_MEAN 61 - 69 

10 Numeric mm2 NEGATIVE_AREA_STD 71 - 79 

11 Numeric mm2 NEGATIVE_AREA_MIN 81 - 89 

12 Numeric mm2 NEGATIVE_AREA_MAX 91 - 99 

13 Numeric mm2 FILL_AREA_MEAN 101 - 107 

14 Numeric mm2 FILL_AREA_STD 109 - 115 

15 Numeric mm2 FILL_AREA_MIN 117 - 123 

16 Numeric mm2 FILL_AREA_MAX 125 - 131 

17 Numeric mm LLH_DEPTH_1_8_MEAN 133 - 137 

18 Numeric mm LLH_DEPTH_1_8_STD 139 - 143 

19 Numeric mm LLH_DEPTH_1_8_MIN 145 - 149 

20 Numeric mm LLH_DEPTH_1_8_MAX 151 - 155 

21 Numeric mm RLH_DEPTH_1_8_MEAN 157 - 161 

22 Numeric mm RLH_DEPTH_1_8_STD 163 - 167 

23 Numeric mm RLH_DEPTH_1_8_MIN 169 - 173 

24 Numeric mm RLH_DEPTH_1_8_MAX 175 - 179 

25 Numeric mm MAX_MEAN_DEPTH_1_8 181 - 185 

26 Numeric mm LLH_WIDTH_1_8_MEAN 187 - 191 

27 Numeric mm LLH_WIDTH_1_8_STD 193 - 197 

28 Numeric mm LLH_WIDTH_1_8_MIN 199 - 203 

29 Numeric mm LLH_WIDTH_1_8_MAX 205 - 209 

30 Numeric mm LLH_OFFSET_1_8_MEAN 211 - 215 

31 Numeric mm LLH_OFFSET_1_8_STD 217 - 221 

32 Numeric mm LLH_OFFSET_1_8_MIN 223 - 227 

33 Numeric mm LLH_OFFSET_1_8_MAX 229 - 233 

34 Numeric mm RLH_WIDTH_1_8_MEAN 235 - 239 

35 Numeric mm RLH_WIDTH_1_8_STD 241 - 245 

36 Numeric mm RLH_WIDTH_1_8_MIN 247 - 251 

37 Numeric mm RLH_WIDTH_1_8_MAX 253 - 257 

38 Numeric RLH_OFFSET_1_8_MEAN 259 - 263 

39 Numeric RLH_OFFSET_1_8_STD 265 - 269 

40 Numeric RLH_OFFSET_1_8_MIN 271 - 275 

41 Numeric RLH_OFFSET_1_8_MAX 277 - 281 

42 Numeric mm LLH_DEPTH_WIRE_REF_MEAN 283 - 287 

43 Numeric mm LLH_DEPTH_WIRE_REF_STD 289 - 293 

44 Numeric mm LLH_DEPTH_WIRE_REF_MIN 295 - 299 

45 Numeric mm LLH_DEPTH_WIRE_REF_MAX 301 - 305 
93

Table 23. File format for the UR##YYYY.RIS file (continued). 

Item Format Units IMS Field Name Comments 

46 Numeric mm RLH_DEPTH_WIRE_REF_MEAN 307 - 311 

47 Numeric mm RLH_DEPTH_WIRE_REF_STD 313 - 317 

48 Numeric mm RLH_DEPTH_WIRE_REF_MIN 319 - 323 

49 Numeric mm RLH_DEPTH_WIRE_REF_MAX 325 - 329 

50 Numeric mm MAX_MEAN_DEPTH_WIRE_REF 331 - 335 

51 Numeric mm LLH_WIDTH_WIRE_REF_MEAN 337 - 341 

52 Numeric mm LLH_WIDTH_WIRE_REF_STD 343 - 347 

53 Numeric mm LLH_WIDTH_WIRE_REF_MIN 349 - 353 

54 Numeric mm LLH_WIDTH_WIRE_REF_MAX 355 - 359 

55 Numeric mm LLH_OFFSET_WIRE_REF_MEAN 361 - 365 

56 Numeric mm LLH_OFFSET_WIRE_REF_STD 367 - 371 

57 Numeric mm LLH_OFFSET_WIRE_REF_MIN 373 - 377 

58 Numeric mm LLH_OFFSET_WIRE_REF_MAX 379 - 383 

59 Numeric mm RLH_WIDTH_WIRE_REF_MEAN 385 - 389 

60 Numeric mm RLH_WIDTH_WIRE_REF_STD 391 - 395 

61 Numeric mm RLH_WIDTH_WIRE_REF_MIN 397 - 401 

62 Numeric mm RLH_WIDTH_WIRE_REF_MAX 403 - 407 

63 Numeric mm RLH_OFFSET_WIRE_REF_MEAN 409 - 413 

64 Numeric mm RLH_OFFSET_WIRE_REF_STD 415 - 419 

65 Numeric mm RLH_OFFSET_WIRE_REF_MIN 421 - 425 

66 Numeric mm RLH_OFFSET_WIRE_REF_MAX 427 - 431 

67 Character(1) T_PROF_DEVICE_CODE 433 - 435 

68 DD-MMM-YYYY DATA_PROCESS_EXTRACT_DATE 447 - 457 
 
 95

APPENDIX B. 

DISTRIBUTION OF THE INDICES 

This appendix contains distributions of each of the indices by various categories. Each 

distribution includes a histogram, a normal probability plot, a list of quantiles, the mean, the 

standard deviation, the confidence interval, the skewness of the distribution, and the kurtosis of 

the distribution. The histogram provides a distribution of the data collected. The histogram in 

figure 35 illustrates that the majority of the data for the negative area index lies between 0 and 

-10,000. The normal probability plot, located to the right of the histogram, is another method for 

viewing the distribution of the data. This type of plot is often used to determine if the data are 

normally distributed. The closer the line presented in the plot is to a straight line, the more the 

data are considered to follow a normal distribution. The quantities are determined by sorting the 

data in ascending order. The value for the 25th percentile is the value found one-quarter of the 

way through the data. The skewness and kurtosis are both values that pertain to the normality of 

the data. Skewness is a measure of the tendency of the deviations to be larger in one direction 

than in the other. Skewness values that have a large absolute value are likely to be from a nonnormal distribution. Kurtosis measures the “heaviness” of the tails of a distribution. A large 

value of kurtosis indicates a heavy-tailed distribution. Kurtosis and skewness values are usually 

less than +1.0. 

Figures 35 through 49 contain the distribution of all of the individual values for each index. 

Figures 50 through 63 provide the distribution of the section means. All of the sections are 

included in these distributions. Figures 64 through 79 provide the distribution of the GPS-1 

(HMAC over granular base) section means. Figures 80 through 94 provide the distribution of the 

GPS-2 (HMAC over stabilized base) section means. The GPS-6 (HMAC overlay of HMAC) 

section mean distributions are provided in figures 95 through 109. The GPS-7 (HMAC overlay 

of PCC) section mean distributions are provided in figures 110 through 124. 
 96

Figure 35. Distribution of the negative area index. 

Neg Area

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0

 0

 0

 0

 -82

 -2539

 -9579

 -18282

 -29687

 -44499

 -68429

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 -6316.62

 8667.60

 40.69

 -6236.86

 -6396.38

 45370.00

 45370.00

-2.8658e8

 75127285

 -2.05

 5.25

 -137.22
 97

Figure 36. Distribution of the positive area index. 

Pos Area

0

10000

20000

30000

40000

50000

60000

70000

80000

.001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 86338

 51961

 39314

 24873

 13739

 4868

 777

 0

 0

 0

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 9138.77

 11060.67

 51.93

 9240.55

 9036.99

 45370.00

 45370.00

414625843

122338458

 1.72

 3.24

 121.03
 98

Figure 37. Distribution of the fill area index. 

Fill Area 

0

10000

20000

30000

40000

50000

60000

70000

80000 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 79877

 48746

 34059

 22250

 14768

 8600

 4900

 2882

 1443

 310

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 11054.19

 8710.74

 40.90

 11134.35

 10974.03

 45370.00

 45370.00

501528624

 75877044

 1.81

 4.80

 78.80
 99

Figure 38. Distribution of the LWP 1.8-m rut depth. 

1.8 m LWP

0

10

20

30

40

50

60

.001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 62.000

 24.145

 17.000

 11.000

 7.000

 4.000

 3.000

 2.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.59

 4.27

 0.02

 5.62

 5.55

 45370.00

 45370.00

253404.00

 18.20

 2.18

 8.26

 76.39
 100

Figure 39. Distribution of the LWP 1.8-m rut width. 

W 1.8 m LWP

0

200

400

600

800

1000

1200

1400

1600

1800 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1800.0

 1797.0

 1786.0

 1752.0

 1688.0

 1524.0

 1219.0

 771.0

 384.0

 0.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1399.10

 385.49

 1.81

 1402.65

 1395.56

 45370.00

 45370.00

 63477346

148600.10

 -1.41

 1.39

 27.55
 101

Figure 40. Distribution of the LWP 1.8-m rut location. 

LWP 1.8 Loc

1700

1900

2200

2500

2800

3100

3400

3700

4000

4300 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 4383.0

 3566.0

 3372.0

 3107.0

 2904.0

 2740.0

 2456.0

 2221.0

 1918.0

 1843.9

 1732.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2692.99

 348.40

 1.64

 2696.20

 2689.79

 45370.00

 45370.00

122181165

121381.24

 -0.09

 0.39

 12.94
 102

Figure 41. Distribution of the RWP 1.8-m rut depth. 

1.8 m RWP

0

10

20

30

40 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 40.000

 22.000

 16.000

 10.000

 7.000

 4.000

 3.000

 2.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.34

 3.95

 0.02

 5.38

 5.31

 45370.00

 45370.00

242353.00

 15.61

 1.83

 4.83

 73.96
 103

Figure 42. Distribution of the RWP 1.8-m rut width. 

W 1.8 m RWP

0

200

400

600

800

1000

1200

1400

1600

1800 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1800.0

 1797.0

 1787.0

 1754.0

 1687.0

 1524.0

 1274.0

 889.0

 443.0

 0.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1419.77

 358.88

 1.68

 1423.07

 1416.46

 45370.00

 45370.00

 64414800

128792.54

 -1.52

 2.03

 25.28
 104

Figure 43. Distribution of the RWP 1.8-m rut location. 

RWP 1.8 Loc

0

200

400

600

800

1000

1200

1400

1600

1800

2000 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 2036.0

 1829.0

 1750.0

 1424.9

 1147.0

 914.0

 665.0

 435.0

 191.0

 111.0

 44.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 919.97

 371.52

 1.74

 923.39

 916.55

 45370.00

 45370.00

 41738989

138024.69

 0.20

 -0.04

 40.38
 105

Figure 44. Distribution of the LWP wire line rut depth. 

3.7 m LWP

0

10

20

30

40

50

60

.001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 62.000

 27.000

 19.000

 12.000

 8.000

 5.000

 3.000

 2.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 6.24

 4.72

 0.02

 6.28

 6.19

 45370.00

 45370.00

283006.00

 22.31

 2.04

 7.39

 75.73
 106

Figure 45. Distribution of the LWP wire line rut width. 

W 3.7 m LWP

0

1000

2000

3000

4000

.001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 4252.0

 3660.0

 3660.0

 3485.0

 3048.0

 1775.0

 1333.0

 863.1

 403.0

 0.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2014.03

 973.74

 4.57

 2022.99

 2005.07

 45370.00

 45370.00

 91376357

948163.83

 0.30

 -1.02

 48.35
 107

Figure 46. Distribution of the LWP wire line rut location. 

LWP 3.7 Loc

1700

1900

2200

2500

2800

3100

3400

3700

4000

4300 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 4383.0

 3552.0

 3353.0

 3065.0

 2861.0

 2692.0

 2438.0

 2134.0

 1892.0

 1837.9

 1732.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2649.46

 355.80

 1.67

 2652.74

 2646.19

 45370.00

 45370.00

120206170

126591.03

 -0.08

 0.26

 13.43
 108

Figure 47. Distribution of the RWP wire line rut depth. 

3.7 m RWP

0

10

20

30

40 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 40.000

 24.000

 17.000

 12.000

 8.000

 5.000

 3.000

 2.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 6.00

 4.32

 0.02

 6.04

 5.96

 45370.00

 45370.00

272067.00

 18.68

 1.66

 3.91

 72.07
 109

Figure 48. Distribution of the RWP wire line rut width. 

W 3.7 m RWP

0

1000

2000

3000

4000

.001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 4252.0

 3660.0

 3660.0

 3485.0

 3048.0

 1756.0

 1377.0

 915.0

 457.0

 0.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2032.40

 954.03

 4.48

 2041.18

 2023.62

 45370.00

 45370.00

 92210054

910177.58

 0.35

 -1.01

 46.94
 110

Figure 49. Distribution of the RWP wire line rut location. 

RWP 3.7 Loc

0

200

400

600

800

1000

1200

1400

1600

1800

2000 .001 .01 .05.10.25 .50 .75.90.95 .99.999

-5 -4 -3 -2 -1 0 1 2 3 4 5

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 2093.0

 1829.0

 1785.0

 1524.0

 1209.0

 918.5

 726.0

 502.1

 212.3

 116.0

 44.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 970.25

 380.55

 1.79

 973.75

 966.75

 45370.00

 45370.00

 44020147

144816.98

 0.18

 -0.13

 39.22
 111

Figure 50. Distribution of the section means of the negative area index. 

Mean(Neg Area)

-50000

-40000

-30000

-20000

-10000

0 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0

 0

 0

 -45

 -536

 -3320

 -9584

 -16872

 -27369

 -40860

 -54774

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

-6315.338

 7862.681

 122.288

-6075.582

-6555.093

 4134.000

 4134.000

-26107607

 61821759

 -1.936

 4.623

 -124.501
 112

Figure 51. Distribution of the section means of the positive area index. 

Mean(Pos Area)

0

10000

20000

30000

40000

50000

60000

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 67362

 46513

 37615

 23385

 13371

 5494

 1508

 337

 44

 0

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 9134.34

 10095.35

 157.01

 9442.18

 8826.51

 4134.00

 4134.00

 37761368

101916081

 1.62

 2.65

 110.52
 113

Figure 52. Distribution of the section means of the fill area index. 

Mean(Fill Area )

0

10000

20000

30000

40000

50000

60000

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 62622

 46200

 32522

 21381

 14519

 8921

 5408

 3352

 1829

 647

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 11053.15

 8041.35

 125.07

 11298.36

 10807.95

 4134.00

 4134.00

 45693733

 64663378

 1.69

 3.97

 72.75
 114

Figure 53. Distribution of the section means of the LWP 1.8-m rut depths. 

Mean(1.8 m LWP)

0

10

20

30

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 33.636

 21.939

 16.091

 10.455

 7.091

 4.364

 3.000

 2.182

 1.273

 0.698

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.584

 3.884

 0.060

 5.702

 5.465

 4134.000

 4134.000

23083.857

 15.088

 1.960

 5.705

 69.562
 115

Figure 54. Distribution of the section means of the LWP 1.8-m rut widths. 

Mean(W 1.8 m LWP)

0

200

400

600

800

1000

1200

1400

1600

1800 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1780.3

 1749.4

 1730.8

 1689.8

 1606.8

 1496.3

 1246.8

 978.7

 714.8

 486.9

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1399.147

 280.627

 4.365

 1407.704

 1390.590

 4134.000

 4134.000

5784073.6

78751.711

 -1.196

 1.254

 20.057
 116

Figure 55. Distribution of the section means of the LWP 1.8-m rut locations. 

LWP 1.8 Loc

2000

3000

4000 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3952.0

 3366.3

 3071.0

 2937.0

 2824.0

 2699.0

 2577.0

 2436.0

 2253.4

 2069.0

 1829.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2692.254

 206.712

 3.215

 2698.558

 2685.951

 4134.000

 4134.000

 11129780

42729.710

 0.029

 1.810

 7.678
 117

Figure 56. Distribution of the section means of the RWP 1.8-m rut depths. 

Mean(1.8 m RWP)

0

10

20

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 28.000

 20.727

 15.330

 10.182

 6.727

 4.182

 2.909

 2.091

 1.182

 0.636

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.340

 3.630

 0.056

 5.450

 5.229

 4134.000

 4134.000

22074.604

 13.179

 1.770

 4.133

 67.985
 118

Figure 57. Distribution of the section means of the RWP 1.8-m rut widths. 

Mean(W 1.8 m RWP)

0

200

400

600

800

1000

1200

1400

1600

1800 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1772.6

 1747.0

 1724.8

 1679.9

 1599.6

 1496.3

 1320.5

 1043.5

 730.3

 471.1

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1419.625

 261.462

 4.067

 1427.598

 1411.652

 4134.000

 4134.000

5868729.2

68362.466

 -1.508

 2.629

 18.418
 119

Figure 58. Distribution of the section means of the RWP 1.8-m rut locations. 

RWP 1.8 Loc

100

300

500

700

900

1100

1300

1500

1700

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1801.0

 1587.6

 1387.9

 1198.5

 1052.0

 914.0

 773.8

 655.0

 509.3

 326.4

 69.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 919.281

 219.765

 3.418

 925.982

 912.580

 4134.000

 4134.000

 3800307

48296.509

 0.252

 0.631

 23.906
 120

Figure 59. Distribution of the section means of the LWP wire line rut depths. 

Mean(3.7 m LWP)

0

10

20

30

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 36.000

 24.423

 18.000

 11.818

 8.000

 4.909

 3.273

 2.273

 1.273

 0.698

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 6.237

 4.304

 0.067

 6.368

 6.106

 4134.000

 4134.000

25783.761

 18.528

 1.827

 4.912

 69.014
 121

Figure 60. Distribution of the section means of the LWP wire line rut widths. 

LWP 3.7 W

0

1000

2000

3000

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3855.0

 3632.3

 3520.3

 3265.5

 2638.5

 1834.0

 1482.0

 1128.5

 763.4

 468.7

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2032.012

 779.466

 12.123

 2055.780

 2008.244

 4134.000

 4134.000

 8400339

607567.72

 0.368

 -0.760

 38.359
 122

Figure 61. Distribution of the section means of the LWP wire line rut locations. 

LWP 3.7 Loc

2000

3000

4000 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3952.0

 3289.8

 3049.3

 2909.0

 2796.0

 2662.0

 2521.0

 2355.0

 2142.8

 1980.7

 1829.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2648.902

 227.078

 3.532

 2655.826

 2641.978

 4134.000

 4134.000

 10950560

51564.309

 -0.142

 1.323

 8.573
 123

Figure 62. Distribution of the section means of the RWP wire line rut depths. 

Mean(3.7 m RWP)

0

10

20

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 28.545

 22.027

 16.455

 11.273

 7.606

 4.909

 3.182

 2.182

 1.273

 0.636

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.996

 3.955

 0.062

 6.116

 5.875

 4134.000

 4134.000

24785.574

 15.643

 1.598

 3.308

 65.967
 124

Figure 63. Distribution of the section means of the RWP wire line rut widths. 

Mean(W 3.7 m RWP)

0

1000

2000

3000

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3851.6

 3633.6

 3522.8

 3261.5

 2638.1

 1833.9

 1482.0

 1128.3

 755.5

 478.3

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2032.165

 778.446

 12.107

 2055.902

 2008.428

 4134.000

 4134.000

8400971.7

605978.17

 0.368

 -0.761

 38.306
 125

Figure 64. Distribution of the section means of the RWP wire line rut locations. 

RWP 3.7 Loc

100

300

500

700

900

1100

1300

1500

1700

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1829.0

 1693.6

 1496.0

 1278.0

 1099.0

 944.0

 818.0

 696.0

 554.0

 367.5

 69.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 969.621

 234.539

 3.648

 976.773

 962.470

 4134.000

 4134.000

 4008415

55008.397

 0.400

 0.667

 24.189
 126

Figure 65. Distribution of the section means of the 

negative area index on GPS-1 test sections. 

Neg Area

-50000

-40000

-30000

-20000

-10000

0 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0

 0

 0

 -156

 -1417

 -5859

 -13885

 -21525

 -34645

 -45650

 -54774

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

-8901.220

 9179.388

 280.230

-8351.350

-9451.090

 1073.000

 1073.000

 -9551009

 84261172

 -1.486

 2.631

 -103.125
 127

Figure 66. Distribution of the section means of the 

positive area index on GPS-1 test sections. 

Pos Area

0

10000

20000

30000

40000

50000 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 49699

 45725

 38828

 21839

 11719

 3992

 1032

 247

 33

 0

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 8154.593

 9902.113

 302.293

 8747.756

 7561.430

 1073.000

 1073.000

 8749878

 98051837

 1.745

 2.801

 121.430
 128

Figure 67. Distribution of the section means of the fill area index 

on GPS-1 test sections. 

Fill Area

0

10000

20000

30000

40000

50000

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 55653

 52313

 37638

 25559

 18802

 12321

 7734

 4998

 2159

 516

 83

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 14232.26

 9163.90

 279.76

 14781.20

 13683.32

 1073.00

 1073.00

 15271214

 83977087

 1.38

 2.59

 64.39
 129

Figure 68. Distribution of the section means of the 

LWP 1.8-m rut depths on GPS-1 test sections. 

LWP 1.8

0

10

20

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 26.000

 23.630

 18.000

 13.000

 9.000

 6.000

 4.000

 3.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 7.097

 4.179

 0.128

 7.347

 6.847

 1073.000

 1073.000

 7615.000

 17.466

 1.268

 2.114

 58.889
 130

Figure 69. Distribution of the section means of the 

LWP 1.8-m rut widths on GPS-1 test sections. 

LWP 1.8 W

0

1000

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1771.0

 1750.6

 1729.0

 1692.0

 1625.0

 1524.0

 1413.0

 1219.0

 866.5

 315.4

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1480.642

 218.095

 6.658

 1493.707

 1467.578

 1073.000

 1073.000

 1588729

47565.614

 -2.347

 9.005

 14.730
 131

Figure 70. Distribution of the section means of the 

LWP 1.8-m rut locations on GPS-1 test sections. 

LWP 1.8 Loc

2000

3000

4000 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3952.0

 3636.6

 3103.0

 2937.0

 2829.5

 2724.0

 2610.5

 2521.0

 2383.0

 2134.4

 1829.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2729.686

 194.228

 5.929

 2741.321

 2718.051

 1073.000

 1073.000

 2928953

37724.555

 0.962

 5.788

 7.115
 132

Figure 71. Distribution of the section means of the 

RWP 1.8-m rut depths on GPS-1 test sections. 

RWP 1.8

0

10

20

30

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 32.000

 28.260

 19.150

 14.000

 9.000

 6.000

 4.000

 3.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 7.365

 4.745

 0.145

 7.650

 7.081

 1073.000

 1073.000

 7903.000

 22.514

 1.589

 3.652

 64.422
 133

Figure 72. Distribution of the section means of the 

RWP 1.8-m rut widths on GPS-1 test sections. 

RWP 1.8 W

0

1000

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1767.0

 1756.0

 1740.1

 1711.0

 1645.0

 1524.0

 1411.5

 1191.0

 780.3

 279.7

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1479.859

 239.717

 7.318

 1494.219

 1465.500

 1073.000

 1073.000

 1587889

57464.244

 -2.055

 6.191

 16.199
 134

 

Figure 73. Distribution of the section means of the 

RWP 1.8-m rut locations on GPS-1 test sections. 

RWP 1.8 Loc

200

400

600

800

1000

1200

1400

1600

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1635.0

 1552.0

 1333.0

 1136.0

 1016.0

 901.0

 768.5

 665.0

 561.7

 419.6

 232.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 902.926

 192.095

 5.864

 914.433

 891.419

 1073.000

 1073.000

 968840

36900.447

 0.401

 0.938

 21.275
 135

Figure 74. Distribution of the section means of the 

LWP wire line rut depths on GPS-1 test sections. 

LWP 3.7

0

10

20

30 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 28.000

 24.630

 20.000

 13.000

 10.000

 7.000

 5.000

 3.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 7.700

 4.481

 0.137

 7.968

 7.431

 1073.000

 1073.000

 8262.000

 20.083

 1.216

 1.957

 58.201
 136

Figure 75. Distribution of the section means of the 

LWP wire line rut widths on GPS-1 test sections. 

LWP 3.7 W

0

1000

2000

3000

4000 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3855.0

 3651.8

 3554.3

 3245.6

 2459.0

 1806.0

 1531.5

 1306.4

 919.3

 315.4

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2031.472

 721.481

 22.025

 2074.690

 1988.253

 1073.000

 1073.000

 2179769

520534.24

 0.607

 -0.285

 35.515
 137

Figure 76. Distribution of the section means of the 

LWP wire line rut locations on GPS-1 test sections.

LWP 3.7 Loc

2000

3000

4000 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3952.0

 3636.6

 3086.5

 2922.6

 2810.0

 2715.0

 2596.5

 2492.4

 2354.4

 2103.8

 1829.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2708.664

 201.038

 6.137

 2720.706

 2696.621

 1073.000

 1073.000

 2906396

40416.100

 0.836

 5.670

 7.422
 138

Figure 77. Distribution of the section means of the 

RWP wire line rut depths on GPS-1 test sections. 

RWP 3.7

0

5

10

15

20

25

30

35 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 34.000

 29.630

 20.000

 15.000

 10.000

 7.000

 4.000

 3.000

 1.850

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 8.027

 5.167

 0.158

 8.337

 7.718

 1073.000

 1073.000

 8613.000

 26.696

 1.528

 3.310

 64.368
 139

Figure 78. Distribution of the section means of the 

RWP wire line rut widths on GPS-1 test sections. 

RWP 3.7 W

0

1000

2000

3000

4000 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3855.0

 3651.8

 3554.3

 3225.8

 2549.0

 1857.0

 1524.0

 1263.4

 892.1

 279.7

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2043.560

 734.902

 22.435

 2087.583

 1999.538

 1073.000

 1073.000

 2192740

 540081.3

 0.512

 -0.450

 35.962
 140

Figure 79. Distribution of the section means of the 

RWP wire line rut locations on GPS-1 test sections. 

RWP 3.7 Loc

1000

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1801.0

 1580.3

 1441.0

 1155.0

 1039.0

 914.0

 805.0

 693.0

 580.7

 449.5

 232.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 930.497

 195.105

 5.956

 942.184

 918.809

 1073.000

 1073.000

 998423

38065.903

 0.564

 1.483

 20.968
 141

Figure 80. Distribution of the section means of the 

negative area index on GPS-2 test sections. 

Neg Area

-40000

-30000

-20000

-10000

0 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0

 0

 0

 -61

 -716

 -3775

 -9722

 -16766

 -26360

 -45519

 -46511

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

-6461.396

 7599.149

 310.493

-5851.597

-7071.194

 599.000

 599.000

 -3870376

 57747063

 -1.911

 4.755

 -117.608
 142

Figure 81. Distribution of the section means of the 

positive area index on GPS-2 test sections. 

Pos Area

0

10000

20000

30000

40000

50000 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 51100

 49234

 41400

 25930

 14944

 6601

 1548

 243

 34

 0

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 10145.85

 10826.77

 442.37

 11014.65

 9277.05

 599.00

 599.00

 6077365

117218985

 1.41

 1.51

 106.71
 143

Figure 82. Distribution of the section means 

of the fill area index on GPS-2 test sections. 

Fill Area

0

10000

20000

30000

40000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 47111

 46026

 30911

 21742

 16405

 10619

 6315

 4043

 1870

 637

 28

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 11960.28

 7387.44

 301.84

 12553.09

 11367.47

 599.00

 599.00

 7164205

 54574275

 1.20

 2.29

 61.77
 144

Figure 83. Distribution of the section means of the 

LWP 1.8-m rut depths on GPS-2 test sections. 

LWP 1.8

0

10

20 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 19.000

 18.000

 14.000

 10.000

 8.000

 5.000

 3.000

 2.000

 1.000

 1.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.9132

 3.3135

 0.1354

 6.1791

 5.6473

 599.0000

 599.0000

3542.0000

 10.9791

 1.0741

 1.2724

 56.0352
 145

Figure 84. Distribution of the section means of the 

LWP 1.8-m rut widths on GPS-2 test sections. 

LWP 1.8 W

0

1000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1771.0

 1760.0

 1738.0

 1701.0

 1638.0

 1521.0

 1345.0

 1081.0

 744.0

 457.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1446.723

 264.114

 10.791

 1467.917

 1425.529

 599.000

 599.000

 866587

69755.990

 -1.615

 3.193

 18.256
 146

Figure 85. Distribution of the section means of the 

LWP 1.8-m rut locations on GPS-2 test sections. 

LWP 1.8 Loc

1900

2100

2300

2500

2700

2900

3100

3300

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3381.0

 3302.0

 3070.0

 2951.0

 2851.0

 2742.0

 2618.0

 2533.0

 2377.0

 2125.0

 1972.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2734.908

 179.292

 7.326

 2749.296

 2720.521

 599.000

 599.000

 1638210

32145.582

 -0.146

 1.168

 6.556
 147

Figure 86. Distribution of the section means of the 

RWP 1.8-m rut depths on GPS-2 test sections. 

RWP 1.8

0

10

20 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 20.000

 19.000

 14.000

 11.000

 8.000

 6.000

 3.000

 2.000

 1.000

 1.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 6.2337

 3.4971

 0.1429

 6.5143

 5.9531

 599.0000

 599.0000

3734.0000

 12.2296

 0.8484

 0.5143

 56.0994
 148

Figure 87. Distribution of the section means of the 

RWP 1.8-m rut widths on GPS-2 test sections. 

RWP 1.8 W

0

1000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1780.0

 1764.0

 1731.0

 1702.0

 1651.0

 1524.0

 1302.0

 988.0

 665.0

 419.0

 55.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1432.427

 292.256

 11.941

 1455.880

 1408.975

 599.000

 599.000

 858024

85413.857

 -1.425

 1.756

 20.403
 149

Figure 88. Distribution of the section means of the 

RWP 1.8-m rut locations on GPS-2 test sections. 

RWP 1.8 Loc

1000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1718.0

 1496.0

 1326.0

 1111.0

 994.0

 881.0

 772.0

 665.0

 525.0

 220.0

 190.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 888.8364

 195.9340

 8.0056

 904.5592

 873.1135

 599.0000

 599.0000

 532413

38390.137

 0.2429

 1.7509

 22.0439
 150

Figure 89. Distribution of the section means of the 

LWP wire line rut depths on GPS-2 test sections. 

LWP 3.7

0

10

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 22.000

 20.000

 16.000

 12.000

 9.000

 6.000

 4.000

 2.000

 1.000

 1.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 6.4725

 3.7411

 0.1529

 6.7727

 6.1723

 599.0000

 599.0000

3877.0000

 13.9955

 1.0417

 1.1207

 57.7996
 151

Figure 90. Distribution of the section means of the 

LWP wire line rut widths on GPS-2 test sections. 

LWP 3.7 W

0

500

1000

1500

2000

2500

3000

3500

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3658.0

 3626.0

 3556.0

 3280.0

 2355.0

 1724.0

 1423.0

 1123.0

 760.0

 457.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1934.215

 763.768

 31.207

 1995.504

 1872.926

 599.000

 599.000

 1158595

583341.03

 0.679

 -0.306

 39.487
 152

Figure 91. Distribution of the section means of the 

LWP wire line rut locations on GPS-2 test sections. 

LWP 3.7 Loc

1900

2100

2300

2500

2700

2900

3100

3300

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3379.0

 3206.0

 3050.0

 2936.0

 2829.0

 2716.0

 2600.0

 2493.0

 2245.0

 2000.0

 1956.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2708.715

 191.104

 7.808

 2724.050

 2693.379

 599.000

 599.000

 1622520

36520.663

 -0.596

 1.946

 7.055
 153

Figure 92. Distribution of the section means of the 

RWP wire line rut depths on GPS-2 test sections. 

RWP 3.7

0

10

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 22.000

 22.000

 16.000

 12.000

 9.000

 6.000

 4.000

 3.000

 1.000

 1.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 6.8164

 3.9270

 0.1605

 7.1315

 6.5012

 599.0000

 599.0000

4083.0000

 15.4211

 0.9136

 0.8318

 57.6109
 154

Figure 93. Distribution of the section means of the 

RWP wire line rut widths on GPS-2 test sections. 

RWP 3.7 W

0

500

1000

1500

2000

2500

3000

3500

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3658.0

 3626.0

 3553.0

 3304.0

 2383.0

 1737.0

 1434.0

 1039.0

 672.0

 471.0

 55.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1927.511

 776.663

 31.734

 1989.835

 1865.187

 599.000

 599.000

 1154579

603205.93

 0.631

 -0.342

 40.294
 155

Figure 94. Distribution of the section means of the 

RWP wire line rut locations on GPS-2 test sections. 

RWP 3.7 Loc

1000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1746.0

 1734.0

 1462.0

 1171.0

 1029.0

 914.0

 803.0

 693.0

 518.0

 220.0

 190.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 921.8932

 212.9221

 8.6998

 938.9792

 904.8071

 599.0000

 599.0000

 552214

45335.805

 0.4992

 2.2358

 23.0962
 156

Figure 95. Distribution of the section means of the 

negative area index on GPS-6 test sections. 

Neg Area

-40000

-30000

-20000

-10000

0 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0

 0

 0

 -72

 -432

 -2929

 -8942

 -14279

 -25532

 -37505

 -40921

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

-5596.845

 6787.867

 336.462

-4935.410

-6258.280

 407.000

 407.000

 -2277916

 46075138

 -1.896

 4.625

 -121.280
 157

Figure 96. Distribution of the section means of the 

positive area index on GPS-6 test sections. 

Pos Area

0

10000

20000

30000

40000

50000

60000

70000 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 68476

 62393

 37694

 22892

 13529

 6378

 1633

 288

 29

 0

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 9478.57

 10632.08

 527.01

 10514.59

 8442.54

 407.00

 407.00

 3857776

113041155

 1.96

 5.11

 112.17
 158

Figure 97. Distribution of the section means of the 

fill area index on GPS-6 test sections. 

Fill Area

0

10000

20000

30000

40000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 45816

 41073

 30614

 18903

 13289

 8828

 5722

 3970

 2249

 821

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 10482.64

 6936.71

 343.84

 11158.58

 9806.70

 407.00

 407.00

 4266435

 48117893

 1.82

 4.61

 66.17
 159

Figure 98. Distribution of the section means of the 

LWP 1.8-m rut depths on GPS-6 test sections.

LWP 1.8

0

10

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 22.000

 20.000

 15.000

 10.000

 7.000

 5.000

 3.000

 2.000

 1.000

 1.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.5971

 3.4031

 0.1687

 5.9287

 5.2654

 407.0000

 407.0000

2278.0000

 11.5811

 1.6936

 3.7881

 60.8016
 160

Figure 99. Distribution of the section means of the 

LWP 1.8-m rut widths on GPS-6 test sections. 

LWP 1.8 W

0

1000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1742.0

 1739.0

 1724.0

 1674.0

 1598.0

 1521.0

 1358.0

 1134.6

 775.4

 499.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1444.263

 236.856

 11.740

 1467.343

 1421.183

 407.000

 407.000

 587815

56100.539

 -1.875

 5.301

 16.400
 161

Figure 100. Distribution of the section means of the 

LWP 1.8-m rut locations on GPS-6 test sections. 

LWP 1.8 Loc

2100

2200

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3298.0

 3293.3

 3087.6

 2953.2

 2832.0

 2715.0

 2604.0

 2472.8

 2334.6

 2191.2

 2152.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2717.509

 185.530

 9.196

 2735.587

 2699.430

 407.000

 407.000

 1106026

34421.398

 -0.036

 0.231

 6.827
 162

Figure 101. Distribution of the section means of the 

RWP 1.8-m rut depths on GPS-6 test sections. 

RWP 1.8

0

10

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 23.000

 20.920

 16.000

 9.000

 7.000

 5.000

 3.000

 2.000

 2.000

 1.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.3686

 3.3633

 0.1667

 5.6963

 5.0408

 407.0000

 407.0000

2185.0000

 11.3121

 1.8999

 5.2247

 62.6491
 163

Figure 102. Distribution of the section means of the 

RWP 1.8-m rut widths on GPS-6 test sections. 

RWP 1.8 W

0

1000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1749.0

 1748.6

 1724.0

 1675.0

 1580.0

 1469.0

 1257.0

 994.4

 767.0

 581.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1392.921

 266.216

 13.196

 1418.862

 1366.980

 407.000

 407.000

 566919

70870.925

 -1.243

 1.856

 19.112
 164

Figure 103. Distribution of the section means of the 

RWP 1.8-m rut locations on GPS-6 test sections. 

RWP 1.8 Loc

300

500

700

900

1100

1300

1500

1700

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1718.0

 1718.0

 1439.6

 1174.2

 993.0

 881.0

 748.0

 638.0

 530.2

 388.2

 382.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 891.1400

 214.8578

 10.6501

 912.0766

 870.2035

 407.0000

 407.0000

 362694

46163.894

 0.8162

 1.5964

 24.1104
 165

Figure 104. Distribution of the section means of the 

LWP wire line rut depths on GPS-6 test sections. 

LWP 3.7

0

10

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 23.000

 21.920

 17.000

 11.000

 7.000

 5.000

 4.000

 2.800

 1.000

 1.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 6.0909

 3.7224

 0.1845

 6.4536

 5.7282

 407.0000

 407.0000

2479.0000

 13.8562

 1.5990

 3.2470

 61.1140
 166

Figure 105. Distribution of the section means of the LWP 

wire line rut widths on GPS-6 test sections. 

LWP 3.7 W

0

500

1000

1500

2000

2500

3000

3500

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3630.0

 3627.7

 3453.8

 3304.6

 2540.0

 1725.0

 1477.0

 1201.2

 775.4

 501.2

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1999.983

 769.005

 38.118

 2074.918

 1925.048

 407.000

 407.000

 813993

591369.04

 0.583

 -0.657

 38.451
 167

Figure 106. Distributions of the section means of the LWP 

wire line rut locations on GPS-6 test sections. 

LWP 3.7 Loc

2100

2200

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3242.0

 3239.2

 3084.2

 2937.2

 2817.0

 2699.0

 2580.0

 2459.8

 2309.8

 2192.0

 2152.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2696.201

 187.355

 9.287

 2714.458

 2677.945

 407.000

 407.000

 1097354

35102.043

 -0.062

 0.160

 6.949
 168

Figure 107. Distribution of the section means of the RWP 

wire line rut depths on GPS-6 test sections. 

RWP 3.7

0

10

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 24.000

 22.920

 17.800

 10.000

 7.000

 5.000

 3.000

 2.000

 2.000

 1.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.8649

 3.6758

 0.1822

 6.2230

 5.5067

 407.0000

 407.0000

2387.0000

 13.5113

 1.8967

 5.1842

 62.6743
 169

Figure 108. Distribution of the section means of the RWP 

wire line rut widths on GPS-6 test sections. 

RWP 3.7 W

0

500

1000

1500

2000

2500

3000

3500

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3630.0

 3627.7

 3462.2

 3324.2

 2494.0

 1722.0

 1388.0

 1049.4

 775.2

 581.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1951.690

 800.832

 39.696

 2029.726

 1873.654

 407.000

 407.000

 794338

 641332.1

 0.573

 -0.707

 41.033
 170

Figure 109. Distribution of the section means of the RWP 

wire line rut locations on GPS-6 test sections. 

RWP 3.7 Loc

1000

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1829.0

 1798.8

 1494.6

 1227.2

 1041.0

 909.0

 776.0

 682.6

 580.4

 394.1

 382.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 931.1671

 228.5625

 11.3294

 953.4391

 908.8951

 407.0000

 407.0000

 378985

 52240.8

 0.9422

 1.6709

 24.5458
 171

Figure 110. Distribution of the section means of the 

negative area index on GPS-7 test sections. 

Neg Area

-30000

-20000

-10000

0

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0

 0

 0

 -65

 -597

 -2777

 -8643

 -18003

 -30009

 -35957

 -35957

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

-6154.402

 8003.841

 582.194

-5005.917

-7302.887

 189.000

 189.000

 -1163182

 64061469

 -1.787

 2.613

 -130.051
 172

Figure 111. Distribution of the section means of the 

positive area index on GPS-7 test sections. 

Pos Area

0

10000

20000

30000

40000

50000

60000 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 57349

 57349

 32808

 21367

 13404

 5349

 1341

 429

 44

 0

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 8691.77

 9753.77

 709.48

 10091.35

 7292.18

 189.00

 189.00

 1642744

 95135963

 2.00

 5.48

 112.22
 173

Figure 112. Distribution of the section means of the 

fill area index on GPS-7 test sections. 

Fill Area

0

10000

20000

30000

40000 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 39500

 39500

 32539

 24592

 13138

 8124

 5459

 3863

 2152

 0

 0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 10722.77

 7943.74

 577.82

 11862.63

 9582.91

 189.00

 189.00

 2026603

 63102945

 1.56

 2.08

 74.08
 174

Figure 113. Distribution of the section means of the LWP 

1.8-m rut depths on GPS-7 test sections. 

LWP 1.8

0

5

10

15

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 20.000

 20.000

 16.250

 10.000

 7.000

 5.000

 3.000

 2.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.5397

 3.5257

 0.2565

 6.0456

 5.0338

 189.0000

 189.0000

1047.0000

 12.4306

 1.7505

 3.5438

 63.6445
 175

Figure 114. Distribution of the section means of the LWP 

1.8-m rut widths on GPS-7 test sections. 

LWP 1.8 W

0

200

400

600

800

1000

1200

1400

1600

1800 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1751.0

 1751.0

 1730.5

 1709.0

 1634.0

 1524.0

 1332.0

 1163.0

 779.5

 0.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1448.529

 255.833

 18.609

 1485.239

 1411.819

 189.000

 189.000

 273772

65450.325

 -1.867

 5.659

 17.662
 176

Figure 115. Distribution of the section means of the LWP 

1.8-m rut locations on GPS-7 test sections. 

LWP 1.8 Loc

2200

2300

2400

2500

2600

2700

2800

2900

3000

3100 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3065.0

 3065.0

 3015.5

 2954.0

 2848.5

 2737.0

 2609.0

 2493.0

 2357.3

 2227.0

 2227.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2726.116

 168.825

 12.280

 2750.341

 2701.891

 189.000

 189.000

 515236

28501.848

 -0.369

 -0.074

 6.193
 177

Figure 116. Distribution of the section means of the RWP 

1.8-m rut depths on GPS-7 test sections. 

RWP 1.8

0

5

10

15

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 21.000

 21.000

 16.000

 10.000

 6.500

 4.000

 3.000

 2.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.2751

 3.4669

 0.2522

 5.7726

 4.7777

 189.0000

 189.0000

 997.0000

 12.0196

 1.7681

 3.7116

 65.7223
 178

Figure 117. Distribution of the section means of the RWP 

1.8-m rut widths on GPS-7 test sections. 

RWP 1.8 W

0

200

400

600

800

1000

1200

1400

1600

1800 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1754.0

 1754.0

 1726.5

 1671.0

 1589.5

 1443.0

 1253.0

 888.0

 690.3

 0.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1382.550

 293.117

 21.321

 1424.610

 1340.490

 189.000

 189.000

 261302

85917.451

 -1.367

 2.263

 21.201
 179

Figure 118. Distribution of the section means of the RWP 

1.8-m rut locations on GPS-7 test sections. 

RWP 1.8 Loc

300

400

500

600

700

800

900

1000

1100

1200

1300 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1292.0

 1292.0

 1258.5

 1121.0

 1015.0

 902.0

 748.0

 594.0

 407.0

 305.0

 305.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 878.0370

 197.9400

 14.3980

 906.4398

 849.6343

 189.0000

 189.0000

 165949

39180.227

 -0.4052

 0.1565

 22.5435
 180

Figure 119. Distribution of the section means of the LWP 

wire line rut depths on GPS-7 test sections. 

LWP 3.7

0

5

10

15

20

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 20.000

 20.000

 19.000

 12.000

 7.500

 5.000

 3.500

 2.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 6.1481

 4.0065

 0.2914

 6.7231

 5.5732

 189.0000

 189.0000

1162.0000

 16.0524

 1.5302

 2.2185

 65.1667
 181

Figure 120. Distribution of the section means of the LWP 

wire line rut widths on GPS-7 test sections. 

LWP 3.7 W

0

500

1000

1500

2000

2500

3000

3500

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3622.0

 3622.0

 3532.3

 3324.0

 2501.0

 1761.0

 1417.5

 1192.0

 786.5

 0.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1981.825

 779.940

 56.732

 2093.740

 1869.911

 189.000

 189.000

 374565

608305.76

 0.539

 -0.583

 39.355
 182

Figure 121. Distribution of the section means of the LWP 

wire line rut locations on GPS-7 test sections. 

LWP 3.7 Loc

2200

2300

2400

2500

2600

2700

2800

2900

3000

3100 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3065.0

 3065.0

 3008.5

 2922.0

 2826.0

 2709.0

 2588.5

 2465.0

 2350.8

 2221.0

 2221.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 2697.725

 172.889

 12.576

 2722.533

 2672.917

 189.000

 189.000

 509870

29890.552

 -0.265

 -0.287

 6.409
 183

Figure 122. Distribution of the section means of the RWP 

wire line rut depths on GPS-7 test sections. 

RWP 3.7

0

5

10

15

20

25 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 23.000

 23.000

 18.000

 11.000

 7.000

 4.000

 3.000

 2.000

 1.000

 0.000

 0.000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 5.7937

 4.0271

 0.2929

 6.3715

 5.2158

 189.0000

 189.0000

1095.0000

 16.2178

 1.6991

 3.0023

 69.5095
 184

Figure 123. Distribution of the section means of the RWP 

wire line rut widths on GPS-7 test sections. 

RWP 3.7 W

0

500

1000

1500

2000

2500

3000

3500

.01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 3622.0

 3622.0

 3532.3

 3325.0

 2437.0

 1690.0

 1358.5

 970.0

 716.3

 0.0

 0.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1917.566

 810.455

 58.952

 2033.860

 1801.273

 189.000

 189.000

 362420

656836.52

 0.554

 -0.581

 42.265
 185

Figure 124. Distribution of the section means of the RWP 

wire line rut locations on GPS-7 test sections. 

RWP 3.7 Loc

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500 .01 .05.10 .25 .50 .75 .90.95 .99

-3 -2 -1 0 1 2 3

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1469.0

 1469.0

 1295.3

 1160.0

 1048.5

 918.0

 773.5

 637.0

 451.0

 307.0

 307.0

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 909.8095

 206.4425

 15.0165

 939.4323

 880.1867

 189.0000

 189.0000

 171954

42618.506

 -0.2202

 0.1456

 22.6907

187

APPENDIX C. 

COMPARISONS OF SECTION MEANS TO DETERMINE NUMBER OF 

TRANSVERSE PROFILES NECESSARY 

Comparisons were made to determine the number of profiles necessary to accurately predict the 

mean. Figures 125 through 146 provide the results from these comparisons. In each of these 

figures, the axis labeled “All” used all of the available profiles to determine the section mean for 

a given survey date. The axis labeled “Whole” used data from every 30 m to determine the 

section mean on a given survey date. Pairwise comparisons were then made between the “All” 

means and the “Whole” means. Figures 125 through 135 used all of the available data to make 

these comparisons. Figures 136 through 146 used only the data obtained by Dipstick® for these 

comparisons. The difference between the “All” value and the “Whole” value was determined for 

each data pair. The mean of these differences is presented as the mean difference. If the value 

labeled “Prob>|t|” is less than 0.05, the test is statistically significant, which indicates that the 

two values from each pair of values are from two different populations with a 95 percent level of 

confidence. 
188

Figure 125. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the negative area index. 

Whole Mean(Neg Area) By All Mean(Neg Area)

-50000

-40000

-30000

-20000

-10000

0

-50000 -30000 -10000

All Mean(Neg Area)

Paired t-Test

Paired t-Test

All Mean(Neg Area) - Whole Mean(Neg Area)

Mean Difference

Std Error

t-Ratio

DF

-50.6488

13.45269

-3.76496

 4133

 Prob > |t|

Prob > t

Prob < t

0.0002

0.9999

<.0001
189

Figure 126. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the positive area index. 

Whole Mean(Pos Area) By All Mean(Pos Area)

0

10000

20000

30000

40000

50000

60000

0 10000 30000 50000

All Mean(Pos Area)

Paired t-Test

Paired t-Test

All Mean(Pos Area) - Whole Mean(Pos Area)

Mean Difference

Std Error

t-Ratio

DF

-41.8659

17.15248

-2.44081

 4133

 Prob > |t|

Prob > t

Prob < t

0.0147

0.9927

0.0073
190

Figure 127. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the fill area index. 

Whole Mean(Fill Area) By All Mean(Fill Area)

0

10000

20000

30000

40000

50000

60000

0 10000 30000 50000

All Mean(Fill Area)

Paired t-Test

Paired t-Test

All Mean(Fill Area) - Whole Mean(Fill Area)

Mean Difference

Std Error

t-Ratio

DF

36.04745

12.67641

2.843664

 4133

 Prob > |t|

Prob > t

Prob < t

0.0045

0.0022

0.9978
191

Figure 128. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the LWP 1.8-m rut depths. 

Whole Mean(1.8 m LWP) By All Mean (1.8 m LWP)

0

10

20

30

0 10 20 30

All Mean (1.8 m LWP)

Paired t-Test

Paired t-Test

All Mean (1.8 m LWP) - Whole Mean(1.8 m LWP)

Mean Difference

Std Error

t-Ratio

DF

0.019334

0.006823

2.833611

 4133

 Prob > |t|

Prob > t

Prob < t

0.0046

0.0023

0.9977
192

Figure 129. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the LWP 1.8-m rut widths. 

Whole Mean(W 1.8 m LWP) By All Mean(W 1.8 m LWP)

0

200

400

600

800

1000

1200

1400

1600

1800

0100 300 500 700 900 1100 1400 1700

All Mean(W 1.8 m LWP)

Paired t-Test

Paired t-Test

All Mean(W 1.8 m LWP) - Whole Mean(W 1.8 m LWP)

Mean Difference

Std Error

t-Ratio

DF

-2.26582

1.137913

 -1.9912

 4133

 Prob > |t|

Prob > t

Prob < t

0.0465

0.9767

0.0233
193

Figure 130. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the RWP 1.8-m rut depths. 

Whole Mean(1.8 m RWP) By All Mean(1.8 m RWP)

0

10

20

0 10 20

All Mean(1.8 m RWP)

Paired t-Test

Paired t-Test

All Mean(1.8 m RWP) - Whole Mean(1.8 m RWP)

Mean Difference

Std Error

t-Ratio

DF

0.001648

0.006309

0.261196

 4133

 Prob > |t|

Prob > t

Prob < t

0.7940

0.3970

0.6030
194

Figure 131. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the RWP 1.8-m rut widths. 

Whole Mean(W 1.8 m RWP) By All Mean(W 1.8 m RWP)

0

200

400

600

800

1000

1200

1400

1600

1800

0100 300 500 700 900 1100 1400 1700

All Mean(W 1.8 m RWP)

Paired t-Test

Paired t-Test

All Mean(W 1.8 m RWP) - Whole Mean(W 1.8 m RWP)

Mean Difference

Std Error

t-Ratio

DF

0.019608

1.103196

0.017773

 4133

 Prob > |t|

Prob > t

Prob < t

0.9858

0.4929

0.5071
195

Figure 132. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the LWP wire line rut depths. 

Whole Mean(3.7 m LWP) By All Mean(3.7 m LWP)

0

10

20

30

0 10 20 30

All Mean(3.7 m LWP)

Paired t-Test

Paired t-Test

All Mean(3.7 m LWP) - Whole Mean(3.7 m LWP)

Mean Difference

Std Error

t-Ratio

DF

0.023208

0.007466

3.108535

 4133

 Prob > |t|

Prob > t

Prob < t

0.0019

0.0009

0.9991
196

Figure 133. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the LWP wire line rut widths. 

Whole Mean(W 3.7 m LWP) By All Mean(W 3.7 m LWP)

0

1000

2000

3000

0 1000 2000 3000

All Mean(W 3.7 m LWP)

Paired t-Test

Paired t-Test

All Mean(W 3.7 m LWP) - Whole Mean(W 3.7 m LWP)

Mean Difference

Std Error

t-Ratio

DF

 -2.5766

2.397228

-1.07482

 4133

 Prob > |t|

Prob > t

Prob < t

0.2825

0.8587

0.1413
197

Figure 134. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the RWP wire line rut depths. 

Whole Mean(3.7 m RWP) By All Mean(3.7 m RWP)

0

10

20

0 10 20

All Mean(3.7 m RWP)

Paired t-Test

Paired t-Test

All Mean(3.7 m RWP) - Whole Mean(3.7 m RWP)

Mean Difference

Std Error

t-Ratio

DF

0.010431

 0.00691

1.509513

 4133

 Prob > |t|

Prob > t

Prob < t

0.1312

0.0656

0.9344
198

Figure 135. Paired t-test comparing section means from all of the profiles versus 

those from profiles taken every 30 m for the RWP wire line rut widths. 

Whole Mean(W 3.7 m RWP) By All Mean(W 3.7 m RWP)

0

1000

2000

3000

0 1000 2000 3000

All Mean(W 3.7 m RWP)

Paired t-Test

Paired t-Test

All Mean(W 3.7 m RWP) - Whole Mean(W 3.7 m RWP)

Mean Difference

Std Error

t-Ratio

DF

-0.98966

2.359387

-0.41945

 4133

 Prob > |t|

Prob > t

Prob < t

0.6749

0.6625

0.3375
199

Figure 136. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the negative area index. 

Whole Mean(Neg Area) By All Mean(Neg Area)

-40000

-30000

-20000

-10000

0

-40000 -30000 -20000 -10000 0

All Mean(Neg Area)

Paired t-Test

Paired t-Test

All Mean(Neg Area) - Whole Mean(Neg Area)

Mean Difference

Std Error

t-Ratio

DF

-118.822

 31.3516

-3.78999

 812

 Prob > |t|

Prob > t

Prob < t

0.0002

0.9999

<.0001
200

Figure 137. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the positive area index. 

Whole Mean(Pos Area) By All Mean(Pos Area

0

10000

20000

30000

40000

0 10000 20000 30000 40000

All Mean(Pos Area

Paired t-Test

Paired t-Test

All Mean(Pos Area - Whole Mean(Pos Area)

Mean Difference

Std Error

t-Ratio

DF

 -108.5

32.32981

-3.35605

 812

 Prob > |t|

Prob > t

Prob < t

0.0008

0.9996

0.0004
201

Figure 138. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the fill area index. 

Whole Mean(Fill Area) By All Mean(Fill Area)

0

10000

20000

30000

40000

50000

0 10000 20000 30000 40000 50000

All Mean(Fill Area)

Paired t-Test

Paired t-Test

All Mean(Fill Area) - Whole Mean(Fill Area)

Mean Difference

Std Error

t-Ratio

DF

100.5295

30.13866

3.335566

 812

 Prob > |t|

Prob > t

Prob < t

0.0009

0.0004

0.9996
202

Figure 139. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the LWP 1.8-m rut depths. 

Whole Mean(1.8 m LWP) By All Mean (1.8 m LWP)

0

10

20

30

0 10 20 30

All Mean (1.8 m LWP)

Paired t-Test

Paired t-Test

All Mean (1.8 m LWP) - Whole Mean(1.8 m LWP)

Mean Difference

Std Error

t-Ratio

DF

0.038019

0.015994

2.377111

 812

 Prob > |t|

Prob > t

Prob < t

0.0177

0.0088

0.9912
203

Figure 140. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick 

for the LWP 1.8-m rut widths. 

Whole Mean(W 1.8 m LWP) By All Mean(W 1.8 m LWP)

0

200

400

600

800

1000

1200

1400

1600

0100 300 500 700 900 1100 1400 1700

All Mean(W 1.8 m LWP)

Paired t-Test

Paired t-Test

All Mean(W 1.8 m LWP) - Whole Mean(W 1.8 m LWP)

Mean Difference

Std Error

t-Ratio

DF

-3.53853

1.714195

-2.06425

 812

 Prob > |t|

Prob > t

Prob < t

0.0393

0.9803

0.0197
204

Figure 141. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the RWP 1.8-m rut depths. 

Whole Mean(1.8 m RWP) By All Mean(1.8 m RWP)

0

10

20

0 10 20

All Mean(1.8 m RWP)

Paired t-Test

Paired t-Test

All Mean(1.8 m RWP) - Whole Mean(1.8 m RWP)

Mean Difference

Std Error

t-Ratio

DF

0.005186

0.014961

0.346651

 812

 Prob > |t|

Prob > t

Prob < t

0.7289

0.3645

0.6355
205

Figure 142. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the RWP 1.8-m rut widths. 

Whole Mean(W 1.8 m RWP) By All Mean(W 1.8 m RWP)

0

200

400

600

800

1000

1200

1400

1600

0100 300 500 700 900 1100 1400 1700

All Mean(W 1.8 m RWP)

Paired t-Test

Paired t-Test

All Mean(W 1.8 m RWP) - Whole Mean(W 1.8 m RWP)

Mean Difference

Std Error

t-Ratio

DF

0.046109

1.940143

0.023766

 812

 Prob > |t|

Prob > t

Prob < t

0.9810

0.4905

0.5095
206

Figure 143. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the LWP wire line rut depths. 

Whole Mean(3.7 m LWP) By All Mean(3.7 m LWP)

0

10

20

30

0 10 20 30

All Mean(3.7 m LWP)

Paired t-Test

Paired t-Test

All Mean(3.7 m LWP) - Whole Mean(3.7 m LWP)

Mean Difference

Std Error

t-Ratio

DF

0.051297

0.018403

2.787479

 812

 Prob > |t|

Prob > t

Prob < t

0.0054

0.0027

0.9973
207

Figure 144. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the LWP wire line rut widths. 

Whole Mean(W 3.7 m LWP) By All Mean(W 3.7 m LWP)

0

1000

2000

3000

0 1000 2000 3000

All Mean(W 3.7 m LWP)

Paired t-Test

Paired t-Test

All Mean(W 3.7 m LWP) - Whole Mean(W 3.7 m LWP)

Mean Difference

Std Error

t-Ratio

DF

-6.03334

4.902696

-1.23062

 812

 Prob > |t|

Prob > t

Prob < t

0.2188

0.8906

0.1094
208

Figure 145. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the RWP wire line rut depths. 

Whole Mean(3.7 m RWP) By All Mean(3.7 m RWP)

0

10

20

0 10 20

All Mean(3.7 m RWP)

Paired t-Test

Paired t-Test

All Mean(3.7 m RWP) - Whole Mean(3.7 m RWP)

Mean Difference

Std Error

t-Ratio

DF

0.024371

0.016403

1.485794

 812

 Prob > |t|

Prob > t

Prob < t

0.1377

0.0689

0.9311
209

Figure 146. Paired t-test comparing section means from all of the profiles 

versus those from profiles taken every 30 m for data collected by Dipstick

for the RWP wire line rut widths. 

Whole Mean(W 3.7 m RWP) By All Mean(W 3.7 m RWP)

0

1000

2000

3000

0 1000 2000 3000

All Mean(W 3.7 m RWP)

Paired t-Test

Paired t-Test

All Mean(W 3.7 m RWP) - Whole Mean(W 3.7 m RWP)

Mean Difference

Std Error

t-Ratio

DF

-3.91533

5.178212

-0.75612

 812

 Prob > |t|

Prob > t

Prob < t

0.4498

0.7751

0.2249

211

APPENDIX D. 

t-TESTS COMPARING VARIOUS PAVEMENT PARAMETERS 

These are the comparisons that were performed in chapter 4. Figures 147 through 157 provide 

the results of the comparisons of each index for the GPS-1 (HMAC over granular base) section 

means and the GPS-7 (HMAC overlay of PCC) section means. The top box of each figure 

provides a graphical review of the results. The middle box provides the results from a t-test for 

comparing means with equal variances at an α-level of 5 percent. The bottom box provides the 

results of a comparison of the variances between the groups and an ANOVA test in case the 

variances are not equal. Figures 158 through 168 provide the results of the comparisons of the 

GPS-1 (HMAC over granular base) and GPS-2 (HMAC over stabilized base) sections by surface 

thickness. Figures 169 through 179 provide the results of the comparisons of granular versus 

stabilized base types for GPS-1 and GPS-2 sections with less than 127 mm of HMAC surface. 

Figures 180 through 190 provide the results of the comparisons of asphalt stabilized bases to 

cement stabilized bases for GPS-1 and GPS-2 sections with less than 127 mm of HMAC surface. 

Figures 191 through 201 provide the results of the comparisons between the freeze (F) zone and 

the no freeze (NF) zone for the GPS-7 test sections. The bottom half of the upper box of 

numbers provides the results of the t-tests comparing each set of values. If the value in the table 

is positive, the difference is statistically significant, which means that the data sets are from two 

different populations with a 95 percent level of confidence. The bottom box provides a 

comparison of the standard deviations. The column of numbers provided under the heading 

“Prob>F” are the probabilities of getting an F-ratio that large given that the standard deviations 

are the same. A value of 0.05 or less is statistically significant. 
212

Figure 147. Paired t-test comparing GPS-1 section means versus 

GPS-7 section means for the negative area index. 

Neg Area By Experiment

-50000

-40000

-30000

-20000

-10000

0

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

7

1

7

 0.00

-3009.20

1

 3009.20

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

7

1

7

-1754.04

 1663.83

1

 1663.83

 -737.16

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 9223.270

 7842.663

MeanAbsDif to Mean

 7279.453

 5820.508

MeanAbsDif to Median

 6948.729

 5147.029

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 3.1731

 12.1945

 11.7720

 8.3967

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.0751

0.0005

0.0006

0.0038

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 24.1372

t-Test

 4.9130

DF Num

 1

DF Den

311.03

Prob>F

<.0001
213

Figure 148. Paired t-test comparing GPS-1 section means versus 

GPS-7 section means for the positive area index. 

Pos Area By Experiment

0

10000

20000

30000

40000

50000

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

7

1

7

 0.000

-919.994

1

 919.994

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

7

1

7

-1880.09

 -522.06

1

 -522.06

 -790.14

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 9677.746

 9686.881

MeanAbsDif to Mean

 7245.494

 7274.208

MeanAbsDif to Median

 6567.539

 6809.755

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.0001

 0.1558

 0.0035

 0.0003

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.9915

0.6931

0.9530

0.9860

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 1.5643

t-Test

 1.2507

DF Num

 1

DF Den

279.36

Prob>F

0.2121
214

Figure 149. Paired t-test comparing GPS-1 section means versus 

GPS-7 section means for the fill area index. 

Fill Area By Experiment

0

10000

20000

30000

40000

50000

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.00

-3693.23

7

 3693.23

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

 -736.38

 2349.29

7

 2349.29

-1752.17

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 9216.679

 7812.726

MeanAbsDif to Mean

 6977.862

 5792.275

MeanAbsDif to Median

 6791.668

 5322.843

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 3.3035

 8.9794

 6.9860

 8.7090

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.0694

0.0028

0.0083

0.0032

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 36.5921

t-Test

 6.0491

DF Num

 1

DF Den

311.75

Prob>F

<.0001
215

Figure 150. Paired t-test comparing GPS-1 section means versus 

GPS-7 section means for the LWP 1.8-m rut depths. 

LWP 1.8 By Experiment

0

10

20

30

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.00000

-1.51693

7

 1.51693

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

-0.34043

0.895616

7

0.895616

-0.81005

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 4.285263

 3.444584

MeanAbsDif to Mean

 3.236836

 2.452134

MeanAbsDif to Median

 3.146320

 2.294118

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 5.2413

 13.7324

 14.1030

 14.8295

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.0222

0.0002

0.0002

0.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 31.0699

t-Test

 5.5740

DF Num

 1

DF Den

324.88

Prob>F

<.0001
216

Figure 151. Paired t-test comparing GPS-1 section means versus 

GPS-7 section means for the LWP 1.8-m rut widths. 

LWP 1.8 W By Experiment

0

1000

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.0000

-28.9194

7

 28.9194

 0.0000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

-18.5940

 -5.0160

7

 -5.0160

-44.2435

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 223.2402

 252.0097

MeanAbsDif to Mean

 151.3384

 185.7543

MeanAbsDif to Median

 142.8970

 178.3824

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 1.2598

 6.6875

 7.5498

 5.3570

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.2619

0.0098

0.0061

0.0206

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 2.3594

t-Test

 1.5360

DF Num

 1

DF Den

262.28

Prob>F

0.1257
217

Figure 152. Paired t-test comparing GPS-1 section means versus 

GPS-7 section means for the RWP 1.8-m rut depths. 

RWP 1.8 By Experiment

0

10

20

30

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.00000

-2.14412

7

 2.14412

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

-0.37377

 1.46197

7

 1.46197

-0.88936

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 4.754991

 3.406699

MeanAbsDif to Mean

 3.529928

 2.437716

MeanAbsDif to Median

 3.379221

 2.250000

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 8.1873

 18.3646

 21.8521

 32.7436

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.0043

<.0001

<.0001

<.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 60.1215

t-Test

 7.7538

DF Num

 1

DF Den

359.26

Prob>F

<.0001
218

Figure 153. Paired t-test comparing GPS-1 section means versus 

GPS-7 section means for the RWP 1.8-m rut widths. 

RWP 1.8 W By Experiment

0

1000

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.000

-103.933

7

 103.933

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

-20.7162

 66.1243

7

 66.1243

-49.2930

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 245.5789

 296.0664

MeanAbsDif to Mean

 170.2922

 231.9840

MeanAbsDif to Median

 158.2667

 223.2990

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 4.5976

 19.0888

 20.8637

 13.1300

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.0322

<.0001

<.0001

0.0003

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 22.4156

t-Test

 4.7345

DF Num

 1

DF Den

254.67

Prob>F

<.0001
219

Figure 154. Paired t-test comparing GPS-1 section means versus GPS-7 

section means for the LWP wire line rut depths. 

LWP 3.7 By Experiment

0

10

20

30

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.00000

-1.57806

7

 1.57806

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

-0.36337

0.914880

7

0.914880

-0.86463

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 4.538929

 3.915987

MeanAbsDif to Mean

 3.440237

 2.847174

MeanAbsDif to Median

 3.345455

 2.671569

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 2.8729

 8.1646

 7.1558

 7.0075

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.0903

0.0043

0.0076

0.0081

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 26.7748

t-Test

 5.1744

DF Num

 1

DF Den

307.72

Prob>F

<.0001
220

Figure 155. Paired t-test comparing GPS-1 section means versus GPS-7 

section means for the LWP wire line rut widths. 

LWP 3.7 W By Experiment

0

1000

2000

3000

4000

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.0000

-65.7585

7

 65.7585

 0.0000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

 -60.977

 -45.529

7

 -45.529

-145.092

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 741.7171

 776.1235

MeanAbsDif to Mean

 605.8859

 643.8401

MeanAbsDif to Median

 575.8719

 616.5490

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.9616

 1.0427

 1.3634

 0.7238

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.3270

0.3074

0.2432

0.3949

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 1.2610

t-Test

 1.1230

DF Num

 1

DF Den

272.53

Prob>F

0.2624
221

Figure 156. Paired t-test comparing GPS-1 section means versus GPS-7 

section means for the RWP wire line rut depths. 

RWP 3.7 By Experiment

0

10

20

30

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.00000

-2.33389

7

 2.33389

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

-0.41029

 1.58509

7

 1.58509

-0.97625

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 5.190945

 3.959517

MeanAbsDif to Mean

 3.871235

 2.915225

MeanAbsDif to Median

 3.749784

 2.647059

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 6.5412

 15.6563

 14.1141

 22.2436

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.0106

<.0001

0.0002

<.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 54.3718

t-Test

 7.3737

DF Num

 1

DF Den

339.45

Prob>F

<.0001
222

Figure 157. Paired t-test comparing GPS-1 section means versus GPS-7 

section means for the RWP wire line rut widths. 

RWP 3.7 W By Experiment

0

1000

2000

3000

4000

1 7

Experiment

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

1

7

1

 0.000

-146.881

7

 146.881

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96175

Abs(Dif)-LSD

1

7

1

 -62.590

 32.649

7

 32.649

-148.931

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

1

7

Count

 1155

 204

Std Dev

 757.9183

 814.9938

MeanAbsDif to Mean

 625.5254

 675.9321

MeanAbsDif to Median

 603.7048

 647.2941

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 2.7842

 1.2861

 2.3665

 1.8793

DF Num

 1

 1

 1

 1

DF Den

 1357

 1357

 1357

 ?

Prob>F

0.0954

0.2570

0.1242

0.1704

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 5.7480

t-Test

 2.3975

DF Num

 1

DF Den

268.65

Prob>F

0.0172
223

Figure 158. Paired t-test comparing GPS-1 and GPS-2 section 

means for the negative area index versus surface thickness. 

Neg Area By Surface Thickness

-50000

-40000

-30000

-20000

-10000

0

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Moderate

Thin

Thick

Moderate

 0.00

 -242.78

-1655.20

Thin

 242.78

 0.00

-1412.42

Thick

 1655.20

 1412.42

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Moderate

Thin

Thick

Moderate

 -985.92

 -955.54

 574.69

Thin

 -955.54

-1378.37

 135.15

Thick

 574.69

 135.15

-1167.46

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 8609.324

 9319.431

 9398.057

MeanAbsDif to Mean

 6451.552

 7508.581

 7246.181

MeanAbsDif to Median

 6057.938

 7233.920

 6652.897

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.9604

 3.9709

 5.1061

 2.4234

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.3830

0.0191

0.0062

0.0886

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 4.7230

DF Num

 2

DF Den

791.72

Prob>F

0.0091
224

Figure 159. Paired t-test comparing GPS-1 and GPS-2 section 

means for the positive area index versus surface thickness. 

Pos Area By Surface Thickness

0

10000

20000

30000

40000

50000

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thin

Moderate

Thick

Thin

 0.00

 -678.32

-1619.90

Moderate

 678.32

 0.00

 -941.57

Thick

 1619.90

 941.57

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thin

Moderate

Thick

Thin

-1557.66

 -675.87

 176.48

Moderate

 -675.87

-1114.16

 -279.49

Thick

 176.48

 -279.49

-1319.32

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 10127.91

 10117.97

 10450.63

MeanAbsDif to Mean

 7671.944

 7604.847

 8160.850

MeanAbsDif to Median

 7004.336

 6748.354

 7524.552

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.1215

 0.8203

 0.7923

 0.2588

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.8856

0.4405

0.4530

0.7720

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 2.5125

DF Num

 2

DF Den

806.67

Prob>F

0.0817
225

Figure 160. Paired t-test comparing GPS-1 and GPS-2 section 

means for the fill area index versus surface thickness. 

Fill Area By Surface Thickness

0

10000

20000

30000

40000

50000

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Thin

Moderate

Thick

 0.00

-1008.11

-1102.48

Thin

 1008.11

 0.00

 -94.37

Moderate

 1102.48

 94.37

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Thin

Moderate

Thick

-1155.36

 -255.92

 33.17

Thin

 -255.92

-1364.07

-1091.53

Moderate

 33.17

-1091.53

 -975.70

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 8582.128

 9362.227

 8989.305

MeanAbsDif to Mean

 6546.949

 7181.002

 6991.482

MeanAbsDif to Median

 6328.358

 6990.104

 6766.818

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.9104

 1.5649

 1.7801

 2.0612

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.4026

0.2095

0.1690

0.1273

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 2.1531

DF Num

 2

DF Den

800.04

Prob>F

0.1168
226

Figure 161. Paired t-test comparing GPS-1 and GPS-2 section 

means for the LWP 1.8-m rut depths versus surface thickness. 

LWP 1.8 By Surface Thickness

0

10

20

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Moderate

Thin

Thick

0.000000

 -0.0942

-0.63057

Moderate

0.094203

0.000000

-0.53636

Thin

0.630567

0.536364

0.000000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Moderate

Thin

Thick

-0.51487

-0.38232

0.067273

Moderate

-0.38232

 -0.4348

0.007891

Thin

0.067273

0.007891

-0.60788

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 4.120192

 4.024786

 3.624049

MeanAbsDif to Mean

 3.147907

 3.011172

 2.885271

MeanAbsDif to Median

 3.031008

 2.965217

 2.821212

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 1.5743

 0.6239

 1.2041

 3.5598

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.2075

0.5360

0.3003

0.0284

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 3.1003

DF Num

 2

DF Den

841.98

Prob>F

0.0455
227

Figure 162. Paired t-test comparing GPS-1 and GPS-2 section 

means for the LWP 1.8-m rut widths versus surface thickness. 

LWP 1.8 W By Surface Thickness

0

1000

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Moderate

Thin

Thick

 0.0000

 -2.8841

-43.7767

Moderate

 2.8841

 0.0000

-40.8927

Thin

 43.7767

 40.8927

 0.0000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Moderate

Thin

Thick

-29.9894

-24.8717

 10.9665

Moderate

-24.8717

-25.3260

 10.1107

Thin

 10.9665

 10.1107

-35.4070

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 209.5359

 204.2866

 299.6773

MeanAbsDif to Mean

 153.6703

 148.3078

 212.6795

MeanAbsDif to Median

 147.9380

 140.5804

 197.0636

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 13.9120

 11.1672

 18.7438

 38.8026

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

<.0001

<.0001

<.0001

<.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 2.8768

DF Num

 2

DF Den

747.77

Prob>F

0.0569
228

Figure 163. Paired t-test comparing GPS-1 and GPS-2 section 

means for the RWP 1.8-m rut depths versus surface thickness. 

RWP 1.8 By Surface Thickness

0

10

20

30

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Thin

Moderate

Thick

0.000000

-0.28597

-0.41606

Thin

0.285968

0.000000

-0.13009

Moderate

0.416060

0.130092

0.000000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Thin

Moderate

Thick

 -0.5758

-0.34399

-0.11685

Thin

-0.34399

-0.67982

-0.46092

Moderate

-0.11685

-0.46092

-0.48626

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 4.285770

 4.666624

 4.462697

MeanAbsDif to Mean

 3.315988

 3.467769

 3.266556

MeanAbsDif to Median

 3.209302

 3.310870

 3.236364

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.6867

 0.1347

 0.5507

 1.9594

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.5034

0.8740

0.5766

0.1409

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 1.1450

DF Num

 2

DF Den

 801.4

Prob>F

0.3187
229

Figure 164. Paired t-test comparing GPS-1 and GPS-2 section 

means for the RWP 1.8-m rut widths versus surface thickness. 

RWP 1.8 W By Surface Thickness

0

1000

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Moderate

Thin

Thick

 0.0000

-32.7824

-38.0128

Moderate

 32.7824

 0.0000

 -5.2304

Thin

 38.0128

 5.2304

 0.0000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Moderate

Thin

Thick

-33.1446

 2.1064

 1.7506

Moderate

 2.1064

-27.9906

-28.7902

Thin

 1.7506

-28.7902

-39.1322

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 251.0544

 237.0325

 289.8882

MeanAbsDif to Mean

 184.6521

 167.7991

 213.2006

MeanAbsDif to Median

 169.1147

 160.7391

 198.2212

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 3.0730

 3.7677

 6.4590

 8.3514

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.0466

0.0233

0.0016

0.0002

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 3.0760

DF Num

 2

DF Den

 785.2

Prob>F

0.0467
230

Figure 165. Paired t-test comparing GPS-1 and GPS-2 section 

means for the LWP wire line rut depths versus surface thickness. 

LWP 3.7 By Surface Thickness

0

10

20

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Moderate

Thin

Thick

0.000000

-0.25123

-0.71014

Moderate

0.251230

0.000000

-0.45891

Thin

0.710145

0.458915

0.000000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Moderate

Thin

Thick

-0.56311

-0.26994

0.094071

Moderate

-0.26994

-0.47554

-0.11908

Thin

0.094071

-0.11908

-0.66483

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 4.418299

 4.412186

 4.137652

MeanAbsDif to Mean

 3.384210

 3.359093

 3.278384

MeanAbsDif to Median

 3.286822

 3.269565

 3.187879

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.5129

 0.1166

 0.1612

 1.0466

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.5989

0.8899

0.8511

0.3511

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 2.7175

DF Num

 2

DF Den

827.68

Prob>F

0.0666
231

Figure 166. Paired t-test comparing GPS-1 and GPS-2 section 

means for the LWP wire line rut widths versus surface thickness. 

LWP 3.7 W By Surface Thickness

0

1000

2000

3000

4000

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Moderate

Thin

Thick

 0.000

 -35.609

-170.667

Moderate

 35.609

 0.000

-135.058

Thin

 170.667

 135.058

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Moderate

Thin

Thick

 -95.755

 -53.014

 65.905

Moderate

 -53.014

 -80.865

 36.771

Thin

 65.905

 36.771

-113.054

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 706.7583

 758.8254

 777.3502

MeanAbsDif to Mean

 584.6481

 622.5829

 599.0490

MeanAbsDif to Median

 564.6698

 589.8630

 567.5303

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 2.9581

 0.3571

 1.0352

 2.4361

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.0522

0.6998

0.3554

0.0875

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 5.0935

DF Num

 2

DF Den

790.56

Prob>F

0.0063
232

Figure 167. Paired t-test comparing GPS-1 and GPS-2 section 

means for the RWP wire line rut depths versus surface thickness. 

RWP 3.7 By Surface Thickness

0

10

20

30

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Thin

Moderate

Thick

0.000000

-0.39618

-0.58561

Thin

0.396179

0.000000

-0.18943

Moderate

0.585608

0.189429

0.000000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Thin

Moderate

Thick

-0.63504

-0.29859

-0.00214

Thin

-0.29859

-0.74976

 -0.4624

Moderate

-0.00214

 -0.4624

-0.53629

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 4.679577

 5.135985

 5.024666

MeanAbsDif to Mean

 3.610797

 3.905312

 3.732525

MeanAbsDif to Median

 3.513178

 3.773913

 3.636364

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.9634

 0.7323

 1.1505

 2.5747

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.3818

0.4810

0.3168

0.0762

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 1.8807

DF Num

 2

DF Den

794.47

Prob>F

0.1532
233

Figure 168. Paired t-test comparing GPS-1 and GPS-2 section 

means for the RWP wire line rut widths versus surface thickness. 

RWP 3.7 W By Surface Thickness

0

1000

2000

3000

4000

Moderate Thick Thin

Surface Thickness

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Thick

Moderate

Thin

Thick

 0.000

 -70.659

-159.422

Moderate

 70.659

 0.000

 -88.763

Thin

 159.422

 88.763

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96166

Abs(Dif)-LSD

Thick

Moderate

Thin

Thick

 -96.975

 -19.093

 53.325

Moderate

 -19.093

 -81.895

 -10.775

Thin

 53.325

 -10.775

-114.493

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Moderate

Thick

Thin

Count

 645

 460

 330

Std Dev

 728.9054

 768.1865

 763.6867

MeanAbsDif to Mean

 602.9505

 634.0347

 588.9161

MeanAbsDif to Median

 582.3690

 607.5804

 566.8970

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 1.1370

 0.6653

 1.1738

 0.8899

DF Num

 2

 2

 2

 2

DF Den

 1432

 1432

 1432

 ?

Prob>F

0.3211

0.5143

0.3095

0.4107

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 4.1669

DF Num

 2

DF Den

801.57

Prob>F

0.0158
234

Figure 169. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the negative area index versus base type. 

Neg Area By Base Type

-40000

-30000

-20000

-10000

0

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Stabiliz

Granular

Stabiliz

 0.00

-2188.24

Granular

 2188.24

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Stabiliz

Granular

Stabiliz

-1332.65

 919.93

Granular

 919.93

-1200.54

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 8612.179

 8643.248

MeanAbsDif to Mean

 6668.947

 6329.013

MeanAbsDif to Median

 6440.922

 5743.136

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.0018

 1.9246

 0.6480

 0.0046

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.9665

0.1658

0.4211

0.9459

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 11.4653

t-Test

 3.3860

DF Num

 1

DF Den

687.78

Prob>F

0.0007
235

Figure 170. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the positive area index versus base type. 

Pos Area By Base Type

0

10000

20000

30000

40000

50000

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Stabiliz

Granular

Stabiliz

 0.00

-3822.08

Granular

 3822.08

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Stabiliz

Granular

Stabiliz

-1587.22

 2311.48

Granular

 2311.48

-1429.87

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 9303.69

 11356.66

MeanAbsDif to Mean

 6863.238

 9085.564

MeanAbsDif to Median

 6097.997

 8480.136

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 7.5652

 15.0219

 20.7700

 14.2206

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.0061

0.0001

<.0001

0.0002

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 23.6846

t-Test

 4.8667

DF Num

 1

DF Den

619.28

Prob>F

<.0001
236

Figure 171. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the fill area index versus base type. 

Fill Area By Base Type

0

10000

20000

30000

40000

50000

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

 0.00

-1969.84

Stabiliz

 1969.84

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-1154.10

 750.59

Stabiliz

 750.59

-1281.10

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 8246.581

 8348.666

MeanAbsDif to Mean

 6316.121

 6432.837

MeanAbsDif to Median

 6161.965

 6298.142

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.0287

 0.1008

 0.0865

 0.0538

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.8655

0.7509

0.7688

0.8166

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 10.0354

t-Test

 3.1679

DF Num

 1

DF Den

685.32

Prob>F

0.0016
237

Figure 172. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the LWP 1.8-m rut depths versus base type. 

LWP 1.8 By Base Type

0

10

20

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

 0.00000

-1.10687

Stabiliz

 1.10687

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-0.54094

0.535395

Stabiliz

0.535395

-0.60047

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 4.089648

 3.621017

MeanAbsDif to Mean

 3.038787

 2.868579

MeanAbsDif to Median

 2.937186

 2.783282

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 2.2601

 0.5284

 0.8201

 5.2027

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.1332

0.4675

0.3655

0.0226

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 14.8295

t-Test

 3.8509

DF Num

 1

DF Den

713.54

Prob>F

0.0001
238

Figure 173. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the LWP 1.8-m rut widths versus base type. 

LWP 1.8 W By Base Type

0

1000

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

 0.0000

-73.2650

Stabiliz

 73.2650

 0.0000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-35.1674

 36.1122

Stabiliz

 36.1122

-39.0374

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 204.6424

 301.5609

MeanAbsDif to Mean

 137.7338

 226.5209

MeanAbsDif to Median

 135.1432

 211.2508

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 13.9394

 27.3833

 46.3915

 53.4883

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.0002

<.0001

<.0001

<.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 13.8785

t-Test

 3.7254

DF Num

 1

DF Den

545.82

Prob>F

0.0002
239

Figure 174. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the RWP 1.8-m rut depths versus base type. 

RWP 1.8 By Base Type

0

10

20

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

 0.00000

-1.41474

Stabiliz

 1.41474

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-0.57052

0.812014

Stabiliz

0.812014

 -0.6333

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 4.566188

 3.437487

MeanAbsDif to Mean

 3.483005

 2.784039

MeanAbsDif to Median

 3.374372

 2.761610

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 13.3275

 8.6258

 13.1841

 27.7149

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.0003

0.0034

0.0003

<.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 22.4963

t-Test

 4.7430

DF Num

 1

DF Den

715.11

Prob>F

<.0001
240

Figure 175. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the RWP 1.8-m rut widths versus base type. 

RWP 1.8 W By Base Type

0

1000

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

 0.0000

-85.7121

Stabiliz

 85.7121

 0.0000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-36.9074

 46.7211

Stabiliz

 46.7211

-40.9689

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 222.4193

 309.8966

MeanAbsDif to Mean

 149.7810

 246.4318

MeanAbsDif to Median

 145.1859

 226.4087

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 13.7585

 29.0503

 54.3865

 39.2519

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.0002

<.0001

<.0001

<.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 17.4245

t-Test

 4.1743

DF Num

 1

DF Den

567.11

Prob>F

<.0001
241

Figure 176. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the LWP wire line rut depths versus base type. 

LWP 3.7 By Base Type

0

10

20

30

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

0.000000

-0.95286

Stabiliz

0.952860

0.000000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-0.59308

0.326297

Stabiliz

0.326297

-0.65835

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 4.323585

 4.183474

MeanAbsDif to Mean

 3.222595

 3.339187

MeanAbsDif to Median

 3.125628

 3.244582

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.1734

 0.2999

 0.3274

 0.3844

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.6772

0.5841

0.5673

0.5353

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 8.9760

t-Test

 2.9960

DF Num

 1

DF Den

697.25

Prob>F

0.0028
242

Figure 177. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the LWP wire line rut widths versus base type. 

LWP 3.7 W By Base Type

0

1000

2000

3000

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

 0.000

-121.715

Stabiliz

 121.715

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-104.365

 11.458

Stabiliz

 11.458

-115.850

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 682.1302

 825.8065

MeanAbsDif to Mean

 556.9888

 665.8650

MeanAbsDif to Median

 536.9573

 638.1950

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 15.6864

 6.7702

 11.0416

 13.0672

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

<.0001

0.0095

0.0009

0.0003

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 4.5161

t-Test

 2.1251

DF Num

 1

DF Den

622.52

Prob>F

0.0340
243

Figure 178. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the RWP wire line rut depths versus base type. 

RWP 3.7 By Base Type

0

10

20

30

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

 0.00000

-1.37205

Stabiliz

 1.37205

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-0.63117

0.705238

Stabiliz

0.705238

-0.70063

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 4.869137

 4.085890

MeanAbsDif to Mean

 3.695462

 3.237892

MeanAbsDif to Median

 3.557789

 3.235294

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 5.2869

 1.8569

 4.4987

 10.7361

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

0.0218

0.1734

0.0343

0.0011

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 16.9207

t-Test

 4.1135

DF Num

 1

DF Den

718.19

Prob>F

<.0001
244

Figure 179. Paired t-test comparing thin-surfaced GPS-1 and GPS-2 

section means for the RWP wire line rut widths versus base type. 

RWP 3.7 W By Base Type

0

1000

2000

3000

Granular Stabiliz

Base Type

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Granular

Stabiliz

Granular

 0.000

-153.812

Stabiliz

 153.812

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96330

Abs(Dif)-LSD

Granular

Stabiliz

Granular

-103.720

 44.236

Stabiliz

 44.236

-115.134

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Granular

Stabiliz

Count

 398

 323

Std Dev

 678.9518

 819.6431

MeanAbsDif to Mean

 553.8407

 650.8271

MeanAbsDif to Median

 540.1784

 622.4799

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 15.4851

 4.8177

 8.5867

 12.6841

DF Num

 1

 1

 1

 1

DF Den

 719

 719

 719

 ?

Prob>F

<.0001

0.0285

0.0035

0.0004

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 7.3060

t-Test

 2.7030

DF Num

 1

DF Den

623.62

Prob>F

0.0071
245

Figure 180. Paired t-test comparing thin-surfaced GPS-2 section means 

for the negative area index versus base type.

Neg Area By Base

-40000

-30000

-20000

-10000

0

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Cement T

Asphalt

Cement T

 0.00

-2610.90

Asphalt

 2610.90

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Cement T

Asphalt

Cement T

-2272.77

 631.88

Asphalt

 631.88

-1633.29

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 9348.833

 6794.374

MeanAbsDif to Mean

 6943.740

 4871.945

MeanAbsDif to Median

 6328.746

 4472.318

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 3.8220

 4.8528

 9.3584

 13.4792

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.0515

0.0283

0.0024

0.0002

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 8.2130

t-Test

 2.8658

DF Num

 1

DF Den

285.85

Prob>F

0.0045
246

Figure 181. Paired t-test comparing thin-surfaced GPS-2 section 

means for the positive area index versus base type. 

Pos Area By Base

0

10000

20000

30000

40000

50000

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Cement T

Asphalt

Cement T

 0.00

-3358.93

Asphalt

 3358.93

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Cement T

Asphalt

Cement T

-2987.57

 757.48

Asphalt

 757.48

-2146.96

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 10179.81

 13112.74

MeanAbsDif to Mean

 7983.32

 10903.86

MeanAbsDif to Median

 7520.56

 10255.38

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 7.9662

 7.9484

 14.1284

 9.6157

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.0051

0.0051

0.0002

0.0019

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 5.5045

t-Test

 2.3462

DF Num

 1

DF Den

178.52

Prob>F

0.0201
247

Figure 182. Paired t-test comparing thin-surfaced GPS-2 section means 

for the fill area index versus base type. 

Fill Area By Base

0

10000

20000

30000

40000

50000

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.00

-4295.98

Cement T

 4295.98

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

-1545.81

 2422.94

Cement T

 2422.94

-2151.05

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 8640.974

 6956.915

MeanAbsDif to Mean

 6593.641

 5470.518

MeanAbsDif to Median

 6416.732

 5222.727

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 3.0141

 3.2273

 3.4343

 6.3976

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.0835

0.0734

0.0648

0.0114

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 23.3455

t-Test

 4.8317

DF Num

 1

DF Den

265.29

Prob>F

<.0001
248

Figure 183. Paired t-test comparing thin-surfaced GPS-2 section means 

for the LWP 1.8-m rut depths versus base type. 

LWP 1.8 By Base

0

10

20

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.00000

-1.41554

Cement T

 1.41554

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

-0.67939

0.592330

Cement T

0.592330

-0.94539

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 3.689110

 3.306122

MeanAbsDif to Mean

 2.920496

 2.606942

MeanAbsDif to Median

 2.835681

 2.418182

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 1.1157

 2.1384

 1.5138

 1.6809

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.2916

0.1446

0.2195

0.1948

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 12.2732

t-Test

 3.5033

DF Num

 1

DF Den

242.66

Prob>F

0.0005
249

Figure 184. Paired t-test comparing thin-surfaced GPS-2 section 

means for the LWP 1.8-m rut widths versus base type. 

LWP 1.8 W By Base

0

1000

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.000

-134.758

Cement T

 134.758

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

-56.2698

 66.5768

Cement T

 66.5768

-78.3013

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 270.7918

 337.5504

MeanAbsDif to Mean

 191.7597

 274.9322

MeanAbsDif to Median

 180.6056

 260.8545

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 3.3414

 9.3991

 13.6298

 7.2508

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.0685

0.0024

0.0003

0.0071

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 13.1584

t-Test

 3.6275

DF Num

 1

DF Den

 183.1

Prob>F

0.0004
250

Figure 185. Paired t-test comparing thin-surfaced GPS-2 section means 

for the RWP 1.8-m rut depths versus base type. 

RWP 1.8 By Base

0

10

20

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.00000

-2.14277

Cement T

 2.14277

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

-0.62697

 1.38308

Cement T

 1.38308

-0.87244

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 3.476660

 2.888316

MeanAbsDif to Mean

 2.710970

 2.331405

MeanAbsDif to Median

 2.704225

 2.190909

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 3.1833

 4.2216

 2.5638

 4.7183

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.0753

0.0407

0.1103

0.0298

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 34.6297

t-Test

 5.8847

DF Num

 1

DF Den

258.68

Prob>F

<.0001
251

Figure 186. Paired t-test comparing thin-surfaced GPS-2 section means 

for the RWP 1.8-m rut widths versus base type. 

RWP 1.8 W By Base

0

1000

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.000

-208.720

Cement T

 208.720

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

 -56.067

 140.784

Cement T

 140.784

 -78.019

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 264.8157

 343.9717

MeanAbsDif to Mean

 187.4494

 291.3719

MeanAbsDif to Median

 171.9484

 290.2818

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 5.2336

 23.4440

 22.9856

 10.2718

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.0228

<.0001

<.0001

0.0014

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 31.0098

t-Test

 5.5686

DF Num

 1

DF Den

 177.4

Prob>F

<.0001
252

Figure 187. Paired t-test comparing thin-surfaced GPS-2 section means 

for the LWP wire line rut depths versus base type. 

LWP 3.7 By Base

0

10

20

30

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.00000

-1.78549

Cement T

 1.78549

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

-0.78223

 0.83767

Cement T

 0.83767

-1.08850

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 4.315832

 3.654102

MeanAbsDif to Mean

 3.408936

 2.865785

MeanAbsDif to Median

 3.356808

 2.690909

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 2.6291

 4.1965

 3.3913

 3.8213

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.1059

0.0413

0.0665

0.0506

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 15.2656

t-Test

 3.9071

DF Num

 1

DF Den

254.67

Prob>F

0.0001
253

Figure 188. Paired t-test comparing thin-surfaced GPS-2 section means 

for the LWP wire line rut widths versus base type. 

LWP 3.7 W By Base

0

1000

2000

3000

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.000

-274.982

Cement T

 274.982

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

-155.697

 86.326

Cement T

 86.326

-216.658

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 815.9333

 818.1795

MeanAbsDif to Mean

 671.5165

 643.3084

MeanAbsDif to Median

 637.3380

 621.8182

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.0014

 0.0554

 0.2554

 0.0011

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.9702

0.8141

0.6136

0.9737

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 8.2090

t-Test

 2.8651

DF Num

 1

DF Den

219.89

Prob>F

0.0046
254

Figure 189. Paired t-test comparing thin-surfaced GPS-2 section means 

for the RWP wire line rut depths versus base type. 

RWP 3.7 By Base

0

10

20

30

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.00000

-2.54059

Cement T

 2.54059

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

-0.74541

 1.63739

Cement T

 1.63739

-1.03726

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 4.185761

 3.308392

MeanAbsDif to Mean

 3.242082

 2.729587

MeanAbsDif to Median

 3.192488

 2.509091

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 4.4270

 4.7311

 3.3077

 7.4955

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.0362

0.0304

0.0699

0.0062

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 35.5115

t-Test

 5.9592

DF Num

 1

DF Den

269.14

Prob>F

<.0001
255

Figure 190. Paired t-test comparing thin-surfaced GPS-2 section means 

for the RWP wire line rut widths versus base type. 

RWP 3.7 W By Base

0

1000

2000

3000

Asphalt Cement T

Base

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

Asphalt

Cement T

Asphalt

 0.000

-335.990

Cement T

 335.990

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.96741

Abs(Dif)-LSD

Asphalt

Cement T

Asphalt

-153.511

 149.983

Cement T

 149.983

-213.616

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

Asphalt

Cement T

Count

 213

 110

Std Dev

 798.0659

 818.9877

MeanAbsDif to Mean

 657.6296

 638.5709

MeanAbsDif to Median

 609.9437

 632.4455

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.1192

 0.1165

 0.1189

 0.0966

DF Num

 1

 1

 1

 1

DF Den

 321

 321

 321

 ?

Prob>F

0.7302

0.7331

0.7305

0.7560

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 12.4220

t-Test

 3.5245

DF Num

 1

DF Den

215.47

Prob>F

0.0005
256

Figure 191. Paired t-test comparing climate for the GPS-7 

section means of the negative area index. 

Neg Area By Freeze

-30000

-20000

-10000

0

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

F

NF

F

 0.00

-7836.63

NF

 7836.63

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

F

NF

F

-1752.69

 4538.96

NF

 4538.96

-4321.72

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 6616.52

 12712.12

MeanAbsDif to Mean

 4959.72

 11206.17

MeanAbsDif to Median

 4433.68

 10968.44

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 27.5627

 23.3755

 40.6032

 23.3016

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

<.0001

<.0001

<.0001

<.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 9.0956

t-Test

 3.0159

DF Num

 1

DF Den

26.178

Prob>F

0.0056
257

Figure 192. Paired t-test comparing climate for the GPS-7 

section means of the positive area index. 

Pos Area By Freeze

0

10000

20000

30000

40000

50000

60000

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

F

NF

F

 0.00

-1952.11

NF

 1952.11

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

F

NF

F

-2251.64

-2284.34

NF

-2284.34

-5552.02

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 9582.76

 11980.21

MeanAbsDif to Mean

 7296.008

 7479.536

MeanAbsDif to Median

 6897.520

 6581.480

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 0.7487

 0.0331

 0.0162

 2.2648

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.3881

0.8558

0.8989

0.1323

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 0.6006

t-Test

 0.7750

DF Num

 1

DF Den

29.265

Prob>F

0.4446
258

Figure 193. Paired t-test comparing climate for the GPS-7 

section means of the fill area index. 

Fill Area By Freeze

0

10000

20000

30000

40000

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.00

-7793.67

F

 7793.67

 0.00

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-4314.81

 4501.28

F

 4501.28

-1749.88

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 6882.41

 11731.05

MeanAbsDif to Mean

 5165.106

 9920.144

MeanAbsDif to Median

 4724.289

 9710.720

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 17.0164

 16.1406

 21.5606

 14.8177

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

<.0001

<.0001

<.0001

0.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 10.4432

t-Test

 3.2316

DF Num

 1

DF Den

26.781

Prob>F

0.0033
259

Figure 194. Paired t-test comparing climate for the GPS-7 

section means of the LWP 1.8-m rut depths. 

LWP 1.8 By Freeze

0

5

10

15

20

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.00000

-2.56211

F

 2.56211

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-1.96357

 1.06381

F

 1.06381

-0.79633

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 3.267551

 4.800347

MeanAbsDif to Mean

 2.288089

 3.881600

MeanAbsDif to Median

 2.131579

 3.640000

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 4.0473

 6.0153

 9.6093

 7.2334

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.0458

0.0152

0.0023

0.0072

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 6.6175

t-Test

 2.5724

DF Num

 1

DF Den

27.772

Prob>F

0.0157
260

Figure 195. Paired t-test comparing climate for the GPS-7 

section means of the LWP 1.8-m rut widths. 

LWP 1.8 W By Freeze

0

1000

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.0000

-74.3911

F

 74.3911

 0.0000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-143.866

 -35.385

F

 -35.385

 -58.345

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 238.2526

 356.6035

MeanAbsDif to Mean

 184.7729

 195.8208

MeanAbsDif to Median

 177.1974

 186.7600

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 2.5770

 0.0479

 0.0838

 8.0174

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.1102

0.8269

0.7726

0.0046

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 1.0135

t-Test

 1.0067

DF Num

 1

DF Den

 27.63

Prob>F

0.3228
261

Figure 196. Paired t-test comparing climate for the GPS-7 

section means of the RWP 1.8-m rut depths. 

RWP 1.8 By Freeze

0

5

10

15

20

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.00000

-2.41816

F

 2.41816

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-1.91485

 0.95704

F

 0.95704

-0.77658

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 3.086071

 5.086911

MeanAbsDif to Mean

 2.201177

 3.878400

MeanAbsDif to Median

 2.019737

 3.640000

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 8.2022

 7.3023

 11.1649

 12.8343

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.0047

0.0076

0.0010

0.0003

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 5.3269

t-Test

 2.3080

DF Num

 1

DF Den

26.978

Prob>F

0.0289
262

Figure 197. Paired t-test comparing climate for the GPS-7 

section means of the RWP 1.8-m rut widths. 

RWP 1.8 W By Freeze

0

1000

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.00000

-6.06105

F

 6.06105

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-162.763

-118.134

F

-118.134

 -66.009

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 267.3935

 412.3589

MeanAbsDif to Mean

 208.9024

 299.0784

MeanAbsDif to Median

 201.9079

 256.3600

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 6.2853

 1.3924

 5.0852

 9.3710

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.0131

0.2396

0.0254

0.0022

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 0.0051

t-Test

 0.0711

DF Num

 1

DF Den

27.414

Prob>F

0.9439
263

Figure 198. Paired t-test comparing climate for the GPS-7 

section means of the LWP wire line rut depths. 

LWP 3.7 By Freeze

0

5

10

15

20

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.00000

-3.40237

F

 3.40237

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-2.20686

 1.71844

F

 1.71844

-0.89500

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 3.640468

 5.529617

MeanAbsDif to Mean

 2.671312

 4.582400

MeanAbsDif to Median

 2.519737

 4.240000

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 7.0730

 7.4196

 12.1925

 8.6688

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.0086

0.0071

0.0006

0.0032

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 8.8350

t-Test

 2.9724

DF Num

 1

DF Den

27.522

Prob>F

0.0061
264

Figure 199. Paired t-test comparing climate for the GPS-7 

section means of the LWP wire line rut widths. 

LWP 3.7 W By Freeze

0

1000

2000

3000

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.000

-476.202

F

 476.202

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-437.046

 142.717

F

 142.717

-177.245

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 761.4174

 906.5596

MeanAbsDif to Mean

 632.8072

 745.9136

MeanAbsDif to Median

 603.1382

 742.0800

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 2.0283

 1.5290

 1.4793

 1.3514

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.1562

0.2179

0.2255

0.2450

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 6.1810

t-Test

 2.4862

DF Num

 1

DF Den

29.828

Prob>F

0.0187
265

Figure 200. Paired t-test comparing climate for the GPS-7 

section means of the RWP wire line rut depths. 

RWP 3.7 By Freeze

0

5

10

15

20

25

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.00000

-3.28368

F

 3.28368

 0.00000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-2.20828

 1.59867

F

 1.59867

-0.89557

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 3.525118

 5.993608

MeanAbsDif to Mean

 2.546918

 4.796800

MeanAbsDif to Median

 2.289474

 4.600000

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 11.5847

 11.6526

 16.1536

 14.6645

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.0008

0.0008

<.0001

0.0001

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 7.0999

t-Test

 2.6646

DF Num

 1

DF Den

26.795

Prob>F

0.0129
266

Figure 201. Paired t-test comparing climate for the GPS-7 

section means of the RWP wire line rut widths. 

RWP 3.7 W By Freeze

0

1000

2000

3000

F NF

Freeze

Each Pair

Student's t

 0.05

Means Comparisons

Dif=Mean[i]-Mean[j]

NF

F

NF

 0.000

-408.883

F

 408.883

 0.000

Alpha= 0.05

Comparisons for each pair using Student's t

t

 1.97363

Abs(Dif)-LSD

NF

F

NF

-454.253

 62.267

F

 62.267

-184.224

Positive values show pairs of means that are significantly different.

Tests that the Variances are Equal

Level

F

NF

Count

 152

 25

Std Dev

 775.050

 1024.175

MeanAbsDif to Mean

 635.1389

 896.7232

MeanAbsDif to Median

 602.9211

 896.6800

Test

O'Brien[.5]

Brown-Forsythe

Levene

Bartlett

F Ratio

 6.5846

 6.7601

 7.4601

 3.6204

DF Num

 1

 1

 1

 1

DF Den

 175

 175

 175

 ?

Prob>F

0.0111

0.0101

0.0070

0.0571

Welch Anova testing Means Equal, allowing Std's Not Equal

F Ratio

 3.6416

t-Test

 1.9083

DF Num

 1

DF Den

28.694

Prob>F

0.0664
267

APPENDIX E. 

COMPARISONS OF TIME-SERIES SLOPES 

The slopes for the time-series data for each test section were determined for each of the indices. 

The distributions of the slopes are provided in figures 202 through 212. The signs of the slopes 

for each of the indices were compared to the signs for the LWP 1.8-m rut depth. These results 

are provided in figures 213 through 222. The top block in each figure is a graphical presentation 

of the results. The second block is a contingency table that provides a count for each cell in the 

table. A “-1” indicates a negative slope, a “0” indicates a zero slope, and a “1” indicates a 

positive slope. The bottom block provides the statistical results for each analysis. 
268

Figure 202. Distribution of the time-series slopes for the negative area index. 

Neg Area

-100

0

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 43.79

 25.12

 11.94

 3.76

 0.91

 0.00

 -1.43

 -4.40

 -12.36

 -40.25

-128.61

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 -0.4660

 7.8519

 0.2788

 0.0813

 -1.0133

 793.0000

 793.0000

-369.5383

 61.6530

 -6.5188

 101.5623

-1684.965
269

Figure 203. Distribution of the time-series slopes for the positive area index. 

Pos Area

-100

0

100 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 95.66

 47.26

 21.83

 5.97

 2.09

 0.00

 -0.30

 -2.52

 -7.02

 -24.07

-153.40

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1.3666

 9.5133

 0.3378

 2.0297

 0.7034

 793.0000

 793.0000

1083.6850

 90.5025

 -2.9778

 109.6023

 696.1461
270

Figure 204. Distribution of the time-series slopes for the fill area index. 

Fill Area

0

100

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 167.09

 44.82

 12.56

 5.48

 1.85

 0.00

 -0.92

 -3.91

 -8.29

 -16.42

 -23.39

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 1.0646

 8.7307

 0.3100

 1.6732

 0.4560

 793.0000

 793.0000

 844.2201

 76.2251

 10.6757

 178.9379

 820.0993
271

Figure 205. Distribution of the time-series slopes for the LWP 1.8-m rut depths. 

1.8 m LWP

-0.02

0.00

0.02

0.04

0.06

0.08

0.09

0.11

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

0.11460

0.02424

0.00722

0.00288

0.00108

0.00011

-0.0001

-0.0011

-0.0034

-0.0073

-0.0105

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 0.0009

 0.0053

 0.0002

 0.0013

 0.0005

 793.0000

 793.0000

 0.7114

 0.0000

 14.1308

 274.7799

 594.3052
272

Figure 206. Distribution of the time-series slopes for the LWP 1.8-m rut widths. 

W 1.8 m LWP

-4

-3

-2

-1

0

1

2

3

4

5

6

7 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 6.7000

 2.8121

 0.4843

 0.1343

 0.0248

-0.0008

-0.0601

-0.1462

-0.3957

-1.0213

-3.7886

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 0.0020

 0.3901

 0.0139

 0.0292

 -0.0252

 793.0000

 793.0000

 1.5521

 0.1522

 6.3847

 135.7229

19933.987
273

Figure 207. Distribution of the time-series slopes for the RWP 1.8-m rut depths. 

1.8 m RWP

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

0.05948

0.01930

0.00635

0.00262

0.00097

0.00001

-0.0003

-0.0014

 -0.004

-0.0092

-0.0174

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 0.0005

 0.0035

 0.0001

 0.0008

 0.0003

 793.0000

 793.0000

 0.4125

 0.0000

 7.3706

 115.8137

 664.1198
274

Figure 208. Distribution of the time-series slopes for the RWP 1.8-m rut widths. 

W 1.8 m RWP

-3

-2

-1

0

1

2

3

4

5

6 .001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 6.0500

 2.1069

 0.6845

 0.1076

 0.0106

-0.0096

-0.0703

-0.1817

-0.4952

-1.3947

-3.0648

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 -0.0048

 0.3978

 0.0141

 0.0230

 -0.0325

 793.0000

 793.0000

 -3.7777

 0.1583

 4.9876

 89.2918

-8351.282
275

Figure 209. Distribution of the time-series slopes for the LWP wire line rut depths. 

3.7 m LWP

-0.02

0.00

0.02

0.04

0.06

0.08

0.09

0.11

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

0.11992

0.02454

0.00748

0.00312

0.00118

0.00009

-0.0002

-0.0013

-0.0042

-0.0076

 -0.011

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 0.0009

 0.0057

 0.0002

 0.0013

 0.0005

 793.0000

 793.0000

 0.7429

 0.0000

 13.5671

 253.0422

 611.2734
276

Figure 210. Distribution of the time-series slopes for the LWP wire line rut widths. 

W 3.7 m LWP

0

10

20

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 22.900

 4.635

 0.923

 0.260

 0.057

 0.000

 -0.208

 -0.530

 -1.712

 -3.452

 -4.788

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 -0.0483

 1.2052

 0.0428

 0.0357

 -0.1324

 793.0000

 793.0000

 -38.3351

 1.4524

 12.5564

 224.5780

-2492.982
277

Figure 211. Distribution of the time-series slopes for the RWP wire line rut depths. 

3.7 m RWP

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

0.06431

0.02086

0.00675

0.00291

0.00111

0.00000

-0.0004

-0.0018

 -0.004

-0.0092

-0.0174

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 0.0006

 0.0038

 0.0001

 0.0008

 0.0003

 793.0000

 793.0000

 0.4504

 0.0000

 7.1897

 107.7201

 668.6312
278

Figure 212. Distribution of the time-series slopes for the RWP wire line rut widths. 

W 3.7 m RWP

0

10

20

.001 .01 .05.10 .25 .50 .75 .90.95 .99 .999

-4 -3 -2 -1 0 1 2 3 4

 Normal Quantile

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 21.200

 4.693

 1.143

 0.286

 0.048

 0.000

 -0.209

 -0.641

 -1.629

 -3.643

 -3.985

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

Sum

Variance

Skewness

Kurtosis

CV

 -0.0510

 1.1322

 0.0402

 0.0280

 -0.1299

 793.0000

 793.0000

 -40.4105

 1.2819

 11.4181

 198.7784

-2221.793
279

Figure 213. Comparison of the signs of the slopes for the negative 

area index versus those for the LWP 1.8-m rut depths. 

Neg Area + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

54 38 261

16 85 21

162 11 145

353

122

318

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 162.53014

 642.11154

 804.64168

RSquare (U)

0.2020

Test

Likelihood Ratio

Pearson

ChiSquare

 325.060

 389.312

Prob>ChiSq

 <.0001

 <.0001

Kappa

-0.02233

Std Err

0.030782

Kappa measures the degree of agreement.
280

Figure 214. Comparison of the signs of the slopes for the 

positive area index versus those for the LWP 1.8-m rut depths. 

Pos Area + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

78 0 191

0 134 1

154 0 235

269

135

389

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 358.71696

 448.18903

 806.90599

RSquare (U)

0.4446

Test

Likelihood Ratio

Pearson

ChiSquare

 717.434

 795.350

Prob>ChiSq

 <.0001

 <.0001

Kappa

0.282199

Std Err

0.031987

Kappa measures the degree of agreement.
281

Figure 215. Comparison of the signs of the slopes for the 

fill area index versus those for the LWP 1.8-m rut depths. 

Fill Area + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

202 0 90

0 134 0

30 0 337

292

134

367

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 503.50434

 309.23303

 812.73737

RSquare (U)

0.6195

Test

Likelihood Ratio

Pearson

ChiSquare

1007.009

1112.241

Prob>ChiSq

 <.0001

 <.0001

Kappa

0.753752

Std Err

0.021122

Kappa measures the degree of agreement.
282

Figure 216. Comparison of the signs of the slopes for the 

LWP 1.8-m rut widths versus those for the LWP 1.8-m rut depths. 

W 1.8 LWP + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

188 0 212

0 134 2

44 0 213

400

136

257

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 383.11178

 419.99660

 803.10838

RSquare (U)

0.4770

Test

Likelihood Ratio

Pearson

ChiSquare

 766.224

 852.681

Prob>ChiSq

 <.0001

 <.0001

Kappa

 0.49865

Std Err

0.025956

Kappa measures the degree of agreement.
283

Figure 217. Comparison of the signs of the slopes for the 

RWP 1.8-m rut depths versus those for the LWP 1.8-m rut depths. 

1.8 RWP + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

175 0 86

0 134 0

57 0 341

261

134

398

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 458.81697

 343.85258

 802.66956

RSquare (U)

0.5716

Test

Likelihood Ratio

Pearson

ChiSquare

 917.634

1024.189

Prob>ChiSq

 <.0001

 <.0001

Kappa

0.701891

Std Err

0.023295

Kappa measures the degree of agreement.
284

Figure 218. Comparison of the signs of the slopes for the 

RWP 1.8-m rut widths versus those for the LWP 1.8-m rut depths. 

W 1.8 RWP + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

181 0 245

0 134 1

51 0 181

426

135

232

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 369.17894

 419.70255

 788.88149

RSquare (U)

0.4680

Test

Likelihood Ratio

Pearson

ChiSquare

 738.358

 819.254

Prob>ChiSq

 <.0001

 <.0001

Kappa

0.429542

Std Err

0.026525

Kappa measures the degree of agreement.
285

Figure 219. Comparison of the sign of the slopes for the 

LWP wire line rut depths versus those for the LWP 1.8-m rut depths. 

3.7 LWP + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

221 0 30

0 134 0

11 0 397

251

134

408

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 645.27117

 152.86041

 798.13159

RSquare (U)

0.8085

Test

Likelihood Ratio

Pearson

ChiSquare

1290.542

1390.195

Prob>ChiSq

 <.0001

 <.0001

Kappa

0.914088

Std Err

 0.01317

Kappa measures the degree of agreement.
286

Figure 220. Comparison of the signs of the slopes for the 

LWP wire line rut widths versus those for the LWP 1.8-m rut depths. 

W 3.7 LWP + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

187 0 199

0 134 0

45 0 228

386

134

273

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 398.16400

 409.11426

 807.27826

RSquare (U)

0.4932

Test

Likelihood Ratio

Pearson

ChiSquare

 796.328

 879.174

Prob>ChiSq

 <.0001

 <.0001

Kappa

0.521971

Std Err

0.025932

Kappa measures the degree of agreement.
287

Figure 221. Comparison of the signs of the slopes for the 

RWP wire line rut depths versus those for the LWP 1.8-m rut depths. 

3.7 RWP + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

180 0 90

0 134 0

52 0 337

270

134

389

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 462.86887

 343.34212

 806.21099

RSquare (U)

0.5741

Test

Likelihood Ratio

Pearson

ChiSquare

 925.738

1031.841

Prob>ChiSq

 <.0001

 <.0001

Kappa

0.705336

Std Err

0.023094

Kappa measures the degree of agreement.
288

Figure 222. Comparison of the signs of the slopes for the 

RWP wire line rut widths versus those for the LWP 1.8-m rut depths. 

W 3.7 RWP + or - By 1.8 LWP + or -

0

0.25

0.5

0.75

1

-1 0 1

1.8 LWP + or -

-1

0

1

Crosstabs

1.8 LWP + or -

Count

-1

0

1

-1 0 1

174 0 213

0 134 0

58 0 214

387

134

272

232 134 427 793

Tests

Source

Model

Error

C Total

Total Count

DF

 4

 787

 791

 793

-LogLikelihood

 380.49433

 426.43443

 806.92876

RSquare (U)

0.4715

Test

Likelihood Ratio

Pearson

ChiSquare

 760.989

 840.081

Prob>ChiSq

 <.0001

 <.0001

Kappa

0.469329

Std Err

0.026968

Kappa measures the degree of agreement.
 289

REFERENCES 

1. Gramling, W.L. and Hunt, J.E. Photographic Pavement Distress Record Collection and 

Transverse Profile Analysis, Report No. SHRP-P-600, National Research Council, 

Washington, D.C., 1993, unpublished. 

2. Distress Identification Manual for the Long-Term Pavement Performance Project, Report 

No. SHRP-P-338, National Research Council, Washington, D.C., 1993. 

3. Henderson, B. and Abukhater, B. Long Term Pavement Performance PROQUAL V2.08 

Users Documentation, June 1998, Publication No. FHWA-TS-98-00-01, Federal Highway 

Administration, McLean, Virginia, June 1998. 

4. The AASHO Road Test, Report 5 Pavement Research, Special Report 61E, Highway 

Research Board, Washington, D.C., 1962. 

5. Simpson, A.L.; Rauhut, J.B.; Jordahl, P.J.; Owusu-Antwi, E.; Darter, M.I.; Ahmad, R.; 

Pendleton, O.J.; and Lee, Y.H. Sensitivity Analyses for Selected Pavement Distresses, 

Report No. SHRP-P-393, National Research Council, Washington, D.C., 1994. 

6. Von Quintus, H. and Killingsworth, B. Analyses Relating to Pavement Material 

Characterizations and Their Effects on Pavement Performance, Report No. FHWA-RD-97-

085, Federal Highway Administration, McLean, Virginia, 1998. 

7. Thomas, G.B., Jr. and Finney, R.L. Calculus and Analytic Geometry, Sixth Edition, 

Addison-Wesley Publishing Company, Reading, Massachusetts, 1984. 

8. Rosner, B. Fundamentals of Biostatistics, Third Edition, PSW-Kent Publishing Company, 

Boston, Massachusetts, 1990. 

9. ASTM C670-96, "Standard Practice for Preparing Precision and Bias Statements for Test 

Methods for Construction Materials," ASTM Standards on Precision and Bias for Various 

Applications, Fifth Edition, American Society for Testing and Materials, West 

Conshohocken, Pennsylvania, 1997.