DATA COLLECTION ISSUES AND THEIR IMPACTS ON THE PAVEMENT
MANAGEMENT DECISIONS
By
Christopher Michael Dean

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Civil Engineering
2012

ABSTRACT
DATA COLLECTION ISSUES AND THEIR IMPACTS ON THE PAVEMENT
MANAGEMENT DECISIONS
By
Christopher Michael Dean
The management of the highway network presents major and complex problems that
challenge highway administrators. The problems are compounded by the long-term economic
climate, which forced highway administrators to reduce costs. Some have adopted data sampling,
others decreased the data collection frequency, and still others reduced the entire pavement
management system operation. Unfortunately, these actions were made without detailed
evaluation of their impacts on the pavement management decisions. Consequently, time series
pavement condition and distress data were obtained from four State Highway Agencies and the
Minnesota Road Research project (MnROAD). The data were used to evaluate the impacts of
data sampling, pavement analysis length, and data imputation on the variability of the data and
the accuracy of pavement management decisions.
It is shown that data sampling causes various degrees of errors in pavement management
decisions, including the identification of project boundaries, selection of treatment type, and
allocation of treatment funds. Furthermore, data sampling yields longer pavement analysis
lengths. It is shown that longer analysis lengths do not necessarily improve the analyses. On the
contrary, longer analyses lengths have significant adverse impacts on various pavement
management decisions. Finally, some of the measured data in the databases were randomly
amputated to simulate missing data and imputed using different methods to bridge the gap. It is
shown that all methods yield differences between the measured and the imputed data. However,
in general, such differences do not significantly impact the pavement management decisions.

TO EVERYONE THAT LOVES AND BELIEVES IN ME

iii

ACKNOWLEDGMENTS

I would like to extend my deepest appreciation to my advisor, Dr. Gilbert Y. Baladi, for
his support, patience, and encouragement throughout my graduate studies. His commitment to
excellence and ever-lasting excitement for research are unparalleled. Without his guidance, this
thesis would not have been possible. I would also like to thank him for the innumerous lessons
that he has taught me throughout my studies. These lessons are timeless and will continue to
serve me throughout my professional career. I am forever indebted to him and grateful for all the
opportunities that he bestowed upon me.
I would also like to thank the other members of my advisory committee, Dr. Neeraj Buch
and Dr. Karim Chatti. Their technical knowledge and support has been crucial to my success.
Many thanks also to Dr. Syed Haider for his research guidance and support.
It is also important to acknowledge the Federal Highway Administration (FHWA) for
sponsoring and funding this study. Thanks to the Colorado Department of Transportation
(CDOT), the Louisiana Department of Transportation and Development (LADOTD), the
Michigan Department of Transportation (MDOT), the Washington State Department of
Transportation (WSDOT), and the Minnesota Road Research project (MnROAD) for their
cooperation during this study. Finally, special thanks to my friend and co-researcher Tyler
Dawson. Many thanks also to Adam Beach, Matthew McCloskey, Ryan Muscott, Corbin St.
Aubin, and Nick Tecca for their efforts in this study.

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TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................................... viii
LIST OF FIGURES ........................................................................................................................ x
CHAPTER 1
INTRODUCTION & RESEARCH PLAN ..................................................................................... 1
1.1
Introduction ......................................................................................................................... 1
1.2
Problem Statement and Research Plan ............................................................................... 3
1.3
Objectives ........................................................................................................................... 5
1.4
Thesis Layout ...................................................................................................................... 5
CHAPTER 2
LITERATURE REVIEW ............................................................................................................... 6
2.1
Introduction to Pavement Management .............................................................................. 6
2.1.1 The Need to Manage Pavements ................................................................................. 7
2.1.2 Pavement Management versus Managing Pavement .................................................. 7
2.1.3 Acts of Managing Pavements ...................................................................................... 8
2.1.4 Network-Level Pavement Management .................................................................... 10
2.1.5 Project-Level Pavement Management....................................................................... 10
2.1.6 Commonalities and Differences Between Network and Project-Level Pavement
Management ............................................................................................................................ 11
2.2
Data Elements and Data Collection Procedures ............................................................... 13
2.3
Data Collection Frequency ............................................................................................... 22
2.4
Pavement Project Boundaries (Data Delineation) ............................................................ 24
2.5
Pavement Performance Data Sampling ............................................................................ 27
2.6
Pavement Survey and Analysis Length ............................................................................ 29
2.7
Data Imputation ................................................................................................................ 31
2.8
Location Referencing Systems ......................................................................................... 35
2.9
Pavement Performance Data Modeling and Remaining Service Life (RSL) ................... 42
2.9.1 The Need for Data Modeling..................................................................................... 42
2.9.2 International Roughness Index (IRI) Modeling ........................................................ 43
2.9.3 Rut Depth Modeling .................................................................................................. 43
2.9.4 Crack Modeling ......................................................................................................... 44
2.9.5 Uses of Data Modeling .............................................................................................. 46
2.10 Life Cycle Cost Analysis (LCCA) .................................................................................... 49
CHAPTER 3
DATA MINING............................................................................................................................ 55
3.1
Foreword ........................................................................................................................... 55
3.2
Introduction ....................................................................................................................... 55
3.3
Data Format, Restructuring, and Unification .................................................................... 56
3.3.1 Pavement Condition and Distress Data from Four State Highway Agencies ........... 62

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3.3.2 Minnesota Road Research Project (MnROAD) ........................................................ 70
3.4
Treated Pavement Section Identification .......................................................................... 71
3.5
Time Series Data Restructuring ........................................................................................ 73
3.6
Cost Data........................................................................................................................... 74
CHAPTER 4
DATA ANALYSES & DISCUSSION ......................................................................................... 77
4.1
Introduction and Research Objectives .............................................................................. 77
4.2
Pavement Performance Data Sampling ............................................................................ 78
4.2.1 Fixed Sampling.......................................................................................................... 80
4.2.2 Random Sampling ................................................................................................... 102
4.2.3 Sample Size ............................................................................................................. 106
4.3
Pavement Performance Data Sampling: Condition State Concept ................................. 109
4.4
Pavement Project Boundary Analysis ............................................................................. 124
4.4.1 Pavement Project Boundary Analysis: Condition and Distress Data Approach ..... 128
4.4.2 Pavement Project Boundary Analysis: RSL Concept ............................................. 136
4.5
The Hidden Costs of Pavement Performance Data Sampling ........................................ 140
4.6
Pavement Analysis Length ............................................................................................. 144
4.6.1 The Impacts of Pavement Analysis Length on the Variability and Modeling of
Pavement Performance Data ................................................................................................. 145
4.6.2 The Impacts of Pavement Analysis Length on PMS Decisions .............................. 159
4.7
Pavement Performance Data Imputation ........................................................................ 161
4.7.1 Linear Interpolation Imputation .............................................................................. 163
4.7.2 Regression Imputation ............................................................................................. 166
4.7.3 Moving Regression Imputation ............................................................................... 170
4.7.4 Multiple Regressions Imputation ............................................................................ 173
4.7.5 Discussion ............................................................................................................... 178
4.7.6 The No-Action (No Imputation) Approach ............................................................. 182
4.7.7 Comparison of the Four Imputation Methods and the No-Action Approach.......... 183
4.7.8 Advantages and Disadvantages of the Four Imputation Methods ........................... 188
CHAPTER 5
SUMMARY, CONCLUSIONS, & RECOMMENDATIONS ................................................... 192
5.1
Summary ......................................................................................................................... 192
5.2
Conclusions ..................................................................................................................... 194
5.3
Recommendations ........................................................................................................... 197
APPENDIX A
PMS DATA ................................................................................................................................ 200
APPENDIX B
PAVEMENT PERFORMANCE DATA SAMPLING FIGURES ............................................. 208
APPENDIX C
PAVEMENT ANALYSIS LENGTH FIGURES ....................................................................... 264

vi

APPENDIX D
PAVEMENT PERFORMANCE DATA IMPUTATION FIGURES......................................... 269
REFERENCES ........................................................................................................................... 286

vii

LIST OF TABLES

Table 2.1 Pavement inventory and monitoring data ..................................................................... 15
Table 2.2 Main advantage(s) and disadvantage(s) of each location reference system ................. 40
Table 2.3 LADOTD linear referencing system error (after Dawson 2012) .................................. 41
Table 2.4 Mathematical functions used to model the data of the indicated distress type ............. 45
Table 2.5 Example distress thresholds .......................................................................................... 48
Table 3.1 Pavement condition and distress data stored by various SHAs .................................... 57
Table 3.2 The pavement condition and distress data received from the four SHAs ..................... 63
Table 3.3 MnROAD database items ............................................................................................. 71
Table 3.4 The number of pavement projects and total length identified in each state ................. 73
Table 3.5 Typical preventive maintenance treatment costs in 2009 for the state of Michigan
(Baladi and Dean 2011) ................................................................................................................ 75
Table 3.6 Typical preventive maintenance treatment costs in 2010 for the state of Michigan
(Baladi and Dean 2011) ................................................................................................................ 76
Table 3.7 Typical material and total treatment costs for the state of Michigan (Baladi & Dean
2011) ............................................................................................................................................. 76
Table 4.1 Mathematical functions used to model the pavement condition and distress data ..... 112
Table 4.2 Pavement condition state, RSL range, and probable pavement treatment actions ..... 113
Table 4.3 Percent of each road changing certain number of condition states based on the IRI data
..................................................................................................................................................... 115
Table 4.4 Solution sequence of the AASHTO unit delineation method (after AASHTO 1993) 125
Table 4.5 Example of the solution sequence of the AASHTO unit delineation method using IRI
data for 2 miles of HWY 24 in Colorado .................................................................................... 126
Table 4.6 Total pavement expenditure, data digitization, and total data collection costs for three
states (Fillastre 2011, Hartgen et al. 2009) ................................................................................. 142

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Table 4.7 Total expenditures, potential savings, and potential misallocation of funds as a result of
the use of ten percent sampling for various pavement networks ................................................ 143
Table 4.8 The number of pavement projects and their total length identified for analysis in each
state ............................................................................................................................................. 146
Table 4.9 Number of analysis sections for various analysis lengths along a 2.2 mile long project
..................................................................................................................................................... 149
Table 4.10 Coefficients of variation for ten pavement analysis lengths based on three years of IRI
and longitudinal cracking data along US-2 in Washington, BMP 89.3 to 99.0 .......................... 157
Table 4.11 Linear interpolation imputation example .................................................................. 164
Table 4.12 Regression imputation example ................................................................................ 167
Table 4.13 Moving regression imputation example ................................................................... 171
Table 4.14 Multiple regressions imputation example ................................................................. 175
Table 4.15 Differences and percent differences between the imputed and the actual IRI data for
four imputation methods (three rates of deterioration and no variability) .................................. 181
Table 4.16 Differences and percent differences between the imputed and the actual IRI data for
four imputation methods (three rates of deterioration and variable data) ................................... 181
Table 4.17 Advantages and disadvantages of four data imputation methods ............................. 189
Table A.1 Measured pavement condition data along I-70 in Colorado ...................................... 202
Table A.2 Formatted pavement condition data along I-70 in Colorado ..................................... 203
Table A.3 Formatted pavement condition data along US-80 in Louisiana................................. 204
Table A.4 Formatted pavement condition data along I-69BL in Michigan ................................ 205
Table A.5 Formatted pavement condition data along I-5 in Washington ................................... 206
Table A.6 Formatted pavement condition data along cell 1 at MnROAD ................................. 207

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LIST OF FIGURES

Figure 2.1 Network and project-levels pavement management (AASHTO 1993, Hudson et al.
1979) ............................................................................................................................................. 12
Figure 2.2 Percent of SHAs using the stated method of pavement condition data collection ...... 21
Figure 2.3 Area scan image for fully-automated data collection (McGhee 2004) ....................... 21
Figure 2.4 Percent of SHAs using the indicated PMS data collection frequency......................... 23
Figure 2.5 A typical pavement response variable versus distance for data delineation (after
AASHTO 1993) ............................................................................................................................ 24
Figure 2.6 The Idealized Approach for data delineation (AASHTO 1993) ................................. 26
Figure 2.7 Mean absolute error for four imputation methods (after Farhan and Fwa 2012) ........ 36
Figure 2.8 Percent of SHAs utilizing stated location referencing systems (after Flintsch et al.
2004) ............................................................................................................................................. 37
Figure 2.9 Illustrative example of yearly error of linear referencing system (Dawson 2012) ...... 41
Figure 2.10 Illustration of the mathematical functions used to model IRI, rutting, and cracking
and to predict future conditions .................................................................................................... 45
Figure 2.11 Illustration of the Remaining Service Life using three mathematical models .......... 50
Figure 2.12 Components of user costs (after Morgado and Neves 2009) .................................... 52
Figure 3.1 Time series transverse cracking data for each severity level and the sum of all levels,
Colorado, HWY 24, direction 2, BMP 329.9 ............................................................................... 60
Figure 3.2 Cumulative time series transverse cracking data showing individual transverse crack
severity level and the sum of all severity levels, Colorado, HWY 24, direction 2, BMP 329.9 . 60
Figure 3.3 The BMP of the first ten 0.1 mile long pavement segments along M-39, control
section 82192, direction 1, Michigan ............................................................................................ 68
Figure 3.4 Longitudinal cracking data after adjusting the BMP for the first ten 0.1 mile long
pavement segments along M-39, control section 82192, direction 1, Michigan .......................... 68
Figure 4.1 Continuous and sampled IRI data along four roads in four different states ................ 83

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Figure 4.2 Continuous and sampled transverse crack length data along four roads in four
different states ............................................................................................................................... 84
Figure 4.3 Sampled (squares) and the range of the continuous IRI data for each mile ................ 87
Figure 4.4 Sampled (squares) and the range of the continuous transverse cracking data for each
mile ............................................................................................................................................... 88
Figure 4.5 Continuous time series IRI data as percent of the sampled data along a portion of the
flexible HWY 24 in Colorado ....................................................................................................... 91
Figure 4.6 Continuous time series IRI data as percent of the sampled data along a portion of the
flexible LA-34 (control section 0.12304) in Louisiana ................................................................ 92
Figure 4.7 Continuous time series transverse crack data as percent of the sampled data along a
portion of the rigid I-69 (control section 77024) in Michigan ...................................................... 93
Figure 4.8 Continuous time series transverse crack data as percent of the sampled data along the
composite SRID 005 in Washington............................................................................................. 94
Figure 4.9 Maximum, minimum, and average percent differences between the continuous and the
sampled transverse cracking, relative to the sampled data, Colorado .......................................... 96
Figure 4.10 Maximum, minimum, and average percent differences between the continuous and
the sampled transverse cracking, relative to the sampled data, Louisiana.................................... 97
Figure 4.11 Maximum, minimum, and average differences between the continuous and the
sampled transverse cracking, relative to the sampled data, Michigan .......................................... 98
Figure 4.12 Maximum, minimum, and average percent differences between the continuous and
the sampled transverse cracking, relative to the sampled data, Washington ................................ 99
Figure 4.13 Continuous and randomly sampled IRI data per mile along four roads in Colorado
..................................................................................................................................................... 104
Figure 4.14 Continuous and randomly sampled transverse cracking data along four roads in
Colorado ...................................................................................................................................... 105
Figure 4.15 Maximum, minimum, and average continuous/sampled transverse cracking ratio
versus sample size along two roads in Michigan ........................................................................ 108
Figure 4.16 Percent of two roads in Colorado and two in Louisiana versus the numbers of
condition state change, IRI data .................................................................................................. 116
Figure 4.17 Percent of two roads in Michigan and two in Washington versus the numbers of
condition state change, IRI data .................................................................................................. 117

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Figure 4.18 Distribution of the numbers of condition state change based on IRI data for the
approximately 97 mile network .................................................................................................. 120
Figure 4.19 Percent of two roads in Washington versus the numbers of condition state change,
rut depth and longitudinal cracking data ..................................................................................... 123
Figure 4.20 Cumulative differences versus beginning mile point along the flexible HWY 24 in
Colorado showing three pavement projects ................................................................................ 127
Figure 4.21 Cumulative differences versus beginning mile point along the flexible HWY 24 in
Colorado showing two pavement projects .................................................................................. 127
Figure 4.22 Project boundaries based on the AASHTO unit delineation method and the
continuous IRI data along 13 miles of the flexible HWY 24 in Colorado ................................. 130
Figure 4.23 Project boundaries based on the AASHTO unit delineation method and the ten
percent sampled IRI data along 13 miles of the flexible HWY 24 in Colorado ......................... 130
Figure 4.24 Project boundaries based on the continuous (100 percent sampled) and the sampled
IRI data along a section of the flexible HWY 24 in Colorado.................................................... 131
Figure 4.25 Project boundaries based on the continuous (100 percent sampled) and the sampled
IRI data along a section of the composite I-94 in Michigan ....................................................... 132
Figure 4.26 Project boundaries based on the continuous (100 percent sampled) and sampled IRI
data along a section of the composite SRID 161 in Washington ................................................ 132
Figure 4.27 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(IRI) data along a section of the flexible HWY 24 in Colorado ................................................. 138
Figure 4.28 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(IRI) data along a section of the composite I-94 in Michigan .................................................... 138
Figure 4.29 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(IRI) data along a section of the composite SRID 161 in Washington ....................................... 139
Figure 4.30 Percent acceptance versus pavement analysis length, thin HMA overlay, Colorado
..................................................................................................................................................... 151
Figure 4.31 Percent acceptance versus pavement analysis length, thin HMA overlay, Louisiana
..................................................................................................................................................... 151
Figure 4.32 Percent acceptance versus pavement analysis length, thin HMA overlay, Washington
..................................................................................................................................................... 152
Figure 4.33 Percent acceptance versus pavement analysis length, single chip seal, Colorado .. 152

xii

Figure 4.34 Percent acceptance versus pavement analysis length, single chip seal, Louisiana . 153
Figure 4.35 Percent acceptance versus pavement analysis length, single chip seal, Washington
..................................................................................................................................................... 153
Figure 4.36 Ratio of the coefficients of variation for the longitudinal cracking and IRI data
versus pavement analysis length along US-2 in Washington, BMP 89.3 to 99.0....................... 157
Figure 4.37 The difference between the imputed and measured data in percent of the measured
data versus the BMP along HWY 24 in Colorado, three data points imputed using the linear
interpolation imputation method ................................................................................................. 164
Figure 4.38 The difference between the RSL values based on imputed and measured data versus
the BMP along HWY 24 in Colorado, three data points imputed using the linear interpolation
imputation method ...................................................................................................................... 165
Figure 4.39 Example regression parameter calculation for regression imputation, missing data at
year 7 ........................................................................................................................................... 167
Figure 4.40 The difference between the imputed and measured data in percent of the measured
data versus the BMP along HWY 24 in Colorado, three data points imputed using the regression
imputation method ...................................................................................................................... 168
Figure 4.41 The difference between the RSL values based on imputed and measured data versus
the BMP along HWY 24 in Colorado, three data points imputed using the regression imputation
method......................................................................................................................................... 169
Figure 4.42 The difference between the imputed and measured data in percent of the measured
data versus the BMP along HWY 24 in Colorado, three data points imputed using the moving
regression imputation method ..................................................................................................... 172
Figure 4.43 The difference between the RSL values based on imputed and measured data versus
the BMP along HWY 24 in Colorado, three data points imputed using the moving regression
imputation method ...................................................................................................................... 173
Figure 4.44 The difference between the imputed and measured data in percent of the measured
data versus the BMP along HWY 24 in Colorado, three data points imputed using the multiple
regressions imputation method ................................................................................................... 176
Figure 4.45 The difference between the RSL values based on imputed and measured data versus
the BMP along HWY 24 in Colorado, three data points imputed using the multiple regressions
imputation method ...................................................................................................................... 177
Figure 4.46 IRI data having three deterioration rates and no variability .................................... 179
Figure 4.47 Variable IRI data having three deterioration rates .................................................. 180

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Figure 4.48 Maximum, minimum, and average percent difference between imputed and
measured data at BMPs 321, 322, 323, 324, and 325 along HWY 24 in Colorado, using four
imputation methods..................................................................................................................... 184
Figure 4.49 Differences between the RSL based on the stated imputation method (second
available data point imputed) and that based on the complete measured data at BMPs 321, 322,
323, 324, and 325 along HWY 24 in Colorado .......................................................................... 185
Figure 4.50 Differences between the RSL based on the stated imputation method (third available
data point imputed) and that based on the complete measured data at BMPs 321, 322, 323, 324,
and 325 along HWY 24 in Colorado .......................................................................................... 185
Figure 4.51 Differences between the RSL based on the stated imputation method (fourth
available data point imputed) and that based on the complete measured data at BMPs 321, 322,
323, 324, and 325 along HWY 24 in Colorado .......................................................................... 186
Figure 4.52 Maximum, minimum, and average difference between RSL values based on imputed
and measured data at BMPs 321, 322, 323, 324, and 325 along HWY 24 in Colorado, using four
imputation methods..................................................................................................................... 187
Figure B.1 Continuous and sampled IRI data along four roads in Colorado .............................. 209
Figure B.2 Continuous and sampled IRI data along four roads in Louisiana ............................. 210
Figure B.3 Continuous and sampled IRI data per mile along four roads in Michigan ............... 211
Figure B.4 Continuous and sampled IRI data per mile along four roads in Washington ........... 212
Figure B.5 Continuous and sampled transverse crack data along four roads in Colorado ......... 213
Figure B.6 Continuous and sampled transverse crack data per mile along four roads in Louisiana
..................................................................................................................................................... 214
Figure B.7 Continuous and sampled transverse crack data per mile along four roads in Michigan
..................................................................................................................................................... 215
Figure B.8 Continuous and sampled transverse crack data per mile along four roads in
Washington ................................................................................................................................. 216
Figure B.9 Sampled (squares) and continuous IRI data per mile along four roads in Colorado 217
Figure B.10 Sampled (squares) and continuous IRI data per mile along four roads in Louisiana
..................................................................................................................................................... 218
Figure B.11 Sampled (squares) and continuous IRI data per mile along four roads in Michigan
..................................................................................................................................................... 219

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Figure B.12 Sampled (squares) and continuous IRI data per mile along four roads in Washington
..................................................................................................................................................... 220
Figure B.13 Sampled (squares) and continuous transverse crack data per mile along four roads in
Colorado ...................................................................................................................................... 221
Figure B.14 Sampled (squares) and continuous transverse crack data per mile four roads in
Louisiana ..................................................................................................................................... 222
Figure B.15 Sampled (squares) and continuous transverse crack data per mile along four roads in
Michigan ..................................................................................................................................... 223
Figure B.16 Sampled (squares) and continuous transverse crack data per mile along four roads in
Washington ................................................................................................................................. 224
Figure B.17 Continuous time series IRI data as percent of the sampled data along HWY 24
(flexible) in Colorado .................................................................................................................. 225
Figure B.18 Continuous time series IRI data as percent of the sampled data along I-70 (rigid) in
Colroado ...................................................................................................................................... 226
Figure B.19 Continuous time series IRI data as percent of the sampled data along HWY 36
(composite) in Colorado ............................................................................................................. 227
Figure B.20 Continuous time series IRI data as percent of the sampled data along HWY 71
(flexible) in Colorado .................................................................................................................. 228
Figure B.21 Continuous time series IRI data as percent of the sampled data along LA-34
(flexible) in Louisiana ................................................................................................................. 229
Figure B.22 Continuous time series IRI data as percent of the sampled data along LA-83 (rigid)
in Louisiana ................................................................................................................................. 230
Figure B.23 Continuous time series IRI data as percent of the sampled data along LA-1
(composite) in Louisiana............................................................................................................. 231
Figure B.24 Continuous time series IRI data as percent of the sampled data along LA-526 (rigid)
in Louisiana ................................................................................................................................. 232
Figure B.25 Continuous time series IRI data as percent of the sampled data along I-94
(composite) in Michigan ............................................................................................................. 233
Figure B.26 Continuous time series IRI data as percent of the sampled data along I-69 (CS
12033, rigid) in Michigan ........................................................................................................... 234

xv

Figure B.27 Continuous time series IRI data as percent of the sampled data along US-31
(flexible) in Michigan ................................................................................................................. 235
Figure B.28 Continuous time series IRI data as percent of the sampled data along I-69 (CS
77024, rigid) in Michigan ........................................................................................................... 236
Figure B.29 Continuous time series IRI data as a percent of the sampled data along SRID 005
(composite) in Washington ......................................................................................................... 237
Figure B.30 Continuous time series IRI data as a percent of the sampled data along SRID 161
(composite) in Washington ......................................................................................................... 238
Figure B.31 Continuous time series IRI data as a percent of the sampled data along SRID 005
(flexible) in Washington ............................................................................................................. 239
Figure B.32 Continuous time series IRI data as a percent of the sampled data along SRID 082
(rigid) in Washington .................................................................................................................. 240
Figure B.33 Continuous time series transverse crack data as percent of the sampled data along
HWY 24 (flexible) in Colorado .................................................................................................. 241
Figure B.34 Continuous time series transverse crack data as percent of the sampled data along I70 (rigid) in Colorado ................................................................................................................. 242
Figure B.35 Continuous time series transverse crack data as percent of the sampled data along
HWY 36 (composite) in Colorado .............................................................................................. 243
Figure B.36 Continuous time series transverse crack data as percent of the sampled data along
HWY 71 (flexible) in Colorado .................................................................................................. 244
Figure B.37 Continuous time series transverse crack data as percent of the sampled data along
LA-34 (flexible) in Louisiana ..................................................................................................... 245
Figure B.38 Continuous time series transverse crack data as percent of the sampled data along
LA-83 (rigid) in Louisiana .......................................................................................................... 246
Figure B.39 Continuous time series transverse crack data as percent of the sampled data along
LA-1 (composite) in Louisiana ................................................................................................... 247
Figure B.40 Continuous time series transverse crack data as percent of the sampled data along
LA-526 (rigid) in Louisiana ........................................................................................................ 248
Figure B.41 Continuous time series transverse crack data as percent of the sampled data along I94 (composite) in Michigan ........................................................................................................ 249

xvi

Figure B.42 Continuous time series transverse crack data as percent of the sampled data long I69 (CS 12033, rigid) in Michigan ............................................................................................... 250
Figure B.43 Continuous time series transverse crack data as percent of the sampled data along
US-31 (flexible) in Michigan ...................................................................................................... 251
Figure B.44 Continuous time series transverse crack data as percent of the sampled data along I69 (CS 77024, rigid) in Michigan ............................................................................................... 252
Figure B.45 Continuous time series transverse crack data as percent of the sampled data along
SRID 005 (composite) in Washington ........................................................................................ 253
Figure B.46 Continuous time series transverse crack data as percent of the sampled data along
SRID 161 (composite) in Washington ........................................................................................ 254
Figure B.47 Continuous time series transverse crack data as percent of the sampled data along
SRID 005 (flexible) in Washington ............................................................................................ 255
Figure B.48 Continuous time series transverse crack data as percent of the sampled data along
SRID 082 (rigid) in Washington ................................................................................................. 256
Figure B.49 Continuous and randomly sampled IRI data per mile along four roads in Louisiana
..................................................................................................................................................... 257
Figure B.50 Continuous and randomly sampled IRI data per mile along four roads in Michigan
..................................................................................................................................................... 258
Figure B.51 Continuous and randomly sampled transverse crack data along four roads in
Louisiana ..................................................................................................................................... 259
Figure B.52 Continuous and randomly sampled transverse crack data along four roads in
Michigan ..................................................................................................................................... 260
Figure B.53 Project boundaries based on the continuous (100 percent sampled) and the sampled
rut depth data along a section of the flexible HWY 24 in Colorado........................................... 261
Figure B.54 Project boundaries based on the continuous (100 percent sampled) and the sampled
transverse cracking data along a section of the flexible HWY 24 in Colorado .......................... 261
Figure B.55 Project boundaries based on the continuous (100 percent sampled) and the sampled
rut depth data along a section of the composite SRID 161 in Washington ................................ 262
Figure B.56 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(rut depth) data along a section of the flexible HWY 24 in Colorado ........................................ 262

xvii

Figure B.57 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(transverse cracking) data along a section of the flexible HWY 24 in Colorado ....................... 263
Figure B.58 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(rut depth) data along a section of the composite SRID 161 in Washington .............................. 263
Figure C.1 Percent acceptance versus pavement analysis length, thin mill and fill, Colorado .. 265
Figure C.2 Percent acceptance versus pavement analysis length, thick HMA overlay, Louisiana
..................................................................................................................................................... 265
Figure C.3 Percent acceptance versus pavement analysis length, double chip seal, Louisiana . 266
Figure C.4 Percent acceptance versus pavement analysis length, thin mill and fill, Louisiana . 266
Figure C.5 Percent acceptance versus pavement analysis length, thick mill and fill, Louisiana 267
Figure C.6 Percent acceptance versus pavement analysis length, thick HMA overlay, Washington
..................................................................................................................................................... 267
Figure C.7 Percent acceptance versus pavement analysis length, thin mill and fill, Washington
..................................................................................................................................................... 268
Figure D.1 The difference between the imputed and measured data in percent of the measured
data versus the BMP along LA 21 (control section 0.02902) in Louisiana, three data points
imputed using the linear interpolation method ........................................................................... 270
Figure D.2 The difference between the imputed and measured data in percent of the measured
data versus cells 1, 2, 3, 5, and 14 at MnROAD, three data points imputed using the linear
interpolation method ................................................................................................................... 270
Figure D.3 The difference between the imputed and measured data in percent of the measured
data versus the BMP along SRID 099 in Washington, three data points imputed using the linear
interpolation method ................................................................................................................... 271
Figure D.4 The difference between the RSL values based on imputed and measured data versus
the BMP along LA 21 (CS 0.02902) in Louisiana, three data points imputed using the linear
interpolation method ................................................................................................................... 271
Figure D.5 The difference between the RSL values based on imputed and measured data versus
the cell number at MnROAD, three data points imputed using the linear interpolation method 272
Figure D.6 The difference between the RSL values based on imputed and measured data versus
the BMP along SRID 099 in Washington, three data points imputed using the linear interpolation
method......................................................................................................................................... 272

xviii

Figure D.7 The difference between the imputed and measured data in percent of the measured
data versus the BMP along LA 21 (control section 0.02902) in Louisiana, three data points
imputed using the regression method ......................................................................................... 273
Figure D.8 The difference between the imputed and measured data in percent of the measured
data versus cells 1, 2, 3, 5, and 14 at MnROAD, three data points imputed using the regression
method......................................................................................................................................... 273
Figure D.9 The difference between the imputed and measured data in percent of the measured
data versus the BMP along SRID 099 in Washington, three data points imputed using the
regression method ....................................................................................................................... 274
Figure D.10 The difference between the RSL values based on imputed and measured data versus
the BMP along LA 21 (CS 0.02902) in Louisiana, three data points imputed using the regression
method......................................................................................................................................... 274
Figure D.11 The difference between the RSL values based on imputed and measured data versus
the cell number at MnROAD, three data points imputed using the regression method ............. 275
Figure D.12 The difference between the RSL values based on imputed and measured data versus
the BMP along SRID 099 in Washington, three data points imputed using the regression method
..................................................................................................................................................... 275
Figure D.13 The difference between the imputed and measured data in percent of the measured
data versus the BMP along LA 21 (control section 0.02902) in Louisiana, three data points
imputed using the moving regression method ............................................................................ 276
Figure D.14 The difference between the imputed and measured data in percent of the measured
data versus cells 1, 2, 3, 5, and 14 at MnROAD, three data points imputed using the moving
regression method ....................................................................................................................... 276
Figure D.15 The difference between the imputed and measured data in percent of the measured
data versus the BMP along SRID 099 in Washington, three data points imputed using the moving
regression method ....................................................................................................................... 277
Figure D.16 The difference between the RSL values based on imputed and measured data versus
the BMP along LA 21 (CS 0.02902) in Louisiana, three data points imputed using the moving
regression method ....................................................................................................................... 277
Figure D.17 The difference between the RSL values based on imputed and measured data versus
the cell number at MnROAD, three data points imputed using the moving regression method 278
Figure D.18 The difference between the RSL values based on imputed and measured data versus
the BMP along SRID 099 in Washington, three data points imputed using the moving regression
method......................................................................................................................................... 278

xix

Figure D.19 The difference between the imputed and measured data in percent of the measured
data versus the BMP along LA 21 (control section 0.02902) in Louisiana, three data points
imputed using the multiple regressions method.......................................................................... 279
Figure D.20 The difference between the imputed and measured data in percent of the measured
data versus cells 1, 2, 3, 5, and 14 at MnROAD, three data points imputed using the multiple
regressions method...................................................................................................................... 279
Figure D.21 The difference between the imputed and measured data in percent of the measured
data versus the BMP along SRID 099 in Washington, three data points imputed using the
multiple regressions method ....................................................................................................... 280
Figure D.22 The difference between the RSL values based on imputed and measured data versus
the BMP along LA 21 (CS 0.02902) in Louisiana, three data points imputed using the multiple
regressions method...................................................................................................................... 280
Figure D.23 The difference between the RSL values based on imputed and measured data versus
the cell number at MnROAD, three data points imputed using the multiple regressions method
..................................................................................................................................................... 281
Figure D.24 The difference between the RSL values based on imputed and measured data versus
the BMP along SRID 099 in Washington, three data points imputed using the multiple
regressions method...................................................................................................................... 281
Figure D.25 Maximum, minimum, and average percent difference between imputed and
measured data at BMPs 3, 4, 5, 6, and 7 along LA 21 (CS 0.02902) in Louisiana, using four
imputation methods..................................................................................................................... 282
Figure D.26 Maximum, minimum, and average percent difference between imputed and
measured data at cells 1, 2, 3, 5, and 14 at MnROAD, using four imputation methods............. 282
Figure D.27 Maximum, minimum, and average percent difference between imputed and
measured data at BMPs 10.5, 10.6, 11.2, 11.6, and 11.7 along SRID 099 in Washington, using
four imputation methods ............................................................................................................. 283
Figure D.28 Maximum, minimum, and average difference between RSL values based on
imputed and measured data at BMPs 3, 4, 5, 6, and 7 along LA 21 (CS 0.02902) in Louisiana,
using four imputation methods ................................................................................................... 283
Figure D.29 Maximum, minimum, and average difference between RSL values based on
imputed and measured data at cells 1, 2, 3, 5, and 14 at MnROAD, using four imputation
methods ....................................................................................................................................... 284
Figure D.30 Maximum, minimum, and average difference between RSL values based on
imputed and measured data at BMPs 10.5, 10.6, 11.2, 11.6, and 11.7 along SRID 099 in
Washington, using four imputation methods .............................................................................. 284

xx

CHAPTER 1
INTRODUCTION & RESEARCH PLAN
1.1

Introduction
The highway systems in the United States and most industrialized nations are considered

to be the largest investments ever made in the history of these nations (Baladi et al. 1992). The
investments are on-going as the highway systems deteriorate and cannot be made to last forever.
A constant flow of money is required on an annual basis to properly and continually maintain,
rehabilitate, and reconstruct the existing highway systems and expand them in areas of growth.
Given the complexity of the highway systems, the size of the required annual investment, and the
state of the economy, the management of the highway systems presents major and complex
problems that challenge highway administrators. The problems could be solved and the
challenge could be met through the design and implementation of an effective, accurate,
comprehensive, and integrated pavement management system (PMS).
The most critical parts of a PMS are considered to be the collection, storage, and analysis
of the pavement performance data (Smith et al. 1998). Each of these parts is briefly described
below:
1.

Data collection - Nearly all State Highway Agencies (SHAs) collect pavement
performance data at 1-, 2-, or 3-year frequency. Some SHAs such as the Washington
State Department of Transportation (WSDOT) survey the pavement network each year.
Others survey half the pavement network each year and still others survey one third of
the pavement network each year. Regardless of the data collection frequency, most
agencies use semi- or fully-automated means of data collection along the outer traffic
(driving) lane (McGhee 2004). Further, some SHAs use sampling techniques where the

1

pavement performance data are collected along a short pavement segment (such as 100,
200, 300 feet, 0.1 mile, etc.) of each one mile and the data are assumed to represent the
pavement conditions along the entire mile (Zimmerman 1995). Given the current
financial situation of most SHAs and in order to reduce data collection costs, many
administrators are under tremendous pressure to sample the pavement performance data.
Unfortunately, the effects of the pavement performance data sampling on the accuracy of
the PMS decisions are not well known. Such effects should be studied in detail before a
decision to sample is made.
2.

Data storage – The data storage practices vary greatly from one SHA to another. Some
SHAs survey and store the pavement performance data for each 0.1 mile pavement
segment along the network while others use greater lengths. For those SHAs that use
sampling, the decision to store the data along different lengths is dictated by the sampling
technique. For instance, if the conditions along a short pavement segment (i.e. 0.1 mile)
are assumed to represent the conditions along 1 mile, then the storage length is also 1
mile. Alternatively, if the conditions along a short pavement segment (i.e. 250 feet) are
assumed to represent the conditions along 0.5 mile, then the storage length is also 0.5
mile. It was thought that, for performance data stored along short pavement segments, the
variability of the pavement condition data from one year to the next makes the analysis of
pavement performance data a difficult task. To reduce data variability and improve data
analysis, some advocate data storage and analysis over greater lengths such as half or one
mile. Longer analysis lengths may not improve the data analysis and may disadvantage or
jeopardize the accuracy of the PMS decisions. Hence, in this research, the impacts, if any,

2

of data analysis lengths on the accuracy of the data analysis results and on the PMS
decisions are assessed and discussed.
3.

Data analysis - For certain data collection cycles, some data elements of some pavement
segments along the network could be missing for various reasons. These include skipping
one data collection cycle for certain pavement sections, equipment malfunctioning,
failure to properly record the data, loss of data due to human error, delays in issuing the
data collection/storage contract, construction zones and so forth. This poses a serious
issue because, typically, at least three data points are required in order to properly model
pavement performance data. Because some data could be missing and less than three data
points may be available, the question may arise of how to analyze the incomplete data
sets. This question could be answered by evaluating how to impute the missing data so
that analysis of the time-series performance data could be improved leading to better and
more accurate PMS decisions (Bennett 2004, Flintsch and McGhee 2009, Zhang and
Smadi 2009). Thus, a study is necessary to evaluate the effects of various data
imputation techniques on the accuracy of the pavement performance data.
Given the SHAs practice regarding data collection, storage, and analysis the goal of this

research study is to evaluate the impacts of pavement condition data collection practices and data
analysis techniques on the accuracy of the PMS decisions.
1.2

Problem Statement and Research Plan
The long-term economic climate has caused some highway administrators to consider

pavement performance data sampling as an alternative to reduce data collection costs. However
the effects of data sampling on the accuracy of the PMS decisions are not well documented. It is
not clear that data sampling ultimately reduces the overall PMS costs. Furthermore, for those

3

SHAs that sample the pavement performance data, the pavement lengths for which the
performance data are stored and analyzed are dictated by the sampling techniques used as stated
in item 2 in the previous section. Longer analysis lengths may not improve the data analysis
results and may artificially decrease the data variability. Thus, the impact of the pavement
analysis length on the variability of the pavement performance data and, ultimately, on the
accuracy of the PMS decisions should be evaluated before a data analysis length is selected.
Finally, for various reasons, data from some data collection cycles along certain pavement
segments may not be documented or are missing, which makes it difficult or impossible to model
and analyze the data. In order to solve this problem, the effects of different data imputation
techniques on the accuracy of the pavement performance data should be evaluated. Accordingly,
a comprehensive research plan was designed to address the three problems through the analyses
of the impacts of data sampling, data analysis length, and data imputation on the accuracy of the
pavement performance data and the PMS decisions.
The research plan consists of the three tasks stated below.
Task 1: Use continuously collected pavement performance data to simulate sampling and study
the effects of sampling on the accuracy of PMS decisions.
Task 2: Use the measured and stored PMS data along each 0.1 mile pavement segment to
calculate the average or cumulative data along longer segments and hence to analyze the
impact of data analysis lengths on the accuracy of PMS decisions.
Task 3: Scrutinize the various data imputation methods to determine whether or not these
methods can be used to impute pavement performance data with little to no impacts on
the accuracy of the pavement performance data and PMS decisions

4

1.3

Objectives
The objectives of this research study are to:

1.

Assess the impacts of pavement performance data sampling on the accuracy of PMS
decisions and quantify the hidden costs of data sampling.

2.

Analyze the effects of data analysis length on the variability of the pavement condition
data and on the accuracy of the PMS decisions.

3.

Study the impacts of various data imputation methodologies on the variability and
accuracy of the pavement condition data and the corresponding PMS decisions.

1.4

Thesis Layout
This thesis consists of five chapters, four appendices, and references as listed below.

Chapter 1 – Introduction & Research Plan
Chapter 2 – Literature Review
Chapter 3 – Data Mining
Chapter 4 – Data Analyses & Discussion
Chapter 5 – Summary, Conclusions, & Recommendations
Appendix A – PMS Data
Appendix B – Pavement Performance Data Sampling Figures
Appendix C – Pavement Analysis Length Figures
Appendix D – Pavement Performance Data Imputation Figures
References

5

CHAPTER 2
LITERATURE REVIEW
2.1

Introduction to Pavement Management
The cost-effective construction, maintenance, rehabilitation, and preservation of

pavements in road systems involve complex decisions to keep the systems performing at
reasonable levels. In the past, these decisions have been left to road supervisors who relied on
their extensive knowledge and experience (FHWA 2011). Since the early 1980s however,
highway administrators and engineers have recognized the need to use a pavement management
system (PMS) to aid in the decision-making process (Zimmerman and Peshkin 2004).
A PMS can be described as a “coordinated set of activities directed toward achieving the
best value possible for the available public funds in providing and operating smooth, safe, and
economical pavements” (Hudson et al. 1979). Although each PMS has its own level of
complexity depending on the geographical, financial, and political conditions in which it
operates, most systems include five key components (Peterson 1987):
1.

Pavement surveys related to condition and serviceability.

2.

Database containing all pavement related information.

3.

Analysis scheme.

4.

Decision criteria.

5.

Implementation procedures.
The FHWA databank indicates that each of the 50 states, the District of Columbia, and

Puerto Rico have some kind of PMS. Forty-two states report that their systems include a method
of prioritization and 20 states include an optimization provision for purposes of budget planning
and project programming (Finn 1998). Thus, it is clear that most states recognize the importance

6

of a PMS; however the degree to which the different components of a PMS are utilized by the
various highway agencies varies significantly.
2.1.1 The Need to Manage Pavements
The FHWA estimates that the roadway systems in the United States consist of
approximately 8,500,000 lane-miles (WSDOT 2010). Furthermore, the systems are considered to
be the single largest investment ever made in the history of industrialized nations (Baladi et al.
1992). This investment is on-going as the highway system deteriorates and cannot be made to
last forever. A constant flow of money is required to properly and continually maintain,
rehabilitate, reconstruct, and preserve the existing pavements while designing and constructing
new pavements in areas of growth. Given the lack of appropriate funding and the size of the
required investment, management of the pavements present a major and complex puzzle that
challenges highway administrators and engineers. Only a high quality and comprehensive PMS
can satisfy the need to manage pavements and direct the investment where needed to make
proper decisions at the proper time (Baladi et al. 1992).
2.1.2 Pavement Management versus Managing Pavement
Managing pavement consists of the various acts of planning, designing, constructing,
maintaining, evaluating, rehabilitating, and preserving the pavements. On the other hand, pavement
management is the coordination of all the activities involved in the planning, financing, designing,
constructing, maintaining, evaluating, and rehabilitating the pavement portion of a public works
program. In other words, pavement management is essentially the comprehensive directing of the
various actions involved in managing pavements. Further, the establishment of documented
procedures regarding the comprehensive coordination of all the pavement management activities is
referred to as a PMS (Dawson 2012).
7

2.1.3 Acts of Managing Pavements
In 1903, the creation of the Office of Road Inquiry of the Department of Agriculture
marked the beginning of the Federal Government’s involvement in highway activities on a
continuing basis. In 1918, the office became the Bureau of Public Roads (BPR) of the
Department of Agriculture. The Great Depression and President Roosevelt’s “New Deal” pushed
for the creation of massive public works projects; one focus was the creation of highways across the
entire nation. Under the reorganization of the Federal Government of 1939, the BPR became the
Public Roads Administration (PRA), which was then transferred to the Federal Works Agency.
Another reorganization of the government in 1949 renamed the PRA to become the BPR again
and transferred the bureau to the Department of Commerce. In 1967, the BPR was again
transferred to the newly formed Department of Transportation. Finally, in 1970 the BPR was
again renamed to its present designation, the Federal Highway Administration (FHWA) (Baladi
et al. 1992, Dawson 2012, Nostrand 1992).
The Federal-Aid Highway Act of 1916 marked the beginning of the modern era of
Federal-aid for highway activities by authorizing the expenditure of $75 million for rural
highway improvements. The enactment of the gasoline tax by various states in 1919 helped
states secure matching funds for highway activities. In 1934, Congress authorized the
expenditure by the states of up to 1.5 percent of the Federal-aid funds for highway planning and
surveying. After World War II, the involvement of the government in the construction and
improvement of the highway system increased substantially. The 1944 act provided
approximately $500 million per year for 3 years, dedicated to the improvement of the highway
system. In 1952, an act directed the Secretary of Commerce to study highway financing and
assess the condition of the highway system. As a result, in 1955, the Clay Committee (Advisory

8

Committee to President Eisenhower on a National Highway Program) reported the need for
modernization of the highway system (Baladi et al. 1992).
The Clay Committee’s report spurred the development of one of the most important acts
in U.S. transportation history; the Federal-Aid Highway Act of 1956. In this act, proceeds from
highway-user taxes were earmarked and placed into a newly created special trust fund, referred
to as the “Highway Trust Fund.” The 1956 act authorized the design and construction of the
approximately 41,000-mile National Interstate and Defense Highway System to be completed
within a period of 15 years and made funds available to the states on a 90-10 matching basis (Baladi
et al. 1992, Dawson 2012).
One downfall of the Federal-Aid Highway Act of 1956 is that it did not include matching
funds for the maintenance and rehabilitation of the highway systems. Therefore, the Federal-Aid
Highway Act of 1976 introduced the 3R program; resurfacing, restoration, and rehabilitation.
The program was financed using federal highway funds. Eventually, in 1981, congress added the
fourth ‘R’ to the program; reconstruction. Finally, on May 21, 1980, the FHWA issued a Federal
Highway Program Manual addition titled ‘pavement management’ that encouraged all states to
strengthen their system of selecting pavement projects by developing a PMS (Nostrand 1992).
By the end of the 1980s more than half of the states were developing or implementing a
PMS. In 1989, the FHWA issued a policy requiring all states to have a PMS that would cover
principal arterials under the states’ jurisdiction. The scope of federal and state involvement in
PMS expanded when Congress passed the Intermodal Surface Transportation Efficiency Act
(ISTEA) of 1991. This act required that all states have a PMS that covers all Federal-Aid
highways. In December 1993, the FHWA issued a regulation regarding all management

9

systems. Section 500.207 contains the required components of a PMS for all Federal-Aid
highways: data collection, data analyses, and update (Botelho 1994).
2.1.4 Network-Level Pavement Management
The pavement management process has two basic working levels, network and project
levels. Each of these levels results in different sets of decisions through different levels of
analysis of the collected data using a shared database. At the network-level, the primary goal of a
PMS is to assess the overall condition of the pavement network and produce a prioritized work
plan by examining various time and budget constraint scenarios. The products of network-level
evaluation and analysis include:
1.

Documenting the distribution of the pavement conditions along the network.

2.

Assessing the impact of budget levels on the health of the pavement network.

3.

Generating a pavement fix (reconstruction, rehabilitation and preservation) strategy to
maximize the longevity of the pavement network and minimize costs. Such strategy
identifies candidate pavement projects or sections based on pavement condition levels or
brackets and it does not include the specific locations of the projects.

4.

The main disadvantage of network-level pavement management is that the design models
are simple and do not adequately consider the detailed factors that are required for
project- level analysis (ASTM 2000, Fwa 2006, Reigle 2000).

2.1.5 Project-Level Pavement Management
At the project level, detailed consideration is given to alternative design, construction,
maintenance, or rehabilitation activities for particular roadway sections or projects. In essence, a
project-level approach utilizes data for individual pavement sections to determine the optimum
maintenance and rehabilitation strategies for priority projects. Project-level pavement
10

management models are typically complex, dealing with technical concerns and requiring
detailed information such as pavement structural thicknesses, time-series distress and roughness
data, as well as deflection data among many other things. Thus, project-level pavement
management requires specific detailed information so that cost-effective decisions can be made
regarding pavement treatment alternatives (AASHTO 1993, Pavement Interactive 2008, Reigle
2000).
Nevertheless, the products of project-level analysis and evaluation include:
1.

The selection of candidate pavement projects and their boundaries.

2.

The selection of treatment types and time.

3.

Alternative treatment designs and their associated costs.

4.

The estimation of the needed future treatments and their associated costs (results of life
cycle cost analysis)

2.1.6 Commonalities and Differences Between Network and Project-Level Pavement
Management
Network and project-level pavement management differ in regards to the required
amount of details. For instance, network-level management requires generalized models to assess
the overall condition of the pavement network while project-level management requires specific
distress and condition models to assess the exact condition of one pavement project. The
management systems for the network and project-levels are mutually dependant, though. One of
the many functions of the network-level PMS is to identify pavement sections within a network
of pavements that require immediate maintenance or rehabilitation actions. In turn, project-level
management may be responsible to determine the optimum pavement treatment time and types
for each specific pavement section identified at the network-level. Thus, detailed data are used at

11

the project-level to develop specific pavement treatment designs for pavement sections that were
identified or ‘flagged’ at the network-level. Hence, it can be stated that network-level pavement
management provides an overall ‘picture’ of the pavement network while project-level
management helps paint a detailed ‘picture’ of specific pavement sections. The two, though,
share the same data system and are mutually dependant (Reigle 2000). Figure 2.1 displays the
general functions of the two different management levels while linking them both to the same
data system.

Figure 2.1 Network and project-levels pavement management (AASHTO 1993, Hudson et al.
1979)
It is the opinion of this author that the terms network- and project-level pavement
management are confusing and do not express the true nature of PMS. The two terms should
read data analysis at the network and project levels. To illustrate, assume that a State Highway
Agency (SHA) collects and stores pavement data along each 0.1 mile pavement segment. The
12

data could be analyzed at the project-level to determine the pavement rate of deterioration, the
pavement remaining service life (RSL) and so forth. Results of the analysis at the project-level
could be summarized to study the distribution of the pavement conditions along the network.
Such distribution could be used for planning, programming and budgeting analysis. This scenario
would generate compatible and consistent network and project level analysis based on the same
basic pavement data.
2.2

Data Elements and Data Collection Procedures
The collection and storage of pavement management data are the most costly parts of the

implementation of a pavement management system (PMS) and are typically the most expensive
parts of keeping a PMS operating. The various data elements of a successful PMS can be
collected using costly or inexpensive methods. The resolution, accuracy, and detail of the
collected data are highly dependent on the selected collection method (Smith et al. 1998). In
recent years, the adoption of methods and technologies associated with improved pavement
management data collection and analysis have improved the function of most PMSs (McGhee
2004).
Pavement condition surveys and related data collection are considered to be key
components for any successful PMS (WSDOT 2012, Peterson 1987). The pavement condition
surveys and related data collection include inventory data and condition/distress data. In general,
inventory data describe the physical characteristics of the pavement and usually do not change
with the time between rehabilitation and significant maintenance activities. The inventory data
can be divided into four categories (Baladi et al. 1992):
1.

As-built data including pavement type (flexible, rigid, composite), width of highway and
shoulder, number of lanes, thickness of each pavement layer, type of asphalt or concrete

13

mix design, joint spacing, type of dowel and tie bars, temperature steel if any, drainage
type (cross drain, edge drain, drainable layers, etc.), quality control and quality assurance
data, incentive payments, if any, and so forth.
2.

Historical data including years of last major activity (rehabilitation, construction,
widening, etc.), materials used in last major activity, type of last improvements, type of
rehabilitation/maintenance projects and their associated costs, etc..

3.

Environmental data including detailed past climatologically-collected data, which could
be obtained from the local office of the National Oceanic and Atmospheric
Administration (NOAA).

4.

Other data including specialized data requiring substantial details including material test
type, material test method, material test procedure, and equipment.

Detailed inventory data are listed in Table 2.1.
In addition to inventory data, a comprehensive PMS database should also include
monitoring data. It is desirable for the monitoring data to include (Baladi et al. 1992):
1.

Pavement distress and roughness.

2.

Surface friction.

3.

Drainage conditions.

4.

Deflection measurements.

5.

Traffic and load information.

Detailed monitoring data are also listed in Table 2.1. Note that data elements presented in Table
2.1 represent the visions of the author as well as the visions of many staff of various SHAs.
Therefore, data in the table must be reviewed on a continuous basis and modified when the need
arises.

14

Table 2.1 Pavement inventory and monitoring data
Data items
Inventory data
 Reference location
 Pavement type
 As constructed asphalt concrete layer
o Layer thickness
o Material properties
o Asphalt mix data
o Number and thicknesses of AC
courses
o QC and QA data
o Cost per ton
o Deviation from design

Example uses of data
 Locate pavement segments and link
various data files
 Deterioration models
 Backcalculation of layer moduli and
deterioration models
 Deterioration models and quality control
 Deterioration models and quality control
 Deterioration models and quality control
 Deterioration models
 Life cycle cost
 Link pavement design to management



As constructed PCC layer
o Layer thickness
o Concrete properties
o Concrete mix data
o Joint spacing
o Dowel and tie bars
o QC and QA data
o Cost per ton
o Deviation from design

 Backcalculation of layer moduli and
deterioration models
 Deterioration models and quality control
 Deterioration models and quality control
 Deterioration models
 Deterioration models
 Deterioration models
 Life cycle cost
 Link pavement design to management



Base layer
o Layer thickness
o Material properties
o QC and QA data
o Cost per ton
o Deviation from design

 Backcalculation of layer moduli and
deterioration models
 Deterioration models and quality control
 Deterioration models and quality control
 Life cycle cost
 Link pavement design to management



Subbase layer
o Layer thickness
o Material properties
o QC and QA data
o Cost per ton
o Deviation from design



Roadbed soil
o Soil classification
o Roadbed modulus
o Hydraulic conductivity
o Cost of rolling per lane-mile

 Backcalculation of layer moduli and
deterioration models
 Deterioration models and quality control
 Deterioration models and quality control
 Life cycle cost
 Link pavement design to management
 Backcalculation of layer moduli and
deterioration models
 Deterioration models and quality control
 Deterioration models and quality control
 Life cycle cost

15

Table 2.1 (cont’d)
Data items
Inventory data (continued)
 Traffic
o ADT
o Mixed traffic volume and weight
o ESAL




Example uses of data
 Capacity, safety and planning
 Traffic spectrum for design purposes
using the M-EPDG
 1993 AASHTO Design Guide and
deterioration models

Environment
o Daily low and high temperatures
o Rain fall
o Snow fall
o Depth of frost penetration
Drainage type
o Location
o Drainage type
o Outlets
o Discharge

Cracking data
 Alligator (bottom up)


Alligator (top-down)



Block



Blow-up



Corner break



Durability “D”



Longitudinal



Mat



Reactive aggregate



Reflective



Slippage



Transverse






Causes of pavement distresses
Causes of pavement distresses
Causes of pavement distresses
Causes of pavement distresses and
deterioration models






Rehabilitation and maintenance
Performance of drainage
Maintenance
Drainage quality

6.

 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action

16

selection of
selection of
selection of
selection of
selection of
selection of
selection of
selection of
selection of
selection of
selection of
selection of

Table 2.1 (cont’d)
Data items
Joint data
 Construction joint in AC pavements


Transverse joints in PCC pavements



Longitudinal joints in PCC pavements



Joint spalling

Other condition data
 Asphalt hardening/oxidation
 Bleeding
 Corrugation
 Depression
 Lane/shoulder drop off or heave
 Lane/shoulder separation
 Patching
 Polished aggregate
 Potholes
 Pumping
 Raveling
 Scaling
 Spalling
 Segregation
 Swell
 Weathering/stripping

Rehabilitation actions
 Type
 Materials
 Year of inception
 Year of construction
 Expected/design life
 Location reference
 Cost

Example uses of data
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action
 Performance models, RSL, and
rehabilitation action

selection of
selection of
selection of
selection of

 Performance models and selection of
rehabilitation action
 Safety problem
 Performance models and selection of
rehabilitation action
 Performance models and selection of
rehabilitation action
 Safety problem
 Safety problem
 Performance models and selection of
rehabilitation action
 Safety problem
 Safety and ride problem, effects of freezethaw cycles
 Voids under slab, select the proper action
 Safety and ride quality issues
 Concrete mix and construction problems
 Deterioration rates
 Causes of cracks and potholes
 Lower layer problems, selection of proper
action
 Presence of water under the asphalt mat
 Determine its service life and performance
 Deterioration models
 Determine the pavement conditions at
inception
 Determine the pavement prior and after
construction
 Identify the proper pavement project
 Life cycle cost

17

Table 2.1 (cont’d)
Data items
Pavement preservation actions
 Type
 Materials
 Year of inception
 Year of construction
 Expected/design life
 Location reference
 Cost

Pavement maintenance actions
 Type
 Materials
 Year of application
 Expected/design life, when applicable
 Location reference
 Cost

Other data
 Date of data collection
 Air and/or pavement temperature
 Reference location*
 Accident type, date and location
 Material specifications
 Special pavement project provisions

Example uses of data
 Determine its service life and performance
 Deterioration models
 Determine the pavement conditions at
inception
 Determine the pavement prior and after
construction
 Link performance to design
 Identify the proper pavement
project/segment
 Life cycle cost
 Determine its service life and performance
 Deterioration models
 Determine the effects on the pavement
conditions
 Link performance to design
 Identify the proper pavement
project/segment
 Life cycle cost





Safety versus pavement conditions
Impact of specifications on performance
Track the propagation of distress
Effects of the provisions on pavement
performance
 Seasonal impacts on the data
 Effects of temperature on crack opening
* It is desirable to include reference location for the beginning and ending of each condition
along the pavement structure. Such data are essential to study the propagation of cracks and
their transformation from low to medium and to high severity levels. Most semi-automated
equipment that are equipped to videotape the pavement surface or to measure the longitudinal
and transverse profiles are equipped with a GPS unit and are capable of recording positions
every 6-inches along the pavement.

18

The methods used by SHAs to collect pavement condition data vary from manual (windshield survey), to semi-automated (videotaping and digitizing the data by reviewing the
videotapes), and to automated (computer identification/recognition of the images of the
pavement distress). Typically, the manual distress survey is conducted in different ways as stated
below (Baladi et al. 2009, FHWA 1995).
1.

Walking survey of 100 percent of the pavement surface in which all distress types,
severities, and quantities are measured and recorded. Some map the distress whereas
others do not.

2.

Walking survey of samples of the pavement surface in which all distress types, severities,
and quantities within the sampled areas are measured or estimated and recorded.

3.

Driving survey in which distress types, severities, and quantities are estimated while
driving on the shoulder at creep speed. Periodic shoulder stops are made at selected areas
to measure the distress and check the estimates.

4.

Driving survey in which some distress types, severities, and quantities are estimated
while driving at the posted speed limit. Periodic shoulder stops are made to verify the
estimates.

5.

Driving survey during which the pavement is assigned a general categorical description
(excellent, very good, good, fair, poor, or very poor) or sufficiency rating number without
identifying individual distress types and their severities and extents. The survey is done at
the posted speed limit.
In general, the results of the manual distress surveys can be questionable due to the

impact of human subjectivity. Many aspects of the data collection process (such as time of day,
training, experience, fatigue, weather, and supervision of the raters) affect the results. For this

19

reason, the state-of-the-practice in data collection has shifted towards semi- and fully-automated
techniques (FHWA 1995, Freeman and Ragsdale 2003, Smith and Change-Albitres 2007). The
semi-automated data collection technique consists of obtaining analog distress images on film or
high resolution video. Sometime later, trained observers view the images and identify and
digitize the type, severity, and extent or quantity of each individual distress (FHWA 1995). In the
fully-automated technique, images are collected on film or high resolution video and image
analyzers identify and digitize the type, severity, and extent or quantity of each individual
distress in real-time or at a later time in the office (Freeman and Ragsdale 2003).
In the past few years, the National Center for Pavement Perseveration (NCPP) conducted
a survey of 43 SHAs in order to assess their PMS practices, including data collection practices.
The results of the survey indicated that, as expected, data collection methods vary from manual,
to semi-automated, and to automated. This can be seen in Figure 2.2. Approximately 35 percent
of the SHAs surveyed utilize automated data collection means while 42 percent use both
automated and wind shield (manual) collection techniques (Dawson 2012, Galehouse 2010).
In an effort to improve the reliability of the collected pavement condition data, there has
been a recent move for all SHAs to utilize fully automated data collection techniques. In this
manner, as it was mentioned previously, an imaging system for cracking survey would be fully
automated and the data digitized in real-time. In addition, laser sensors are used to measure to
measure the pavement longitudinal and transverse profiles and to calculate the pavement rut
depths and roughness such as the International Roughness Index (IRI) (Wang and Gong 2002).
Data image processing techniques are used to identify and analyze the distress type, severity, and
quantity. An example of this is shown below in Figure 2.3.

20

14%

Automated

35%

Wind Shield
Automated &
Windshield
None

42%

9%

43 SHAs

Figure 2.2 Percent of SHAs using the stated method of pavement condition data collection

2,048 pixels (transversely), about 3 meters wide

Figure 2.3 Area scan image for fully-automated data collection (McGhee 2004)

21

A significant advantage of the fully-automated technique is that it removes the subjective
distress identification and rating from the various pavement management personnel. Thus, one
would expect the data to be more reliable and consistent than manual and semi-automated
condition data. However, although a fully-automated technique is optimal for PMS data
collection, significant improvement needs to occur such that crack recognition becomes more
reliable. Currently, ‘tight’ cracks may be missed due to minimal crack width. Further, especially
in rigid pavements, it is possible that more distress will be recorded than is actually exists due to
the presence of the sawn joints (Wang and Smadi 2011). Thus, fully-automated data collection
and distress identification is the optimal procedure for SHAs but significant gains in technology
need to be made before this can be fully-implemented with confidence.
2.3

Data Collection Frequency
The goals and objectives of a particular SHA dictate the type and details of the pavement

distress data to be collected, as well as the method and frequency of data collection. In general,
the frequency of pavement distress data collection can be divided into three categories (Haider et
al. 2007):
1.

Short frequency (1 to 2 years); the data are typically used to develop or calibrate
pavement performance models.

2.

Long frequency (3 to 4 years); the data are typically used for assessing the general
condition of the pavement network.

3.

Localized monitoring; the data are typically used to address unexpected pavement
performance.
In general, pavement conditions are monitored by most SHAs at 1-, 2-, or 3-year

frequencies (McGhee 2004). An NCPP survey of 43 SHAs found that approximately 63 percent

22

of the surveyed agencies use a PMS data collection frequency of 1 year whereas 28 percent of
the agencies collect data at a 2 year frequency as shown in Figure 2.4 (Galehouse 2010). It
should be noted that some SHAs collect sensor-based data (roughness and rut depth) more
frequently than image-based (cracking) data. However, it has been shown that, to make accurate
pavement decisions; image based condition data (cracking) should be collected every year and
sensor data could be collected less frequently (Haider et al. 2010).

2%
7%

0 Years

28%

1 Year
2 Years
3 Years

63%

43 SHAs

Figure 2.4 Percent of SHAs using the indicated PMS data collection frequency

23

2.4

Pavement Project Boundaries (Data Delineation)
When selecting pavement projects for treatments, especially those that are of great

significance, pavement monitoring activities are undertaken to obtain measurements which
assess various pavement response variables. These variables include pavement deflection,
serviceability, rut depth, and friction number among many others. In general, the measured
response variable indicates changes from one location to another with some points experiencing
changes of major magnitude. At the locations of significant changes in the response variable, the
overall performance of the pavement segments on either side of the locations will be noticeably
different. Hence, it is likely that the locations of these significant changes define the pavement
project boundaries. Figure 2.5 illustrates a typical plot of a response variable as a function of
distance along a highway segment. Four moderate to significant changes in the response variable
can be seen at certain locations. Hence, four separate pavement treatments may be warranted
(i.e., four separate overlay design thicknesses) (AASHTO 1993).

Pavement response variable

Unit 3

Unit 4

Unit 1
Unit 2

Distance along the pavement
Figure 2.5 A typical pavement response variable versus distance for data delineation (after
AASHTO 1993)

24

Two data delineation methods exist to help SHA employees identify the locations of
significant changes in the response vehicle and hence, locate the pavement project boundaries.
These methods (sometimes referred to as methods of unit delineation) are called the Idealized
Approach and the Measured Pavement Response Approach.
For the Idealized Approach, the engineer should isolate each unique factor influencing
potential pavement performance. These factors include:
1.

Pavement type.

2.

Construction history (including rehabilitation and major maintenance).

3.

Pavement cross section (layer material type/thickness).

4.

Subgrade (foundation).

5.

Traffic.

6.

Pavement Condition.

Under ideal circumstances, the historic pavement database is used to evaluate these factors. The
analysis units, or the project boundaries, are determined by a unique combination of each of the
pavement performance factors. An example of such method is shown in Figure 2.6. If accurate
records have been kept, this idealized approach based on historical data has more merit in
delineating the data than a procedure which relies on performance indicators. This is because
changes in one or more design factors (which indicate points of delineation) are not always
evident through observation (AASHTO 1993).

25

Figure 2.6 The Idealized Approach for data delineation (AASHTO 1993)
The Measured Pavement Response Approach is a favored alternative to the Idealized
Approach because one may not be able to accurately determine the practical extent of the factors
influencing pavement performance described previously and must rely upon the analysis of a
measured pavement response variable (i.e. deflection) for unit delineation. The SHA engineer
should first develop a plot of the measured pavement response variable as a function of the
distance along the project, as shown in Figure 2.5. Once the plot of a pavement response variable
has been completed, it could be used to delineate the data using several techniques. The simplest
of these techniques is visual examination to determine where relatively unique similarity
between data points occurs.

26

In addition, several analytical techniques are available for data delineation; the AASHTO
1993 recommended technique is the cumulative difference, which is readily programmable in
computers. This method was used in this study and it is detailed in Chapter 4 of this thesis. The
cumulative difference method removes the subjectivity of data delineation through mathematical
analysis. Nonetheless, other data delineation methods that exist include grouping pavement
segments with similar conditions and/or rates of deterioration, and selecting boundaries based on
a visual inspection without quantifying the conditions of the pavement section.
2.5

Pavement Performance Data Sampling
In recent years, administrators of various SHAs have been asked to reduce the costs of

pavement distress data collection and decrease the time period between data collection and data
digitization. It is thought by many that the reduction in costs and time could be easily
accomplished by sampling the pavement distress data. For some SHAs, the term “sampling”
implies continuously videotaping the pavement surface conditions along the entire pavement
network and digitizing the data using a sampling technique. That is, digitize the data along a
short pavement segment (such as 100, 200, 300 feet, or 0.1 mile) of each one mile and assume
the digitized data represent the pavement conditions along the entire mile. For other SHAs,
“sampling” implies surveying short pavement segments (e.g., wind shield survey or walking
survey) and assigning the results to a longer pavement section. Regardless of the sampling
technique or method used, it is evident that sampling reduces the direct costs and time for data
digitization. However, the short- and long-term costs and benefits of sampling cannot be
determined unless the impacts of sampling on the accuracy of the pavement decision processes
are analyzed.

27

The collection and evaluation of the time series pavement condition data is an essential
part of the selection of cost-effective pavement preservation strategy and, in general,
substantially influence the entire pavement decision process (Cafisco et al. 2002). The pavement
condition data collection practice is typically limited by the available resources, practicality, and
other constraints within SHAs. The National Cooperative Highway Research Program (NCHRP)
synthesis of highway practice 222 states that some of the practical constraints can be attributed to
the size and variability of the conditions of the pavement network. The accuracy of the data is
limited by the frequency of the data collection and by the representation of the selected samples
(Zimmerman 1995). Sampling of pavement condition data requires less time and money than
continuous data collection. However, the question becomes could sampling deliver accurate
pavement condition prediction without excessive amounts of data (Robertson et al. 2004)? In the
NCHRP 2004 synthesis of highway practice 334, 42 states, the District of Columbia, 2 FHWA
offices, 10 Canadian provinces and territories, and Transport Canada (airfields) were surveyed
regarding pavement condition data collection (McGhee 2004). It was found that:
1.

Most agencies use an automated means for data collection along the entire outer traffic
lane every other year.

2.

For pavement cracking:
a)

Nine agencies survey 100% of the lane to be evaluated.

b)

Three agencies collect cracking data along samples of varying length.

c)

Five agencies sample 10% to 30% of the roadway using a random sampling
technique.

28

d)

Others reported that they videotape 100% of the survey lane but, for each one
mile, they digitize the data along 50 to 1,000 feet segments. The data along these
segments are assumed to represent the pavement condition along the entire mile.

3.

For pavement roughness:
a)

Many agencies collect the data along the entire surveying lane and they report the
data for each 0.1-mile interval.

b)

The Canadian provinces report the roughness data at 50-meter to 100-meter
intervals.

c)

In the District of Columbia, the reporting intervals are measured by one city
block.

d)

The State of Arizona uses a reporting interval of 1 mile.

In another report, the Ministère des Transports du Quebec reports the use of sampling of
a 30-meter pavement section for every 100-meter pavement segment (30 percent sampling)
(Tremblay et al. 2004). The above information indicates that the sampling and reporting intervals
vary greatly from one road agency to another, with the intent to properly assess the current
pavement condition and reduce the time and cost of the data collection.
2.6

Pavement Survey and Analysis Length
As it was stated in the previous section, the collection and analyses of pavement

condition data are essential steps to support decisions regarding the selection of cost-effective
pavement treatments (Cafisco et al. 2002). Some SHAs collect, store, and analyze pavement
condition data along 0.1 mile pavement survey or segment lengths while others use different
survey lengths. In reality, the pavement data collection practice is limited by resources,
practicality, and economical constraints within the SHAs. The NCHRP synthesis of highway

29

practice 334 indicates that data collection practices varies greatly from one highway agency to
another. For example, some collect, store, and analyze the data for each 0.1 mile pavement
segment while others use different lengths (McGhee 2004). As a result, the data storage needs
vary significantly. For example, a SHA that collects, stores, and analyzes pavement condition
data for each 0.1 mile pavement segment requires ten times the data storage capacity compared
to another agency that uses 1 mile intervals. The consequences of reporting the data using longer
pavement segments include the loss of detail of the pavement surface conditions along the road.
In more general terms, data that are collected, reported, and analyzed along longer pavement
segments may lack the necessary details to accurately understand the variability and distribution
of the pavement conditions along a given pavement section. In addition, the pavement survey or
analysis length restricts the determination of project boundaries and data delineation. To
illustrate, data stored along each 0.1 mile pavement segment would lead to project boundaries for
project length within 0.1 mile distance (e.g., 6.3, 7.1, or 1.5 miles). On the other hand, the project
boundaries based on data stored and analyzed along each 1 mile pavement segment are restricted
to whole mile numbers such as 6, 8, or 3 miles.
Furthermore, the variability of pavement condition data along short survey and analysis
lengths complicates the modeling of pavement conditions over time and the assessment of the
overall pavement performance. Recently, some engineers and highway administrators have
suggested that increasing the pavement survey and analysis lengths over which the conditions are
analyzed may decrease the data variability and simplify the modeling of pavement conditions
over time (Fillastre 2011). The thought behind this is that longer analysis lengths decrease data
variability and simplify the modeling of pavement condition leading to improved PMS decisions

30

and proper management of the pavement network. It is shown in Chapter 4 that the pavement
analysis length does not have any impact on the accuracy of the PMS decision or operation.
2.7

Data Imputation
Some SHAs collect the time-series pavement condition data on a bi-yearly basis and store

the data for each 0.1 mile pavement segment. For some 0.1 mile pavement segments along a
network, a data collection cycle for certain years may be skipped or some of the distress or
condition data are missing or not reported. Such scenarios are due to various reasons including
equipment malfunction, failure to properly record the data, loss of data due to human error,
delays in issuing the data collection contract, construction zones, outliers, and so forth. Hence,
for certain years, some time series data could be missing from the database. Some of the missing
data elements could be crucial to commence data analysis. As a result, some of the SHAs staff or
the PMS manager or engineers may impute the missing data element so that analysis of the timeseries condition data could be improved leading to better and more accurate PMS decisions
(Bennett 2004, Farhan and Fwa 2012, Flintsch and McGhee 2009, Zhang and Smadi 2009).
Data imputation is the practice of ‘filling in’ missing data with plausible values. Data
imputation is an attractive approach to analyzing incomplete data sets. When completed
properly, imputation solves the missing data problem. However, a naïve or unprincipled
imputation methods could create more problems than they solve by distorting estimates and
increasing the standard errors (Little and Rubin 1987). Currently, though, the principles of
statistical quality assurance in terms of imputation of missing data are well developed but their
application and performance to the imputation of pavement management data is unclear (Farhan
and Fwa 2012).

31

Before one can accurately impute the missing data, it is important to understand why the
data are missing. It was stated that missing data elements can informally be thought of as being
caused by some combination of random processes, processes which are measured, and processes
which are not measured (Graham et al. 2003, Wayman 2003). More specifically, the missing data
mechanisms can be placed in one of the following three categories (Little and Rubin 1987,
Wayman 2003):
1.

Missing completely at random (MCAR) – The MCAR data cases are no different than
non-missing cases, in terms of the analysis being performed. These cases can be thought
of as randomly missing from the data and the only real penalty in failing to account for
missing data is loss of statistical significance or power.

2.

Missing at random (MAR) – The MAR data depends on known values and is described
fully by variables observed in the data set. Thus, accounting for the values which ‘cause’
the missing data will produce unbiased results in the analysis.

3.

Missing not at random (MNAR) – The MNAR data can be missing in an unmeasured
fashion that is often termed ‘non-ignorable.’ The missing data depends on events or
items for which the person analyzing the data cannot quantify. Thus, this is the most
damaging mechanism for missing data.
Depending on the missing data mechanism, different data imputation techniques could be

used to estimate the values of the missing data. In general, all data imputation techniques can be
considered as either ‘single’ or ‘multiple’ imputation. For single imputation, a definite value is
substituted for a missing value based on an established procedure. After such substitution,
standard statistical methods for complete data analysis can be used on the entire data set. The
single imputation method is widely used because of its simplicity and efficiency. This method

32

does not require the user to have extensive statistical knowledge (Zhang et al. 2008). However, it
has been shown that single imputation can reduce the variance of the variable in question,
creating a bias in the data. Nonetheless, the most common single imputation techniques are
summarized below (Farhan and Fwa 2012, Little and Rubin 1987, and Zhang et al. 2008).
1.

Mean substitution – In this approach, the missing physical values are imputed using the
mean value of a data set over time. It has been shown that this approach adds no new
information since the overall mean will remain constant and the variance of the data set
will be decreased proportionally to the number of missing data. Furthermore, given that
pavement distress values increase over time, imputation by mean substitution would
result in considerable errors. Regardless, Equation 2.1 can be used for mean substitution.

1 n
x  *  xi
n

Equation 2.1

i 1

2.

Linear interpolation/extrapolation – The missing data are computed by interpolating
between, or extrapolating from the adjacent, available data points. Graphically, this
amounts to substituting missing data by connecting a straight line to the two adjacent data
points near the missing data. This method assumes a linear correlation in the data.
Equation 2.2 can be used for linear interpolation and extrapolation.

y2 
3.

( x2  x1 ) * ( y3  y1 )
 y1
( x3  x1 )

Equation 2.2

Regression substitution – The missing data are imputed using the proper regression line
based on available information. For example, missing IRI data could be imputed by
modeling the available data as a function of time using an exponential function, missing

33

rut depth data could be imputed by modeling the available data as a function of time
using a power function, and cracking based on a logistic or s-shaped curve.
Although single imputation is often preferred because it does not require significant
statistical knowledge and is relatively simple, the decrease in variance of the complete data set as
a result of the imputed values poses problems for some researchers and SHA employees. To
solve this problem, the multiple imputation method is recommended. Multiple imputations can
be accomplished using the following steps:
1.

Missing values for any variable are predicted using existing values from other variables.

2.

The predicted values are substituted for the missing values to complete the data set.

3.

This process is performed multiple times, producing multiple imputed data sets.

4.

Standard statistical analysis is carried out on each imputed data set, producing multiple
analysis results.

5.

Results of the statistical analyses are then combined to produce one overall analysis.
Essentially, the multiple imputation technique is used to produce plausible versions of the

substituted values, and thus, different plausible versions of how the data may appear in the
population. Averaging over these versions could result in more accurate conclusions (Wayman
2003). However multiple imputation techniques require significant statistical knowledge and can
be hard to implement.
In a research study published recently, Farhan and Fwa (2012) utilized a highway
pavement condition survey database consisting of 29 years of data to assess the performance of
various imputation approaches in estimating missing distress data. The distress data that were
analyzed include alligator, longitudinal, and transverse cracking as well as IRI and rut depth. To
assess each imputation method, data points were artificially removed from the pavement

34

performance database. Each triplet was intended to represent three consecutive time periods, or
data collection cycles. Hence, for each distress type, 12 of the available 29 data points were
removed from the database. Using four different imputation techniques (mean substitution, linear
interpolation, regression substitution, and multiple imputations), the imputed data were
compared to the measured data using mean percent absolute error. Few results of the study are
summarized in Figure 2.7. As it can be seen in the figure, the mean substitution method resulted
in the highest error, followed by the regression substitution method and the interpolation method.
The multiple imputation method proposed in the study yielded the smallest errors for all distress
types (Farhan and Fwa 2012). However, besides the rut depth data, the differences in the error
between multiple imputation and regression substitution or interpolation are not significant.
Given that multiple imputation requires substantial statistical background, it is the opinion of the
author of this thesis that regression substitution or interpolation would suffice.
2.8

Location Referencing Systems
One of the basic requirements of a successful PMS is to have an efficient pavement

condition data collection program to help facilitate accurate pavement management decisions
(Farhan and Fwa 2012). In fact, any recommendations or decisions regarding pavement
treatments must be based on the analysis of quantifiable data including the pavement condition
data (Holt and Gramling 1991). The procedure for which SHAs store the pavement condition
data has evolved over time, however one issue persists: the accuracy of the location reference
systems (Flintsch et al. 2004). The use of an accurate location reference system is essential for
pavement management engineers to evaluate the proper time-series pavement condition data and
to formulate correct and cost-effective pavement management decisions.

35

12

40

10

Mean absolute error (%)

Mean absolute error (%)

50

30
20
10
0
Mean
Interpolation Regression Multiple
substitution
substitution imputation
a) Transverse crack/mi (Lane 1)

Mean absolute error (%)

Mean absolute error (%)

50
40
30

20
10
0

Mean
Interpolation Regression Multiple
substitution
substitution imputation
c) Rut depth- right wheelpath (in)

8
6
4
2
0
Mean
Interpolation Regression Multiple
substitution
substitution imputation
b) Transverse crack/mi (Lane 2)

70
60
50
40
30
20
10
0

Mean
Interpolation Regression Multiple
substitution
substitution imputation
d) Average longitudinal cacking (ft)

Figure 2.7 Mean absolute error for four imputation methods (after Farhan and Fwa 2012)
36

A location referencing system is formally defined as “an automated system used to
manage the collection and storage of spatial information at exact locations” (Iowa DOT 1998).
The proper use of a location referencing system greatly impacts the utility of the pavement
condition data collected and stored in the PMS database (Deighton and Blake 1993). In general,
three types of location referencing systems exist and are used in the PMS databases:
1.

Linear location referencing system

2.

Global positioning system (GPS)

3.

Geographical information system (GIS)
It should be noted that a GIS is considered to be a relational database that includes the

location reference system while the linear location referencing and GPS are strictly location
referencing systems. Figure 2.8 displays the results of a survey of 46 SHAs regarding the types
of location referencing systems used to support pavement data collection and storage activities
(Flintsch et al. 2004). The data in the figure imply that some SHAs use duel or triple location
referencing systems.

Percent of agencies

100
80
60
40
20
0
Milepoints
Global
and mileposts Positioning
System
(GPS)

Linknodes

Others

National
Differential
GPS
(NDGPS)

Figure 2.8 Percent of SHAs utilizing stated location referencing systems (after Flintsch et al.
2004)

37

Indeed, traditionally, some SHAs reference the pavement condition data using various
linear location referencing techniques. These include link/node locations, reference points or
offsets, and most commonly route names and mileposts or milepoints. For the route name and
milepost referencing method, each roadway is identified using a unique name and the distance
along the route is specified from a particular origin. The distance units are either marked with
signs along the route to mark data collection points in the field (Flintsch et al. 2004) or not
marked and the distance from the origin is estimated using the car odometer. The main advantage
of a linear referencing system is that it is well-developed and understood by most of the agency
staff. One significant shortcoming is that mileposts lack accuracy and hence, the same point on
the pavement structure may move substantially from one data collection cycle to the next due to
various reasons including realignment, rehabilitation, or other pavement activities (Flintsch et al.
2004). This effectively changes the size and location of individual pavement sections and
negatively impacts the analysis of time-series condition data.
The second most common location referencing system used by SHAs is the GPS. The
GPS is ‘a satellite-based navigation system made up of a network of 24 satellites placed into
orbit by the U.S. Department of Defense. GPS satellites circle the earth twice a day in a very
precise orbit and transmit signal information to earth. The GPS receivers take this information
and use triangulation to calculate the user’s exact location’ (Garmin 2012). Thus, GPS holds a
significant advantage over linear referencing systems in that it is considered to be accurate to
within approximately 50 feet (Garmin 2012). Furthermore, the use of GPS as a location
reference system allows for more automation and less user input in the field. The differential cost
to outfit pavement management users with GPS units is affordable and data collection with GPS
will result in time and costs savings as well as more accurate data (McNerney and Rioux 2000).

38

The fact that GPS technology is a relatively new component of a PMS, though, poses a
significant problem. The past historical pavement condition data of a particular SHA were
collected and stored using a certain location referencing system (likely a linear system). Hence,
the location reference system must be converted properly to integrate the data with the GPS
database. This conversion is almost always complicated and can create significant discrepancies
in the time-series data. The shortcomings of the GPS include potential problems with the signal
due to heavy foliage and/or buildings blocking satellite signals as well as general equipment
malfunction (Flintsch et al. 2004). Further, the agency staff must be trained to use the GPS
properly.
The least-commonly used reference location system is the GIS. A GIS is ‘a computerized
database management system for accumulating, storage, retrieval, analysis, and display of spatial
data’ (Elhadi 2009). In a GIS, textual databases can be combined with digitized maps to enable
the display of various data on a map. A GIS has minimal location referencing error due to its
ability to collate and cross-reference many types of data by location (Foote and Huebner 1995).
Besides unparalleled accuracy, the advantages of a GIS include the ability to visually display the
results of pavement management analyses on a map of the highway network, view network
conditions through dynamic color-coding, and access particular pavement section data through
the map interface (Elhadi 2009). Hence it is clear that GIS is a powerful tool that can be used
significantly in pavement management. However, the current structure of most PMSs adversely
influences the use of GIS. The staff of the agency must be subjected to training before a GIS can
be fully implemented. Finally, the integration of historically collected pavement condition data in
the GIS database may be a difficult task and in some scenarios may not be possible.

39

For the benefits of the readers, the main advantages and disadvantages of each of the
previously described location referencing systems are summarized in Table 2.2.
Table 2.2 Main advantage(s) and disadvantage(s) of each location reference system
Location reference system
Linear

GPS

GIS

Main advantage(s)
Ease-of-use and typically
physically visible roadside
markers
Improved accuracy and
automated input

Minimal error and improved
integration of PMS elements
in ‘visual’ database

Main disadvantage(s)
Lack of accuracy, especially
from year-to-year
Integration of data with
historical linearlyreferenced data and need for
technological knowledge
Cost, integration of data
with historically linearly
referenced data, and
technological knowledge

Case Study - Louisiana Department of Transportation and Development (LADOTD)
As previously mentioned, the most common location referencing system in use by SHAs
is a linear system consisting of route names and mile posts or milepoints. This location
referencing method lacks accuracy and adversely impacts the collection and organization of
time-series pavement condition data. Essentially, the size and location of pavement segments
can change from one year to the next as shown in Figure 2.9 (Dawson 2012).
In an effort to quantify the error of a linear location reference system, Dawson utilized
pavement condition data from the Louisiana Department of Transportation and Development
(LADOTD). The quantification of error was accomplished by comparing the Beginning Mile
Points (BMPs) and recorded GPS data of 37,843 0.1 mile long pavement segments using the
Pythagorean Theorem. It was found that only 36.8 percent of 0.1 mile pavement segments have
error ranging from 0 to ± 50 feet. Furthermore, the error in the linear referencing system is as
much as approximately ± 530 feet. This means that the pavement condition data recorded for a

40

0.1 mile long pavement segment one year may be recorded for an entirely different 0.1 mile long
pavement segment the next year. Detailed results of the error calculations are listed in Table 2.3.

Figure 2.9 Illustrative example of yearly error of linear referencing system (Dawson 2012)

Table 2.3 LADOTD linear referencing system error (after Dawson 2012)

Range of distance
between the assigned
BMPs (feet)
± ≤ 10

The number of pavement segments from the
LADOTD included in the analyses and the
percentage within each range
Total population of 0.1 mile long pavement
segments is 37,843
15.0 %

± 11 to 50

21.8 %

± 51 to 100

26.7 %

± 101 to 250

23.6 %

± 251 to 528
± > 529

8.4 %
4.5 %

.

41

The analyses results listed in Table 2.3 highlight the main disadvantage of the linear
referencing system in that it may provide inconsistent location references from one year to the
next. However, despite the possibility for significant error, the linear system is the most
commonly used system amongst SHAs. This is no surprise because, as noted earlier, the system
has been established and used for a long period of time. In recent years though, some SHAs have
began to shift towards the use of GPS to improve accuracy in location referencing. However the
problem still exists to integrate the historical linearly referenced data and the new GPS data. In
order to solve this problem, several agencies have started using duel location referencing systems
(linear and GPS) as a first step towards total conversion to GPS.
2.9

Pavement Performance Data Modeling and Remaining Service Life (RSL)
The importance of pavement performance data modeling and the concept of remaining

service life are discussed in the following sections.
2.9.1 The Need for Data Modeling
As it was mentioned previously, cost-effective pavement management recommendations
and/or decisions must be based on the analysis of quantifiable data, including the pavement
condition data (Holt and Gramling 1991). The condition data of any pavement segment include
two sets of information, the condition at a given time (which can be determined using the
collected pavement condition data from one data collection cycle) and the pavement rate of
deterioration over time (which can be determined from a minimum of three cycles of pavement
condition data). Thus, information about past and current pavement condition are often needed
to assess the rate of deterioration of a given pavement segment and to predict its future
conditions. Different pavement segments may have the same condition in one year but their rates
of deterioration could be significantly different. Therefore, in order to assess pavement

42

performance over time it is necessary to model the data using the appropriate mathematical
functions. In other terms, curves are fitted through the various measures of pavement condition
to show past and predicted pavement performance (AASHTO 2001).
2.9.2 International Roughness Index (IRI) Modeling
One of the pavement surface conditions is pavement roughness or smoothness measures.
The Highway Performance Monitoring System (HPMS) of the Federal Highway Administration
(FHWA 2005) requires the states to provide consistent, comparable, realistic, universal and
practical pavement surface roughness measurements. These measurements of road roughness are
referred to as the International Roughness Index (IRI). Lower IRI values indicate a smoother
pavement surface and better ride quality. Typically, the IRI is expressed in terms of inch/mile,
meter/kilometer, or millimeter/meter (Lenz 2011). In general, the IRI increases exponentially
over time (as the pavement ages, it develops cracks, and becomes uneven) (Dawson 2012).
Therefore, pavement roughness (IRI) data are typically modeled as a function of time using an
exponential function (Smith et al. 2002).
2.9.3 Rut Depth Modeling
Rut depth, or rutting, is a load related distress and is the result of the accumulation of
plastic (permanent) deformations in the pavement layers along the wheel paths of flexible and
composite pavements. The rutting in composite pavements are typically confined to the HMA
overlay, whereas rutting in flexible pavements could be the accumulation of rut in all layers and
the roadbed soil. Rigid pavements are not susceptible to rutting caused by plastic deformation or
lateral movement of materials due to traffic loading. Rigid pavement rutting is typically caused
by mechanical dislodging due to studded tire wear (Dean et al. 2011, Naiel 2010). Pavement
rutting is a functional and structural distress that could lead to hazardous conditions when the rut
43

channel is filled with water causing hydroplaning. Rutting typically occurs early in the service
life of asphalt and/or composite pavements and its progression decreases over time as the
pavement materials become denser due to loading. Hence, a power function is typically used to
model rut depth data as a function of time (Odermatt et al. 1999).
2.9.4 Crack Modeling
The most common pavement distress, regardless of pavement type, is cracking. Various
types of cracking exist including fatigue (alligator), longitudinal, and transverse cracking
(FHWA 2003). Pavement cracking could be caused by insufficient pavement thickness, poor
drainage, low material strength, unexpected heavy traffic loads, and/or aging among many other
things. In any case, a cracked pavement should be investigated to determine the root cause of
cracking. Regardless of the cracking type (i.e. alligator, longitudinal, and transverse cracking),
the propagation and deterioration of cracks typically follows three stages. In the first stage, few
cracks appear in the early pavement service life. In the second stage, new cracks appear and old
cracks propagate and deteriorate rapidly. In the third stage, the pavement reaches crack
saturation status and the number of new cracks decreases significantly. Thus a logistic, S-shaped
curve is typically used to model cracking data as a function of time (Dawson 2012, Yang 2004).
In most cases, though, not enough time-series data points are available to model the s-shaped
function. In such scenario, early cracking data can be modeled using the exponential function
whereas for older pavement sections, the data could be modeled using a power function.
The appropriate mathematical models for roughness, rut depth, and cracking are
summarized in Table 2.4 and shown in Figure 2.10.

44

Table 2.4 Mathematical functions used to model the data of the indicated distress type
Pavement distress type
and units*

Model form

Generic equation

IRI (inch/mile)

Exponential

IRI   exp

Rut depth (inch)

Power
2

Rut   t

Crack 

Logistic (Sshaped)

Cracking (feet, feet , or
number of cracks)

t

Max
  t 



1  exp 

Where, α, β, γ, ω, θ, and μ are regression parameters, t = elapsed time (year), and Max =
the maximum value of cracking (the threshold)
*English units are displayed for each distress type, however metric units are used as well

Cracking

Rutting

IRI

60
Idealized

Predicted

50

Condition

40
30
20
10
0
0

5

10
15
Elapsed time (year)

20

25

Figure 2.10 Illustration of the mathematical functions used to model IRI, rutting, and cracking
and to predict future conditions

45

2.9.5 Uses of Data Modeling
The modeling of pavement performance data is essential to pavement management at
both the network and project levels. In its broadest sense, the major purposes of monitoring and
modeling pavement performance data are to (Lytton 1987):
1.

Objectively determine the current pavement conditions of each pavement section along
the network.

2.

Estimate the pavement rate of deterioration and future conditions.

3.

Estimate the pavement remaining service life (RSL) and the time for pavement treatment.
The resulting information is used to formulate a management plan of actions. The

specific use of pavement performance data modeling at the network level includes:
1.

Prioritizing pavement treatment projects.

2.

Determining budgetary needs or constraints.

3.

Assessing the overall health of the pavement network.

4.

Communicating with lawmakers and the users.
The specific uses of pavement performance data modeling at the project level include

(Lytton 1987):
1.

Analysis of specific pavement segments.

2.

Design of detailed pavement treatments for pavement projects.

3.

Analysis of life cycle costs for various pavement treatment design alternatives.

4.

Estimation of pavement treatment benefits.
One common project and network level pavement performance parameter that is

calculated by modeling the pavement condition data is referred to as the Remaining Service Life
(RSL). For each pavement distress type, the RSL of a pavement section is the time in years

46

between now or the year when the latest distress data point was collected and the year when the
pavement distress reaches a certain distress threshold value (Baladi et al. 1991). Hence, one RSL
value can be calculated for each distress type and the lowest value should be assigned to the
pavement section in question. When the RSL of a pavement section reaches zero value, it
implies that the pavement has started to provide substandard service quality in terms of ride
quality, safety, functionality, structural capacity or any combination thereof.
A significant advantage of the RSL concept is that it combines the severity and extent of
the distress as well as the rate of the pavement deterioration. Thus, the RSL is preferred over
other modeling techniques such as pavement distress indices. Various pavement sections may
have similar distress indices but significantly different rates of deterioration. Thus, the RSL
solves the main problem of the individual and combined distress indices, allowing SHAs to make
proper pavement management decisions regarding the past and future service life of the
pavement structures.
The steps enumerated below can be used to calculate the RSL based on the time-series
distress data.
1.

Data Mining – Construction and maintenance records should be examined to identify the
boundaries of pavement projects. The available time series distress data for each 0.1 mile
pavement segment along these projects should be downloaded from the database.

2.

Threshold – For each distress type, establish a distress threshold value such that when the
pavement conditions reach the threshold value the pavement is in substandard condition
and in need of immediate action. Examples of distress threshold values are listed in Table
2.5 (Titus-Glover et al. 2010).

47

Table 2.5 Example distress thresholds
Distress
IRI
Rut Depth
Alligator Cracking
Longitudinal Cracking
Transverse Cracking

3.

Threshold
200 inch/mile
0.5 inch
10% (105.6 feet or 316.8 feet2)
700 feet
700 feet or 58 full-width cracks

Acceptance Criteria – For each pavement segment within a given pavement section or
project, subject the available time series pavement distress and condition data (from step
1) to the two acceptance criteria stated below. The objective is to determine whether or
not portions of the project should be excluded from the analyses (Dawson 2012, Dean
2012). The two acceptance criteria are:
1.

Three data points – For treated pavement sections, a minimum of three data points
before treatment (BT) and three data points after treatment (AT) are required to
model the data using a non-linear function; any model can fit one or two data
points. For pavement sections that were not subjected to treatment or no distress
data are available before treatment, a minimum of three data points are required
after construction.

2.

Positive regression parameters – Positive regression parameters of the pavement
deterioration model are required for time-series distress data that are consistent
for pavement sections that did not receive any treatment. Negative regression
parameters imply that the pavement is self-healing with time (decreasing distress)
without any treatments, which is not reasonable and cannot be used to study the
pavement deterioration.

48

4.

Data Modeling – For the pavement segments that satisfy the two acceptance criteria,
model the time series pavement condition data using the proper mathematical function
listed in Table 2.4 and shown in Figure 2.10.

5.

RSL – For each pavement segment and for each equation (distress type) obtained in the
previous step, calculate the time (tth) at which the distress is expected to reach its
threshold value. The RSL is the difference in years between the calculated time and the
pavement surface age as stated in Equation 2.3.
RS = tth - SA ≤ DS – SA

Equation 2.3

Where tth = time at which the threshold value is reached in years;
SA = surface age in years; and
DSL = design service life in years.
It should be noted that the constraint on the RSL value to be equal to or less than the
difference between the DSL and SA is mainly for new pavement sections where the pavement
shows little to no deterioration. Such constrain should not be used when the pavement section in
question starts to show measurable amount of distress. Further, the inclusion of the DSL in the
equation enhances the feedback from the pavement management to the pavement design process.
Figure 2.11 shows an idealized illustration of the RSL using the three mathematical models.
2.10

Life Cycle Cost Analysis (LCCA)
In general, highway pavements are designed and constructed to provide services for a

limited time period, often referred to as the pavement service life. Over time, the combined
effects of traffic loads and environmental factors accelerate the pavement deterioration rates and
reduce its level of serviceability. Maintenance, preservation, and rehabilitation treatments are
designed and applied to pavement sections to slow their rates of deterioration and to extend their

49

Cracking

Rutting

IRI

60
Predicted

Idealized
50

Condition

40

Threshold
RSL - Rutting

30

RSL - Cracking

20
10

RSL - IRI
0
0

5

10

15

20

25

Elapsed time (year)

Figure 2.11 Illustration of the Remaining Service Life using three mathematical models
service lives. The application of any pavement treatment requires traffic control (lane closures
and/or detours), which significantly impacts traffic flow, increases travel time, and increases
vehicle operating costs (VOC). The costs and benefits of pavement treatments are comprised of
many elements including:
1.

The agency costs of the pavement treatment, which consist of many attributes including:


Material and contractual costs.



The cost of traffic control in the work zone, which is defined as an area along the
highway system where maintenance and construction operations adversely affect
the number of lanes opened to traffic or affect the operational characteristics of
traffic flow through the work zone (Chien et al. 2002).

50



2.

Quality assurance and quality control (QA/QC) costs.
The costs of future treatments.

The agency benefits, which could be measured by the life of the treatment or the life
extension of the treated pavement sections. It should be noted that, for any given
treatment, the net benefits to the agency should be calculated by the impact of the given
treatment on the weighted average longevity (or the remaining service life) of the
pavement network.

3.

The user costs, which are also comprised of many attributes including (Daniels et al.
2000, Lewis 1999):


Time delay user costs or work zone user costs, which are defined as the associated
costs of time delays due to lane closures because of roadway construction,
rehabilitation, and maintenance activities.



Costs incurred by those highway users who cannot use the facility because of
either agency or self imposed detour requirements.



Vehicle operating costs in terms of fuel, wear and tear, and depreciation over the
delay periods.



Accident costs.



Environmental costs due to air pollution caused by excessive uses of gasoline or
diesel fuel due to lower speed and time delay, including noise pollution.

4.

The user benefits which are comprised of improved serviceability and ride quality that
would lower the VOC and improve traffic flow.
The user costs due to planned changes in highway capacity or improvement in pavement

condition by means of road maintenance, rehabilitation and/or reconstruction can also be divided

51

into two categories; work zone costs and non-work zone costs (Daniels et al. 2000, Lewis 1999).
These two general categories and their various components are shown in Figure 2.12.
User Costs

Workzone
Operations

Vehicle
Operating Costs
1. Fuel
Consumption
2. Tire Wear
3. Oil & Lubrication
consumption

Non Workzone
Operations

Delay
Costs

Accident
Costs

1. Stopping
Delay
Costs

1. Property
Damage
Only

2. Queue
Delay
Costs

2. Injury
Costs

Environmental
Costs
1. Vehicle
Emissions
2. Noise
Pollution

3. Fatality
Costs

4. Vehicle
Maintenance
5. Vehicle
Depreciation

Figure 2.12 Components of user costs (after Morgado and Neves 2009)

Estimation of the work zone user costs requires significant and detailed information on
the work zone length, speed restrictions, lane closures, VOC, and traffic capacity in the work
zone. For instance, work zone length (the length of the pavement that is subjected to
maintenance) has a significant impact on the user costs when the demand is greater than the
capacity of the traffic control practices. Hence, it is important to estimate an optimal work zone
length which minimizes both user and construction costs. Various models have been developed

52

to estimate optimal work zone lengths for both two and four lane freeways by minimizing both
construction and additional user costs (Hall et al. 2003).
Traffic control procedures also have a significant impact on the agency and user costs in
work zones. Some traffic control procedures may accelerate construction, therefore decreasing
the time the work zone is in place. In this way, the agency cost increases while the user cost
decreases. On the other hand, some traffic control procedures may cause the duration of the work
zone to increase, which may cause the agency cost to decrease and the user cost to increase.
Hence, there is a direct relationship between traffic control procedures, agency cost, and user
cost. Analyses indicate that the cost effectiveness of traffic control procedures depends on
several site factors and should be evaluated on a site-by-site basis (Dudek et al. 1986).
In addition, as shown in Figure 2.12, non-work zone user costs are comprised of the costs
associated with standard travel such as VOC, accident, and environmental costs. The delay time
is assumed to be zero. The VOC are also a function of several other variables including vehicle
type, vehicle speed, speed changes, gradient, curvature, and pavement surface (Morgado and
Neves 2009).
Given that LCCA requires extensive data from both the agency and user-perspectives, it
is usually only performed to consider pavement treatment alternatives for pavement projects
greater than one million dollars in value. When performed properly, LCCA has applications for
many areas of interest to State and local transportation agencies. Common applications of LCCA
include the following (FHWA 2011):
1.

Designing, selecting, and documenting the most affordable means of accomplishing a
specified project or objective. For instance, if a bridge must be replaced, LCCA can be

53

used to select the replacement option that would cost the least over the expected life of
the bridge.
2.

Evaluating pavement preservation strategies. The costs of each strategy can be evaluated
relative to the expected effects it will have on delaying the costs of expensive
rehabilitations or reconstructions.

3.

Performing value engineering (VE). Value engineering must be applied to all Federal-aid
highway projects on the National Highway System with an estimated cost of $25 million
or more. Among other requirements, the VE team must consider the lowest life cycle cost
means of accomplishing a project.

4.

Project planning and implementation, especially the use and timing of work zones. LCCA
allows the analyst to balance higher agency and/or contractor costs associate with offpeak work hours against reduced traveler delay costs associated with fewer work zones
during peak hours.

54

CHAPTER 3
DATA MINING
3.1

Foreword
The data mining phase of this research study was completed through the combined effort

of several individuals to organize and store massive amounts of pavement management system
(PMS) data obtained from various sources. Hence, the material in this chapter is the combined
work of various individuals including the author of this thesis, Dr. Tyler Dawson, and Dr. Gilbert
Baladi et al (Dawson 2012, Baladi et al. 2012). Nonetheless, the complete data mining materials
are included in this thesis for the convenience of the reader and to ensure clarity and promote
understanding.
3.2

Introduction
The pavement condition and distress, treatment types, and cost data used in this research

study were obtained from the PMS units of the following State Highway Agencies (SHAs) and
pavement study.
1.

The Colorado Department of Transportation (CDOT).

2.

The Louisiana Department of Transportation and Development (LADOTD).

3.

The Michigan Department of Transportation (MDOT).

4.

The Washington State Department of Transportation (WSDOT).

5.

The Minnesota Road Research Project (MnROAD).
The geographical locations of the four SHAs and MnROAD are distributed throughout

the USA with varying network size, traffic, climate, etc. Hence, the pavement data are somewhat
representative of the pavement network in the USA.

55

At the onset of this research, pavement condition and distress data for only nine
pavement sections were requested from each of the four SHAs. These data were received and
analyzed; later the entire PMS databases were requested to broaden the extent of the analyses
and to incorporate the entire sets of available data from each SHA. The databases were received
in various formats (Microsoft Excel spreadsheets, Microsoft Access files, text documents, and so
forth). Further, the pavement condition and distress data were expressed using various
measurement units (SI and English) and various formats such as area, length, count, average,
maximum, etc. The data were transferred to Microsoft Excel files and the units of measurements
were converted and unified for analyses.
3.3

Data Format, Restructuring, and Unification
The first step in support of the pavement condition and distress data analyses, discussed

in Chapter 4, was to convert each of the four PMS databases obtained from the four SHAs, to
one uniform format for analyses. The database conversions were conducted as listed below:
1.

The pavement condition and distress data from the States of Colorado, Louisiana, and
Washington were received in Microsoft Access format. The data analyses (see Chapter 4)
were conducted in-part using the Matlab computer program, which does not read
Microsoft Access files. Hence, the data were converted to Microsoft Excel files. In
addition, the data from Washington and Louisiana were stored in separate Excel files, one
file for each data collection year. This was accomplished by sorting the data by the data
collection year and copying each year individually to a new Excel file. The data from
Colorado were already stored by year.

2.

The pavement condition and distress data received from MDOT were stored in several
formats including Microsoft Excel and Text files such as EI2, WI2, ER3, WR3, etc.

56

Numerous attempts were made to convert the data without any success. Consequently,
the data were left in their original formats.
As stated earlier, the pavement condition and distress data were reported using various
units of measurements and measurement types as listed in Table 3.1. Since the data from each
SHA were used in this study, and in order to conduct uniform analyses, some of the data
elements were re-arranged and/or re-configured to produce uniform data structure using uniform
units of measurement. The restructuring and re-configuration did not affect the accuracy and/or
the variability of the data. Such restructuring and re-configuration were dependent on the
pavement condition or distress type as detailed below.
Table 3.1 Pavement condition and distress data stored by various SHAs
Condition or
distress
Roughness
Rut depth
Alligator
cracks

Units and types of measurements reported by SHAs
SI
English
Types of measurements
Average
m/km
in/mi
Each wheel path
wheel paths
Maximum and
Average rut
mm
inch
average rut depth
depth
m and
2
m

ft and
2
ft

Percent of length

Longitudinal
cracks

ft

Cumulative length
along the pavement
segment

Transverse
cracks



m
m and
count

ft and
count

Count

Percent of
area

Cumulative
length

Units used in the
analysis
Average IRI
(inch/mile)
Average rut depth
(inch)
Length along the
pavement segment
(ft)
Cumulative length
along the pavement
segment (ft)
Cumulative length
along the pavement
segment (ft)

Roughness – Each of the four SHAs collects pavement roughness data in terms of the
International Roughness Index (IRI). The data are recorded in either SI units (m/km) or
English units (in/mi). In this study the data reported in SI units were converted to English
units. In addition, the roughness data for each 0.1 mile long pavement segment were
reported, depending on the SHA, for each wheel path and/or the average IRI of the two
57

wheel paths along the pavement segment in question. The average IRI measurements of
the two wheel paths per pavement segment were used in the analysis.


Rut Depth – The rut depth data are collected and stored in either SI units (mm) or English
units (in). In this study the data reported in SI units were converted to English units. In
addition, for each 0.1 mile long pavement segment, the rut depth data were reported,
depending on the SHA, as the average of each wheel path, the average of the pavement
segment, or the average and the maximum rut depths of the pavement segment in
question. The average rut depth measurements per pavement segment were used in this
study.



Alligator Cracking - The alligator cracking data are collected and stored in terms of
2

2

length (m or ft), area (m or ft ), percent of the pavement length, or percent of area. In
addition, the alligator cracking data for each 0.1 mile long pavement segment were
reported, depending on the SHA, over the entire pavement width (12 feet) or in the wheel
paths (3 foot width per wheel path) of the pavement segment in question. In this study the
alligator cracking data were converted to linear feet by dividing the area by the width. For
2

example, a pavement segment with 600 ft of alligator cracking, and full lane width
measurement criteria, was divided by 12 feet, yielding 50 linear feet of alligator cracking.


Longitudinal Cracking - The cumulative length of longitudinal cracks are collected and
stored in either SI units (m) or English units (ft). In this study the cumulative longitudinal
crack length data were converted to English units and used in the analysis.



Transverse Cracking - The transverse cracking data are collected and stored in either SI
units (m), English units (ft), or by count (number). The latter was reported as the number
of transverse cracks in certain length categories (such as 0 to 1 foot, 2 to 3 feet, etc.) or
58

simply the number of transverse cracks without crack lengths. In this study, the
cumulative length of transverse cracks in feet was used in the analysis. The cumulative
length of transverse cracks was calculated by multiplying the crack count by the average
reported length. For example, one crack in the 0 to 1 foot long category was counted as
0.5 foot long, while a crack in the 6 to 12 feet category was counted as a 9 feet long
crack. Transverse crack data reported by count only (no crack lengths were included),
were assumed to extend across the 12 feet wide lane and therefore their cumulative length
was calculated by multiplying the crack count by 12 feet.


Severity levels – Most cracking data are stored under three separate severity levels: low,
medium, and high. The problem of such data is that the crack severity level rating is a
function of the judgment of the surveyor who is reviewing and digitizing the electronic
images. Such judgment is a function of the degree of training and experience of the
individual surveyor. In addition, the same pavement segment may not be reviewed by the
same surveyor each year or each data collection cycle. Thus, a crack may be labeled high
severity in one year and medium severity next year and vice versa. Figures 3.1 and 3.2
depict the time series data for each transverse crack severity level along a portion of
highway 24 in Colorado. The data in the figures show that:
1.

The transverse crack length changes from one data collection cycle to the next
without a pavement treatment. For example, the high severity transverse crack
length is about 150 feet in year 2000, then only about 10 feet in 2001, and is
finally absent in year 2002. Likewise, the medium severity transverse crack length
is about 130 feet in year 2000, 150 feet in year 2001, and only about 10 feet in
year 2002.

59

Low severity

Medium

High

Total length

Transverse cracking (ft)

400
350
300
250

200
150
100

50
0
1998

1999

2000
2001
Time (year)

2002

2003

Figure 3.1 Time series transverse cracking data for each severity level and the sum of all levels,
Colorado, HWY 24, direction 2, BMP 329.9
Low severity

Medium

High

400

Transverse cracking (ft)

350

300
250
200
150
100

50
0
1999

2000

2001

2002

Time (year)

Figure 3.2 Cumulative time series transverse cracking data showing individual transverse crack
severity level and the sum of all severity levels, Colorado, HWY 24, direction 2, BMP 329.9

60

On the other hand, the low severity transverse crack length increases from about
60 feet, to 110 feet, and to 310 feet over the same time period. The reduction in
the lengths of medium and high severity transverse cracks could be attributed to
the rater assigning low severity to the same cracks which were previously
assigned medium or high severity. It could also be related to the pavement
temperature at the time of data collection. Higher temperature causes decreases in
crack opening and hence, in severity level.
2.

The individual severity levels show high variability when modeled in time series,
as indicated by exponential models determined for each transverse crack length
severity level. In fact, the models indicate that the medium and high severity
transverse crack length is decreasing with time without a pavement treatment.

To overcome the two problems of data inconsistency and high variability, the sum of all
severity levels for each crack type was obtained and used in the analysis. This yielded more
consistent data that can be modeled for analysis as shown in Figures 3.1 and 3.2.
The crack severity level data could be used, though, to roughly estimate the amount of
required work. For example, so many feet of cracks in the medium and high severity levels need
to be sealed or patched. Low severity cracks are typically not sealed or patched. Likewise, for
concrete pavements, low severity transverse cracks may be subjected to dowel bar retrofit, while
medium and high severity cracks are typically not.
A summary of the data characteristics and information of each of the four SHAs and how
they were re-arranged and re-structured to yield uniform sets of data for analysis are detailed in
the next few subsections.

61

3.3.1 Pavement Condition and Distress Data from Four State Highway Agencies
Table 3.2 lists the pavement condition and distress types, severity levels, and
measurement units reported by each of the four SHAs. For each agency, some statistical
information regarding the pavement network and a summary of the data characteristics and how
they were reformatted and restructured to the uniform set of data are detailed in the next few
subsections.
a)

Colorado Department of Transportation (CDOT)
CDOT has 9,134 miles (22,912 lane-miles) of pavement and 3,406 bridges under its

jurisdiction. The annual traffic is in excess of 48 billion vehicle-miles. Forty percent of that
traffic is carried on the Interstate system (I-25, I-70, I-76, I-225, and I-270) which accounts for
about ten percent of the network length. In 2009, 7.2 million miles of pavement were cleared of
snow and 248,000 tons of asphalt materials and 178,800 gallons of liquid asphalt were used to
repair damaged pavement surfaces (Hartgen et. al. 2009, CDOT 2010).
Pavement condition and distress data for three flexible, three rigid, and three composite
pavement sections were originally requested and received from CDOT. Later, upon request
CDOT provided their entire pavement condition and distress database covering the period from
1998 through 2009. The condition and distress data were collected every year, every other year,
or every third year depending on the road and direction of travel. The data were collected on a
continuous basis and recorded in the database for each 0.1 mile long pavement segment. The
applicable data types, severity levels, and measurement units contained in the database are listed
in Table 3.2.

62

Table 3.2 The pavement condition and distress data received from the four SHAs
SHA

CDOT

LADOTD

MDOT

WSDOT

Pavement condition information
Condition or distress type
Severity level
Measurement unit
2
Alligator cracking
Feet / segment
IRI
Inch/mile
Longitudinal cracking
Feet/ segment
Rut depth
Inch
Transverse cracking
Count/ segment
2
Low, medium, and
Feet (wheel paths)/
Alligator cracking
high
segment
IRI
Inch/ mile
Low, medium, and
Longitudinal cracking
Feet/ segment
high
Rut depth in right or left
Inch
wheel path
Low, medium, and
Transverse cracking
Feet/ segment
high
Alligator cracking consists
25 levels depending
of two categories (right
on the length and
Percent of length
and/or left wheel path)
associated distress
IRI
Inch/ mile
Longitudinal cracking
49 levels for flexible,
consists of 3 categories for
rigid and composite
rigid and 5 for flexible &
pavements depending
Percent of length
composite pavements
on crack length and its
depending on location in the
associated distress
lane
Rut depth
Inch
Transverse cracking
consists of two categories
Twelve levels for rigid
for rigid, composite and
and composite and 16
flexible pavements
levels for flexible
Count per segment
depending on crack opening
depending on length
for rigid and composite, and
and width of the
crack irregularity for
associated distresses
flexible pavements
Low, medium, and
Percent of 2 wheel
Alligator cracking
high
paths of a segment
IRI
Meter/ kilometer
Low, medium, and
Longitudinal cracking
% of segment
high
Rut depth
Millimeter
Low, medium, and
Transverse cracking
Count/ segment
high
63

The data were adjusted where necessary to unify the measurement units and severity
2

levels as discussed above. The alligator cracking data were provided as lane area (ft ) and were
divided by the lane width (12 ft) to obtain linear feet. The reported number of transverse cracks
was multiplied by the lane width (12 ft) to obtain cumulative linear feet. The IRI, longitudinal
cracking, and rut depth data were not adjusted. Note that no distress severity levels were reported
with the full database. Examples of the original and converted data are listed in Tables A.1 and
A.2 of Appendix A and the entire database is available upon request from the Department of
Civil & Environmental Engineering at Michigan State University (MSU) (CDOT 2010).
b)

Louisiana Department of Transportation and Development (LADOTD)
LADOTD has 15,987 miles (38,458 lane-miles) of pavement and 8,060 bridges under its

jurisdiction. The large number of bridges is due to the extensive areas of land near the
Mississippi River and Delta, which are near or below sea level. The Interstate system (I-10, I-12,
I-20, I-49, I-55, I-59, I-110, I-210, I-220, I-310, I-510, I-610, and I-910) makes up about six
percent of the pavement network length. In 2006, approximately six percent of the network was
maintained through sealing or resurfacing (LADOTD 2007, Hartgen et. al. 2009).
Pavement condition and distress data for three flexible, three rigid, and three composite
pavement sections were originally requested and received from LADOTD. Later, upon request
LADOTD provided their entire pavement condition and distress database covering the period
from 1995 through 2009. The condition and distress data were recorded in 1995, 1997, 2000,
2003, 2005, 2007, and 2009. The data were collected on a continuous basis and stored in the
database for each 0.1 mile long pavement segment. The applicable data types, severity levels,
and measurement units contained in the database are listed in Table 3.2. The alligator cracking
2

data were provided as wheel path area (ft ) and were divided by the assumed wheel path width

64

of 3 ft to obtain linear feet. The rut depth data were provided as the average of each wheel path.
The average of the averages of the two wheel paths was taken as the average rut depth. The IRI,
longitudinal cracking, and transverse cracking data were not adjusted. Note that the low,
medium, and high severity distresses were summed. Examples of the formatted data are listed in
Table A.3 of Appendix A and the entire database is available from the Department of Civil &
Environmental Engineering at MSU (LADOTD 2010).
It should be noted that rut depth data were collected by ultra-sounding in 1993 and 1995,
then by 3-point laser system from 1997 to 2005, then by continuous laser scanning after 2005.
There is no correlation between equipment. An error in the rut depth collection software was
discovered by the staff of LADOTD and the rut depth data collected after 2005 were corrected
and replaced the original data. It should also be noted that sealed cracks are not counted as
cracks.
c)

Michigan Department of Transportation (MDOT)
MDOT has about 9,700 miles (27,503 lane-miles) of pavement and 5,400 bridges under

its jurisdiction. The Interstate system consists of I-69, I-75, I-94, I-96, I-194, I-275, I-475, I-496,
I-675, and I-696. In 2006, about 400 miles of pavement and 300 bridges were improved (MDOT
2010, Hartgen et. al. 2009).
Pavement condition and distress data for three flexible, three rigid, and three composite
pavement sections were originally requested and received from MDOT. Later, upon request
MDOT provided their entire pavement condition and distress database covering the period from
1992 through 2009. The condition and distress data were typically recorded every other year,
alternating annually for each direction of travel. The data were collected on a continuous basis
and recorded for each 0.1 mile long pavement segment. The applicable data types, severity

65

levels, and measurement units contained in the database are listed in Table 3.2. The alligator and
longitudinal cracking data were provided as decimal percent of the length of each segment (528
feet) and were multiplied by the segment length to obtain linear feet. The transverse cracking
data were provided as the count of cracks with certain range of length and were multiplied by the
average length in each range to obtain linear feet. The IRI and rut depth data were provided in
inch/mile, and inch, respectively and hence, were not adjusted. Note that the cracking data are
collected under several classifications and the length was summed. Examples of the formatted
are listed in Table A.4 of Appendix A and the entire database is available from the Department
of Civil & Environmental Engineering at MSU (MDOT 2010).
The MDOT pavement condition and distress data are stored in several formats scattered
among thousands of individual files. Each file contains portions of the pavement condition and
distress database. For example, the IRI, rut depth, and cracking data are each stored separately in
different data files having different formats for each 0.1 mile long pavement segment. In
addition, the majority of each data type is stored in different files for each control section. For a
given control section and a given pavement data collection cycle, the linear location reference
system in the IRI and rut depth files often do not match that in the cracking files. For example,
the beginning mile points (BMPs) for the sensor collected data (IRI and rut depth) and the
videotaped data (cracking) are not consistent along portions of M-39, control section 82192,
direction 1. In 2001, a portion of the videotaped data were collected for the pavement segments
with BMPs 0.0, 0.131, 0.256 and so on; while the sensor collected data were collected for
pavement segments with BMPs 0.0, 0.1, 0.2 and so on. To further complicate the situation,
similar problems exist in time series where the BMPs of the pavement segments float back and
forth from one data collection cycle to the next. Figure 3.3 shows the BMPs of the first 10

66

pavement segments along M-39, control section 82192, direction 1 from 5 data collection cycles
(1999 to 2007). The data in the figure indicate that the BMPs of the pavement segments shift
significantly back and forth from one year to the next. Further, few of the pavement segments are
more or less than 0.1 mile long and some of the segments were not surveyed in few years.
Countless attempts were made to adjust the BMPs using especially written Matlab based
computer programs to match the data for each pavement segment within each data collection
cycle (sensor and videotaped data) and between various data collection cycles. Some of the data
were matched by shifting each BMP along the pavement to coincide with a reference BMP (the
oldest data collection cycle). In the example, the data collected from 2001 to 2007 were shifted
forward or backward to match the BMPs of the data collected in 1999. The difficulties arise
because the required shift in the BMPs for each 0.1 mile long pavement segment within a data
collection cycle is not constant. Further, for the same 0.1 mile long pavement segment, the
required shift in the BMP from one data collection cycle to the next is not constant. Such shifts
were often greater than 0.1 mile. Nevertheless, Figure 3.4 shows the resulting time series
longitudinal crack data after adjusting the BMP of each 0.1 mile long pavement segment by
hand. The data in the figure indicate that the shifted BMPs result in highly variable time series
cracking data. Such variability did not allow:
1.

Modeling the data as a function of time.

2.

Calculating consistent rate of deterioration.

3.

Estimating the benefits of treatments.

67

2009

Data collection year

2007
2005
2003

2001
1999

1997
0.0

0.2

0.4

0.6
0.8
1.0
Beginning mile point

1.2

1.4

1.6

Figure 3.3 The BMP of the first ten 0.1 mile long pavement segments along M-39, control
section 82192, direction 1, Michigan
1st BMP

2

3

4

5

6

7

8

9

10

Longitudinal crack length (ft)

180
150
120

90
60

30
0
1997

1999

2001
2003
2005
Time (calendar year)

2007

2009

Figure 3.4 Longitudinal cracking data after adjusting the BMP for the first ten 0.1 mile long
pavement segments along M-39, control section 82192, direction 1, Michigan

68

Finally, for about a four month period, countless attempts were made to unify the BMP of
each 0.1 mile long pavement segment between the various data collection cycles. Unfortunately,
none of these attempts were even partially successful. Therefore, it was decided to exclude the
MDOT pavement condition and distress data from most analyses in this study.
d)

Washington State Department of Transportation (WSDOT)
WSDOT has about 7,000 miles (18,392 lane-miles) of pavement and 3,400 bridges under

its jurisdiction. The Interstate system consists of I-5, I-10, I-82, I-90, I-405, and I-705 (Hartgen
et. al. 2009, WSDOT 2010).
Similar to the other three states, pavement condition and distress data for three flexible,
three rigid, and three composite pavement sections were originally requested and received from
WSDOT. Later, upon request WSDOT provided their entire pavement condition and distress
database covering the period from 1969 through 2007. The condition and distress data were
collected and recorded primarily every other year from 1969 to 1988 and every year starting in
1989. The data were collected on a continuous basis and recorded for each 0.1 mile long
pavement segment. The applicable data types, severity levels, and measurement units contained
in the database are listed in Table 3.2. The alligator cracking data were provided as percent of the
length of the two wheel paths in the segment (1028 feet). In this study, the data were divided by
100 and multiplied by the segment wheel path length to obtain linear feet. The Longitudinal
cracking data were provided as percent of the length of each segment (528 feet). Once again, the
data were divided by 100 and multiplied by the segment length (528 feet) to obtain linear feet.
The transverse cracking data were provided as the count of the number of cracks and were
multiplied by the lane width (12 feet) to obtain linear feet. Note that, in the analysis of the
cracking data, the sum of the low, medium, and high severity levels was used. The IRI and rut

69

depth data, which are recorded in SI units (m/km and mm) were converted to English units
(in/mile and inch), respectively. Examples of the formatted data are listed in Table A.5 of
Appendix A and the entire database is available from the Department of Civil & Environmental
Engineering at MSU (WSDOT 2010).
3.3.2 Minnesota Road Research Project (MnROAD)
The MnROAD test facility is located near Albertville, Minnesota. The pavement testing
facility was constructed between 1992 and 1994 through a joint venture between the Minnesota
Department of Transportation (MnDOT) and the Minnesota Local Road Research Board
(LRRB). The test facility consists of two road sections divided into fifty five 500-foot long
segments or “cells”. One road section is a 3.5 mile mainline section along I-94 carrying about
28,500 vehicles per day. The other is a 2.5 mile long low volume road utilizing a controlled fiveaxle semi tractor-trailer (MnROAD 2008, MnDOT 2011). The pavement condition and distress
types, severity levels, and measurement units contained in the database are listed in Table 3.3.
The longitudinal, transverse, and alligator cracking data were not restructured or reconfigured.
Note that, in the data analysis of each cell, the sum of the low, medium, and high severity
cracking data was used. The IRI and rut depth data were converted from SI to English units.
Examples of the formatted data are listed in Table A.6 of Appendix A and the entire database is
available from the Department of Civil & Environmental Engineering at MSU.

70

Table 3.3 MnROAD database items
Condition or distress type
Alligator cracking
IRI
Longitudinal cracking (wheel
path or non wheel path and
sealed or not sealed)
Rut depth
Transverse cracking (sealed
or not sealed)

3.4

Severity level
Low, medium, and high

Measurement unit
Feet/cell
Meter/ kilometer

Low, medium, and high

Feet/cell
Millimeter

Low, medium, and high

Feet/cell

Treated Pavement Section Identification
Following the conversion and restructuring of the pavement condition and distress

databases, exhaustive searches were conducted of the CDOT, LADOTD, and WSDOT databases
and data files to identify pavement sections that were subjected in the past to one of the
following six most common treatment types:
1.

Thin (< 2.5 inch) hot mix asphalt (HMA) overlay of asphalt surfaced pavement.

2.

Thick (≥ 2.5 inch) HMA overlay of asphalt surfaced pavement.

3.

Single chip seal.

4.

Double chip seal.

5.

Thin (< 2.5 inch) mill and fill of asphalt surfaced pavement.

6.

Thick (≥ 2.5 inch) mill and fill of asphalt surfaced pavement.
It should be noted that, the pavement treatment files provided by each of the three SHAs

were used in the identification of treated pavement sections. This identification consists of
determining the acceptable time window of the treatment calendar year such that the database
likely contains three or more data collection cycles before treatment (BT) and three or more data
collection cycles after treatment (AT). For example, if the database contains data collection
cycles for the calendar years 1994, 1996, 1999, 2000, 2002, 2004, 2006, and 2008, then the

71

acceptable treatment time window is between the years 2000 and 2003. This increases the
probabilities that every 0.1 mile long pavement segment has three or more available data points
BT and AT. In general, the section identification implies that for those states that collect data
every other year, an absolute minimum of 12 years of time series data (6 years BT and 6 years
AT) are required. Whereas for the State of Washington, which collects the data every year, an
absolute minimum of 6 years of data are required (3 years BT and 3 years AT).
It is important to note that, in this study as well as in others, such data search is difficult,
laborious, and time consuming. The difficulties that were, or could be, encountered include:


For some pavement sections, the PMS database of some SHAs, especially those who
collect pavement condition and distress data on a bi-annual basis, did not contain the
minimum of three time series data points BT and/or AT.



Many pavement sections were subjected to treatment more frequently than the required
time span listed above.



For a significant number of pavement sections, accurate and consistent records regarding
the applications of routine, reactive, and preventive maintenance treatments do not exist
in the database.



For those SHAs who collect pavement condition and distress data using a sampling
technique, the availability of three time series data points could be significantly reduced.
Nevertheless, for each SHA, the number of pavement sections or projects that were

identified for analysis, the cumulative length of these sections for each treatment type, and the
total length of all projects of all SHAs identified for analyses are listed in Table 3.4.

72

Table 3.4 The number of pavement projects and total length identified in each state
Number and total length of pavement projects in three
SHAs
Total, all SHAs
Treatment
Colorado
Louisiana
Washington
type
Projects Length Projects Length Projects Length Projects Length
1
70
104.6
18
45.5
48
130.9
136
281
2
59
252
4
22.7
63
274.7
3
69
495.8
46
242.1
7
20.4
122
758.3
4
12
40.5
12
40.5
5
2
9.1
11
36.5
21
93
34
138.6
6
32
139
32
139
Total
141
609.5
178
755.6
80
267
399
1632.1
Treatment type: 1 = Thin (< 2.5 inch) HMA overlay of asphalt surfaced pavements;
2 = Thick (≥ 2.5 inch) HMA overlay of asphalt surfaced pavements;
3 = Single chip seal;
4 = Double chip seal;
5 = Thin (< 2.5 inch) mill and fill of asphalt surfaced pavements;
6 = Thick (≥ 2.5 inch) mill and fill of asphalt surfaced pavements.

3.5

Time Series Data Restructuring
For each treated pavement section identified above, the pavement condition and distress

data for each 0.1 mile long pavement segment along the section were restructured in a time series
format. A Matlab based computer program was written to search the database and retrieve the
corresponding condition and distress data based on the user inputs of:


The beginning and the ending mile point (BMP and EMP) of the pavement project.



The route and control section number and the direction of traffic.
For each pavement section/project, the output of the Matlab program consists of one

Excel file containing six worksheets; one sheet per condition and distress type and one listing the
treatment type, treatment time, and project boundaries (BMP and EMP).

73

3.6

Cost Data
Limited cost data were received from the three SHAs. When cost data were available

they were extremely limited in detail. For example, the treatment cost consists of the total
contract cost. The cost data did not include the breakdown of cost relative to materials, preoverlay activities, safety improvements (e.g., guardrails), signing, mobilization charges,
incentive/disincentives, and so forth. Detailed cost data are required to determine the costeffectiveness of each treatment. Nevertheless, when available, only the material and labor costs
data were used to determine the cost-effectiveness of the treatment. Extraneous cost items in the
contract (guardrails, sign replacement, etc.) were not included in the analyses. Similarly, the
equipment mobilization cost is a significant portion of the cost of short pavement projects and
small portions of longer projects. In most cases, this information was not available, but under
ideal circumstances should be included in the database and in the analyses. Further, since the
pavement conditions and distress levels along a given pavement project vary substantially, the
amount of pre-treatment work and cost would also vary. Hence, a complete set of cost data
should include the cost of the treatment along each 0.1 mile of the pavement section. This would
allow analysis of the optimum time at which the pavement treatment is the most cost effective.
The lack of sufficient and detailed cost data did not allow comprehensive analysis of the
treatment costs in this study. Regardless, analyses of treatment benefits (effectiveness) were
undertaken. The analysis procedures and the results are detailed and discussed in Chapter 4. Note
that, Baladi & Dean 2011 obtained, from MDOT, general cost data of various preventive
maintenance treatment actions. The data are summarized in Tables 3.5 and 3.6 for the years 2009
and 2010, respectively. The data in the tables detail the entire range of project costs, which
include project locations and possible provisions of the contracts. Table 3.7 summarizes the

74

general material costs and the total costs including materials, engineering fees, culverts and slope
work, etc. Finally, equipment mobilization is typically about $50,000. The cost data (listed in
Tables 3.5 and 3.6) were used to conduct life cycle cost analysis (LCCA) of light (frequent) and
heavy (less frequent) pavement treatments in urban and rural areas. A summary of the analyses
procedures and results is presented in Chapter 4. Detailed LCCA results are discussed elsewhere
(Baladi et al. 2012, Dean 2012).

Table 3.5 Typical preventive maintenance treatment costs in 2009 for the state of Michigan (Baladi
and Dean 2011)
Treatment type
Cold milling bituminous/HMA surface

Minimum
2
$0.26/yd
$0.01/ton

Cost per unit in 2009
Average
Maximum
2
2
$0.69/yd
$7.43/yd
$6.34/ton
$11.50/ton

Non structural bituminous/HMA
overlay
Over band crack fill
Bituminous crack treatment
Chip seal

$39.54/ton

$52.73/ton

$100.85/ton

$2,145/RBMI
$3,092/RBMI

$4,191/RBMI
$4,210/RBMI

$13,150/RBMI
$17,000/RBMI

Double chip seal

$2.57/ yd

Micro-surface with Warranty
HMA ultra-thin with low volume
warranty
HMA ultra-thin with medium volume
warranty
Paver placed surface seal

$2.55/ yd

$1.24/yd

2

$2.08/ yd
$2.72/ yd
$5.19/ yd

2
2
2
2
2
2

$1.38/yd

2

$2.78/ yd
$3.09/ yd
$2.35/ yd
$2.86/ yd
$5.74/ yd

2
2
2
2
2
2

2

$1.66/ yd
$2.98/ yd
$3.91/ yd
$2.70/ yd
$3.07/ yd
$6.00/ yd

Diamond grinding concrete pavement
$2.90/ yd
$3.14/ yd
$3.18/ yd
Resealing transverse pavement joints
$0.69/ft
$0.97/ft
$2.00/ft
with hot-poured rubber
Resealing longitudinal joints with hot$0.59/ft
$0.92/ft
$1.50/ft
poured rubber
Crack sealing concrete pavement
$1.00/ft
$1.12/ft
$2.00/ft
2
Yd = square yard with 1 inch depth, RBMI = roadbed mile, ft = foot

75

2
2
2
2
2
2

Table 3.6 Typical preventive maintenance treatment costs in 2010 for the state of Michigan (Baladi
and Dean 2011)
Treatment type

Cost per unit in 2010
Minimum
Average
Maximum
2
2
2
$0.01/ yd
$0.72/ yd
$7.00/ yd
$0.01/ton
$0.45/ton
$1.00/ton

Cold milling bituminous/HMA
surface
Non structural
bituminous/HMA overlay
Over band crack fill
Bituminous crack treatment
Chip seal

$45.00/ton

$57.54/ton

$110.00/ton

$2,935/rbmi
$1,757/rbmi
2
$1.28/ yd

$4,418/rbmi
$4,447/rbmi
2
$1.51/ yd

$13,600/rbmi
$12,541/rbmi
2
$1.65/ yd

Double chip seal

$2.69/ yd

2

$2.75/ yd

2

2
2

$2.81/ yd

2
2

Micro-surface with Warranty
$2.55/ yd
$3.48/ yd
$5.00/ yd
HMA ultra-thin with low
2
2
2
$2.50/ yd
$2.58/ yd
$3.00/ yd
volume warranty
HMA ultra-thin with medium
2
2
2
$2.55/ yd
$2.58/ yd
$2.60/ yd
volume warranty
2
2
2
Paver placed surface seal
$5.19/ yd
$5.74/ yd
$6.00/ yd
Diamond grinding concrete
2
2
2
$2.90/ yd
$3.14/ yd
$3.18/ yd
pavement
Resealing transverse pavement
$0.95/ft
$1.88/ft
$4.00/ft
joints with hot-poured rubber
Resealing longitudinal joints
$0.96/ft
$1.03/ft
$2.40/ft
with hot-poured rubber
Crack sealing concrete
$0.10/ft
$0.58/ft
$2.47/ft
pavement
2
Yd = square yard with 1 inch depth, rbmi = roadbed mile, ft = foot
Table 3.7 Typical material and total treatment costs for the state of Michigan (Baladi & Dean 2011)
Treatment type
HMA Reconstruction
PCC Reconstruction
Rubblization & HMA
overlay
Unbonded PCC Overlay

HMA Reconstruction
PCC Reconstruction

Road type
Freeway

Non-Freeway
Material cost only
$476,000/lane-mile
$272,000/lane-mile
$359,000/lane-mile
$325,000/lane-mile
$238,000/lane-mile

$263,000/lane-mile

$263,000/lane-mile
$262,000/lane-mile
Total cost including materials, engineering fees, culverts
and slope work, etc.
$1,000,000/mile
$1,200,000/mile
$1,300,000/mile
-

76

CHAPTER 4
DATA ANALYSES & DISCUSSION
4.1

Introduction and Research Objectives
In this chapter, the analysis methods used in this research and the analysis results are

presented and discussed. The analyses methods, results, and discussion are based on the problem
statement, research plan, and objectives included in Chapter 1. For convenience, and to facilitate
complete understanding, the problem statement and the research objectives are repeated below.
The long-term economic climate has caused some highway administrators to consider
pavement performance data sampling as an alternative to reduce data collection costs. However
the effects of data sampling on the accuracy of the PMS decisions are not well documented. It is
not clear that data sampling ultimately reduces the overall PMS costs. Furthermore, for those
SHAs that sample the pavement performance data, the pavement lengths for which the
performance data are stored and analyzed are dictated by the sampling techniques used as stated
in Chapter 1. Longer analysis lengths may not improve the data analysis results and may
artificially decrease the data variability. Thus, the impact of the pavement analysis length on the
variability of the pavement performance data and, ultimately, on the accuracy of the PMS
decisions should be evaluated before a data analysis length is selected. Finally, for various
reasons, data from some data collection cycles along certain pavement segments may not be
documented or are missing, which makes it difficult or impossible to model and analyze the data.
In order to solve this problem, the effects of different data imputation techniques on the accuracy
of the pavement performance data should be evaluated. Accordingly, a comprehensive research
plan was designed to address the three problems through the analyses of the impacts of data

77

sampling, data analysis length, and data imputation on the accuracy of the pavement
performance data and the PMS decisions.
The specific objectives of the research are stated below.
1.

Assess the impacts of pavement performance data sampling on the accuracy of PMS
decisions and quantify the hidden costs of data sampling.

2.

Analyze the effects of data analysis length on the variability of the pavement condition
data and on the accuracy of the PMS decisions.

3.

Study the impacts of various data imputation methodologies on the variability and
accuracy of the pavement condition data and the corresponding PMS decisions.

4.2

Pavement Performance Data Sampling
As stated in Chapter 3, some SHAs collect pavement condition and distress data on a

continuous basis and store the data over short pavement segments (0.1 mile, 0.5 mile, or 1 mile),
whereas others use sampling techniques to reduce the time and costs of data collection. It is
typically assumed that the pavement conditions of one mile, two miles, or longer pavement
sections can be represented by the pavement conditions along shorter pavement segments such as
100, 200, or 500 ft. Some SHAs obtain electronic images of the pavement surface on a
continuous basis along the entire network but only digitize a small “representative” sample of the
data. The assumption herein is that digitized sample of the pavement performance data represents
the conditions of a longer pavement section. Regardless, pavement performance data sampling
is typically accomplished using either randomly selected short pavement segments or physically
fixed short pavement segments.
In this research, time series pavement condition and distress data that were continuously
collected along four road networks were obtained. The four sources of the data (see Chapter 3)

78

are the Colorado Department of Transportation (CDOT), the Louisiana Department of
Transportation and Development (LADOTD), the Michigan Department of Transportation
(MDOT), and the Washington State Department of Transportation (WSDOT). The pavement
condition data of the four SHAs are reported for each 0.1 mile segment along their pavement
networks. The International Roughness Index (IRI) and the transverse and longitudinal cracking
data received from the four SHAs were used to analyze the effects of sampling and sample size
on the accuracy of the pavement management decisions. This was accomplished by sampling the
continuous data along several miles of various pavement sections using two sampling
techniques; fixed and random sampling. The effects of sample size on the PMS decisions were
studied using the fixed sampling technique and the sample size varied from 10 to 60 percent
using 10 percent increments. The six sample sizes were obtained as follows:
1.

Ten percent sampling: the pavement condition and distress data of the first 0.1 mile long
pavement segment of each one mile.

2.

Twenty percent sampling: the pavement condition and distress data of the first two 0.1
mile long pavement segment of each mile.

3.

Thirty percent sampling: the pavement condition and distress data of the first three 0.1
mile long pavement segments of each mile.

4.

Forty percent sampling: the pavement condition and distress data of the first four 0.1 mile
long pavement segments of each mile.

5.

Fifty percent sampling: the pavement condition and distress data of the first five 0.1 mile
long pavement segments of each mile.

6.

Sixty percent sampling: the pavement condition and distress data of the first six 0.1 mile
long pavement segments of each mile.

79

For each sample size, it was assumed that the pavement condition and distress of the
sampled pavement segments represent the pavement condition and distress of the entire mile. In
the random sampling technique, for each mile of pavement, the pavement conditions and distress
of a randomly selected 0.1 mile long pavement segment along each mile were assumed to
represent the pavement conditions and distress of the entire mile.
4.2.1 Fixed Sampling
Recall that CDOT, LADOTD, MDOT, and WSDOT report and store the measured IRI
and pavement distress data for each 0.1 mile long pavement segment along the road network.
Such data are labeled herein as continuous data. Using the continuous pavement condition and
distress data from the four states, the effects of 10 percent sampling on the accuracy of the
pavement distress data were analyzed. In this manner, for each data collection cycle, the
pavement data of the first 0.1 mile long pavement segment of each 1 mile road section were
assumed to represent the pavement conditions and distress along the entire mile. For each
analyzed road in the four SHAs, the same analysis steps were used and they are outlined below.
Step 1 – Differences Between the Sampled and the Continuous Data – In this step, the
differences between the ten percent sampled and the continuous pavement condition and distress
data were studied. Recall that the pavement condition and distress data along the first 0.1 mile
long pavement segment of each one mile pavement section were assumed to represent the
conditions and distress along the entire mile. Hence, the sampled data consist of one data point
for each one mile of road whereas the continuous data provide ten data points per mile. The solid
lines in Figures 4.1 and 4.2 depict, respectively, the sampled IRI and transverse cracking data
while the individual data points in the figures represent the continuous IRI and transverse
cracking data for each 0.1 mile long pavement segment of the road. It is important to note that, in

80

most SHAs, the longitudinal and transverse pavement profiles along the road network are
measured by the same vehicle. The two profiles are automatically analyzed and the IRI and rut
depth data are recorded for each road survey segment within the road network. Hence, most
SHAs do not sample IRI or rut depth data. The IRI data are used herein to show the effects of
sampling on sensor-collected data whereas the transverse cracking data are used to show the
impact of sampling on image based data.
The data in Figure 4.1 indicate that the higher is the variability of the measured IRI data,
the higher are the differences between the sampled and the continuous IRI data. To illustrate, the
degree of uniformity of the continuous IRI data in Figure 4.1 varies substantially amongst the
four roads as does the degree at which the sampled data represent the continuous data as stated
below.
1.

The degree of uniformity of the continuous IRI data in Figure 4.1d for the twenty miles
long composite pavement section along SRID 005 in Washington is the highest amongst
the four roads in Figure 4.1. Likewise, the sampled data represent the continuous data
throughout the twenty miles section of the road.

2.

Except for about eleven 0.1 mile long pavement segments (localized segments), the
degree of uniformity of the continuous IRI data in Figure 4.1a for the thirteen miles long
flexible pavement section along HWY 24 in Colorado is very good. Likewise, the
sampled data represent the continuous data throughout the thirteen miles section except at
the localized segments of the road. At some of these localized areas, the continuous data
are more than four times higher than the sampled data.

3.

The uniformity of the continuous IRI data for the eighteen miles long composite
pavement section along I-94 in Michigan is similar to that of HWY 24 in Colorado as

81

shown in Figure 4.1c. The exception is that more localized data variability can be found
along I-94 than along HWY 24. Likewise, the sampled data represent the uniform
continuous data throughout the eighteen miles section except at the localized areas where
the data variability is high. At some of these areas, the continuous data are more than
twice and less than half of the sampled data.
4.

Figure 4.1b shows high variability of the continuous IRI data of the 11 miles long flexible
pavement section along LA-34 in Louisiana. The figure also shows that the sampled data
do not represent the continuous data along the majority of the eleven mile road section.

Similar results were obtained for other roads and are shown in Figures B.1 through B.4 of
Appendix B.
Figure 4.2 depicts the sampled and the continuous transverse cracking data along the
same four road sections shown in Figure 4.1. The data in Figure 4.2 indicate that the variability
of the continuous transverse cracking data is much higher than the IRI data of Figure 4.1.
Consequently, the sampled data in Figure 4.2 often misrepresent the continuous data for almost
all roads that were analyzed. For example, the sampled transverse cracking data for HWY 24 in
Colorado (Figure 4.2a) either significantly overestimate or underestimate the continuous data for
almost each mile point. This scenario is substantially magnified along LA-34 in Louisiana where
the continuous transverse cracking data are highly variable as shown in Figure 4.2b. At some
locations, the continuous transverse cracking data indicate 0 feet of cracking while the sampled
data indicate 1000 feet of cracking. In a few cases, though, the differences between the sampled
and the continuous transverse cracking data are not significant. This can be seen from mile points
8 to 18 along I-94 in Michigan (Figure 4.2c) as well as from mile points 62 through 70 and 72

82

321

Data sampled per mile

Data sampled per mile

350
300
250
200
150
100
50
0

323
325
327
329
331
333
a) Mile point along HWY 24 (flexible), Colorado
Year 1999

250

0

2

4

Data per 0.1 mile

6

8

10

b) Mile point along LA-34 (flexible), LADOTD
Year 1997, control section 0.12304
Data sampled per mile

Data per 0.1 mile

Data per 0.1 mile

150

200

IRI (in/mile)

IRI (in/mile)

Data per 0.1 mile
IRI (in/mile)

IRI (in/mile)

Data sampled per mile

300
250
200
150
100
50
0

150
100
50
0

100
50

0
0

2

4

6

8

10

12

14

16

18

58

60

62

64

66

68

70

72

74

76

78

80

d) Mile point along SRID 005 (composite), WSDOT
Year 2002

c) Mile point along I-94 (composite), MDOT
Year 2001, control section 81104

Figure 4.1 Continuous and sampled IRI data along four roads in four different states

83

Transverse crack length (feet)

400
300
200
100
0
321

Transverse crack length (feet)
.

Data per 0.1 mile

Data sampled per mile

120

Data per 0.1 mile

60
30
0
2
4
6
8
10 12 14 16
c) Mile point along I-94 (composite), MDOT
Year 1993, control section 81104

18

Data per 0.1 mile

1000
800
600
400
200
0
0

90

0

Data sampled per mile

323
325
327
329
331
333
a) Mile point along HWY 24 (flexible), CDOT
Year 1999
Transverse crack length (feet)

Transverse crack length (feet)

Data sampled per mile

500

2
4
6
8
10
b) Mile point along LA-34 (flexible), LADOTD
Year 1995, control section 0.12304
Data sampled per mile

400
350
300
250
200
150
100
50
0
58

Data per 0.1 mile

60 62 64 66 68 70 72 74 76 78 80
d) Mile point along SRID 005 (composite), WSDOT
Year 2008

Figure 4.2 Continuous and sampled transverse crack length data along four roads in four different states

84

through 76 along SRID 005 in Washington (Figure 4.2d). Nevertheless, similar results were
obtained for other roads and are shown in Figures B.5 through B.8 of Appendix B.
The above discussion regarding the sampling of the IRI and transverse cracking data
indicates that:
1.

For uniform pavement condition and distress (such as in a newly constructed or
rehabilitated pavement sections), the sampled data accurately represent the continuous
data. Otherwise, when the pavement condition and distress are highly variable, the
sampled data significantly misrepresent the pavement condition and distress.

2.

In general, ten percent sampling appears to represent the sensor-based continuous data
more accurately than the image-based data (cracking). This is no surprise given the
methods that are used to collect the data. The IRI data are collected by laser sensors using
fully-automated techniques. On the other hand, the cracking data are collected using
semi-automated techniques that require the input of trained SHA or contractor employees
to review and digitize the video images of the pavement surface. Thus, human
subjectivity impacts the cracking data as one employee may view crack lengths and
severity levels different than another employee. As a result, the variability of the cracking
data is relatively high and consequently, the ability of ten percent sampling to represent
the continuous pavement distress is questionable.
Step 2 – One Year Data Variability/Range – In this step, for a given data collection

year, and for each one mile section along the road, the sampled and the range of the continuous
IRI and transverse cracking data were compared and studied. Figures 4.3 and 4.4 depict the
sampled and the range of the continuous IRI and transverse cracking data, respectively. In the
two figures, the sampled data for each one mile of the four roads are represented by a square

85

whereas the range of the continuous data along each mile is represented by the solid straight
lines. The intent of these figures is to convey the fact that the ten percent sampled data may be at
the low or high end or at the average of the continuous data. Stated differently, the sampled data
could underestimate or overestimate the continuous data or the true pavement conditions and
distress. For example, Figure 4.3a shows that for most mile points along HWY 24 in Colorado,
ten percent sampling results in underestimation of the continuous IRI data. That is, the sampled
data fall on the low end of the continuous data range. A similar scenario can be seen in Figure
4.3b for the IRI data along LA-34 in Louisiana. On the other hand, the sampled data along I-94
in Michigan appear to underestimate the IRI at some mile points and overestimate the data at
other mile points.
Perhaps the results are even more evident for the cracking data. Considering the data
shown in Figure 4.4b, it can be seen that the ten percent sampled transverse cracking data could
be as little as 0 feet of cracking for one mile of road while the continuous transverse cracking
data show a range from zero to 1500 feet for the same one mile pavement section. The reverse
scenario can also be seen in the same figure for the same road. The sampled data indicate that
approximately 1000 feet of transverse cracking is present along one mile of LA-34 starting at
mile point 7. However, the continuous data show that transverse cracking varies from zero to
1000 feet along the same one mile of road. The above discussion indicates that ten percent
sampling may significantly underestimate or overestimate the true pavement conditions and
distress.
The data in Figures 4.3 and 4.4 also indicate that data variability impacts the degree of
accuracy at which ten percent sampled data represent the continuous data. In the figures, the
length of each solid line represent the range or the variability of the ten data points along each

86

400
IRI (in/mile)

IRI (in/mile)

400
300
200
100

300
200
100
0

0
321

323

325

327

329

331

0

333

4

6

8

10

b)Mile point along LA-34 (flexible), LADOTD
Year 1997, control section 0.12304

a) Mile point along HWY 24 (flexible), CDOT
Year 1999

400

IRI (in/mile)

400
IRI (in/mile)

2

300
200
100
0

300

200
100
0

0

2

4

6

8

10

12

14

16

58 60 62 64 66 68 70 72 74 76 78 80
d) Mile point along SRID 005 (composite),
WSDOT Year 1999

c) Mile point along I-94 (composite), MDOT
Year 2001, control section 81104

Figure 4.3 Sampled (squares) and the range of the continuous IRI data for each mile

87

Transverse crack length (feet) .

Transverse crack length (feet)
.

400

300
200
100
0
321

323

325

327

329

331

333

2500
2000
1500

1000
500
0
0

2

6

8

10

b) Mile point along LA-34 (flexible), LADOTD
Year 1995, control section 0.12304

a) Mile point along HWY 24 (flexible), CDOT
Year 1999
400

400
Transverse crack length (feet)

Transverse crack length (feet)

4

300
200
100
0
0

2

4

6

8

10

12

14

16

c) Mile point along I-94 (composite), MDOT
Year 1993, control section 81104

300
200
100
0
58

60

62

64

66

68

70

72

76

78

80

d) Mile point along SRID 005 (composite), WSDOT
Year 2008

Figure 4.4 Sampled (squares) and the range of the continuous transverse cracking data for each mile

88

74

one mile of road. Thus, shorter solid lines indicate smaller range or lower variability and longer
lines indicate greater range or higher variability of the continuous data. The squares in the
figures, on the other hand, represent the sampled data. It can be seen that the sampled data (the
squares) represent the continuous data when the solid lines are short or the variability of the
continuous data is low. The above observations can be clearly seen in Figure 4.4d for the
transverse cracking data along SRID 005 in Washington. Smaller ranges of the transverse
cracking data such as at mile points 62 through 66 yield sampled data that are representative of
the continuous data. Wider ranges of the transverse cracking data such as at mile points 60, 61,
and 79 yielded sampled data that are not representative of the continuous data or the true
distribution of the pavement conditions and distress. Similar results were found for other roads
and are shown in Figures B.9 through B.16 of Appendix B.
Step 3 – Time Series Data Variability - The previous two steps addressed the
differences between the samples and the continuous IRI and transverse cracking data for a given
year. In this step, the effects of sampling on the differences between the continuous and the
sampled data were analyzed using the time series (multi-year) data for various roads from the
four SHAs. To accomplish this, the IRI and the transverse cracking data were sampled for each
data collection cycle or distress survey year. Similar to the previous two steps, for each year of
data and for each one-mile pavement section, the measured data along the first 0.1 mile long
segment was assumed to represent the pavement conditions along the entire one mile long
section. For each one mile pavement section and for each data collection year, the sampled data
were divided by itself producing the constant 100 percent line along the entire road. The
continuous data for each 0.1 mile long pavement segment within each one mile section was also
divided by the sampled data of that mile. This yielded the data points shown by the various

89

symbols in the figures. Each data symbol represents one data collection year as indicated in the
legend of each figure. Four examples of the results are shown in Figures 4.5 through 4.8.
The data in Figures 4.5 and 4.6 indicate that, for some miles along the roads, the
continuous IRI data may be more than 200 percent higher than the sampled data. For instance,
the continuous IRI data along mile point 321 of I-94 in Michigan (Figure 4.5) range from
approximately 120 percent to nearly 240 percent the sampled data. The data along mile point 330
of the same road can be as much as 250 percent the sampled data. Similar results can be seen for
various mile points along the roads in the other states. Regardless, in general, it can be stated that
most continuously measured IRI data lie within + 50 percent of the ten percent sampled data.
The data in Figures 4.7 and 4.8 show similar results for the transverse cracking data.
However, the differences between the continuously measured transverse cracking data relative to
the sampled data increase significantly. In some cases along each of the roads, the continuous
data may be more than 1000 percent greater than the sampled data. In fact, as it can be seen for I69 in Michigan shown in Figure 4.7, the continuous transverse cracking data may be as much as
approximately 9500 percent greater than the sampled data. Regardless, despite the significant
variation for some locations along each of the roads, it can be stated that, in general, most
continuously measured transverse cracking data are within + 100 percent of the ten percent
sampled data. It should be noted that the above discussion addresses two roads from two states
for IRI and two roads for the other two states for transverse cracking. The main reason is the size
of the figures and to avoid unnecessary repetition. Nevertheless, similar results for other roads
were obtained and are shown in Figures B.17 through B.48 in Appendix B.

90

Sampled

1999

2000

2003

2005

2007

Continuous IRI data as percent of the sampled data .

260
240
220
200
180
160
140
120
100
80
60
40
20
0
321

323

325

327

329

331

333

Mile point

Figure 4.5 Continuous time series IRI data as percent of the sampled data along a portion of the flexible HWY 24 in Colorado

91

Sampled

1997

2000

2003

2005

Continuous IRI data as percent of the sampled data .

450
400
350
300

250
200
150
100
50
0
0

2

4

6

8

10

Mile point

Figure 4.6 Continuous time series IRI data as percent of the sampled data along a portion of the flexible LA-34 (control section
0.12304) in Louisiana

92

Continuous transverse crack data as percent of the sampled .
data

Sampled

10000

1997

1999

2001

2005

2007

9000
8000
7000

6000
5000
4000
3000
2000
1000
0
0

2

4

6

8

10

12

Mile point

Figure 4.7 Continuous time series transverse crack data as percent of the sampled data along a portion of the rigid I-69 (control section
77024) in Michigan

93

Continuous transverse crack data as a percent of sampled
data

Sampled

1999

2000

2001

2002

2003

2004

2005

62

64

66

68

70

72

74

2006

2007

2008

4000
3500
3000
2500
2000
1500
1000
500

0
58

60

76

78

80

Mile point
Figure 4.8 Continuous time series transverse crack data as percent of the sampled data along the composite SRID 005 in Washington

94

Furthermore, one would expect the degree at which the ten percent sampled data
represent the continuous data to decrease as the pavement deteriorates over time without any
applied treatments. That is, the pavement condition and distress data increase and show higher
variability along the road as the pavement ages. Thus, the ten percent sampled data would likely
become less representative of the continuous data as shown in the previous sections. In order to
prove this point, the impacts of ten percent sampling on the historical time-series transverse
cracking data were also analyzed using the percent differences between the continuous and
sampled data relative to the sampled data of each pavement section. The maximum, minimum,
and average percentages were calculated and plotted for each data collection year and for various
roads in each state as shown in Figures 4.9 through 4.12.
The data in Figure 4.9a, for HWY 71 in Colorado, show that the range of the percent
difference between the continuous and the sampled transverse crack data increases from year
1999 to 2000 but decreases from year 2000 to 2001. From year 2001 to 2002, the range of the
percent difference increases again before decreasing significantly in year 2003. This can be
explained using the CDOT maintenance records. The records indicate that crack sealing
treatments were applied in 2002. Hence, the range of the percent difference between the
continuous and the sample data decreases in year 2003 (CDOT does not count sealed transverse
cracks). Stated differently, the crack sealing treatment in 2002 decreased the variability of the
transverse cracking data and hence, the differences between the sampled and continuous data
also decreased. It should be noted that the reduction in the range of the percent differences
between the sampled and the continuous data from 2000 to 2001 could be due to either data
variability or a treatment that was applied but not documented.

95

Percent differences between the
continuous and the sampled
transverse cracking data

Up to 15600 %, Sample = 1 ft,
Continuous = 156 ft
8000
6000
4000
2000
0
-2000
1998

1999

2000

2001

2002

2003

2004

Percent differences between the
continuous and the sampled
transverse cracking data

Year of data collection
a) HWY 71 (flexible), BMP 194-201

800
600
400
200
0
-200
1998

1999

2000
2001
2002
2003
Year of data collection
b) HWY 24 (flexible), BMP 321-334

2004

Figure 4.9 Maximum, minimum, and average percent differences between the continuous and the
sampled transverse cracking, relative to the sampled data, Colorado

96

Percent differences between the
continuous and the sampled
transverse crack data

Up to 3500 %, Sample = 1 ft,
Continuous = 35 ft
2500
2000
1500
1000
500
0
-500
1994

1996

1998
2000
2002
2004
2006
Year of data collection
a) LA-526 (rigid), BMP 0-13, control section 0.80908

Percent differences between the
continuous and the sampled
transverse cracking data

Up to 97300 %, Sample = 1 ft,
Continuous = 973 ft
1500
1250
1000
750
500
250
0
-250
-500
1994

1996

1998
2000
2002
2004
2006
Year of data collection
b) LA-1 (composite), BMP 0-12, control section 0.06404

Figure 4.10 Maximum, minimum, and average percent differences between the continuous and
the sampled transverse cracking, relative to the sampled data, Louisiana

97

Percent differences between the
continuous and the sampled
transverse cracking data

Up to 13050%, Sample = 1 ft,
Continuous = 130.5 ft

8000
6000
4000
2000
0
-2000
1992

1994

1996

1998

2000

2002

2004

2006

2008

Year of data collection
a) I-94 (composite), BMP 0-18, control section 81104

Percent differences between the
continuous and the sampled
transverse cracking data

Up to 23200%, Sample = 1 ft
Continuous = 232 ft
2000
1500
1000
500
0
-500
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010
Year of data collection
b) US-31 (flexible), BMP 0-18, control section 61075

Figure 4.11 Maximum, minimum, and average differences between the continuous and the
sampled transverse cracking, relative to the sampled data, Michigan

98

Percent differences between the
continuous and the sampled
transverse cracking data

1200
1000

800
600
400
200

0
-200
1998

2000

2002

2004

2006

2008

2010

Percent differences between the
continuous and the sampled
transverse cracking data

Year of data collection
a) SRID 161 (composite), BMP 8.93-17.93

4000
3500
3000
2500
2000
1500
1000
500
0
-500
1998

2000

2002

2004

2006

2008

2010

Year of data collection
b) SRID 005 (composite), BMP 59.7-79.7

Figure 4.12 Maximum, minimum, and average percent differences between the continuous and
the sampled transverse cracking, relative to the sampled data, Washington

99

No maintenance records were available for HWY 24 in Colorado (Figure 4.9b); however,
it is likely that no treatments were applied between 1999 and 2003 (no distress data were
collected in the years 2001 and 2002). This is evidenced by the fact that the range of the percent
differences between the continuous and the sampled data increases from 1999 to 2003.
Furthermore, the average transverse crack length increases from approximately 177 feet in 1999
to nearly 231 feet in 2003. Thus, the transverse cracks are becoming more variable over time and
the range of the percent differences increases.
Similarly, the data in Figure 4.10a for LA-526 in Louisiana can also be explained using
the maintenance records of the LADOTD. The records indicate that concrete pavement patching
treatments were applied in 1998, 1999, 2000, and 2005. Hence, the decreases in the range of
percent differences between the continuous and the sampled data from 1997 to 2000 as well as
from 2003 to 2006 coincide with the reduction in pavement distress variability due to the
patching treatments. Stated differently, as the transverse cracking becomes more uniform (due to
pavement treatments), the sampled data more accurately represent the continuous data.
No maintenance records were available for LA-1 (Figure 4.10b) but it is likely that some
type of pavement treatment was applied between years 2000 and 2003. This is because the range
of the percent differences between the continuous and the sampled data increase from 1997 to
2000 but shows a significant decrease in 2003. Maintenance records were also not available from
MDOT for I-94. However, the data in Figure 4.11a appear to correspond to pavement treatments
between 1993 and 1995 as well as between 1997 and 1999. Further, the ten percent sampled data
do not accurately represent the continuous data along the newly reconstructed section of US-31
in Michigan shown in Figure 4.11b. The premature transverse cracking data along the road are
highly variable with an anomaly in 1997.

100

Finally, the data in Figure 4.12a show little to no percent differences between the
continuous and the sampled data from years 2003 to 2007 along SRID 161 in Washington. The
maintenance records from WSDOT show that in 2004 and 2005 the existing roadway was
resurfaced and planed. It is possible that this work could have begun in 2003 and was not
documented until 2004 and 2005. Thus, the variability of the transverse cracking data was
reduced causing the percent differences between the continuous and the sampled data to
decrease.
WSDOT maintenance records do not show any treatments for SRID 005 (Figure 4.12b)
between the years 1998 and 2008. The slight decrease in the range of percent differences
between the continuous and the sampled data from one year to the next (i.e. 2001 to 2002, 2003
to 2004, and 2006 to 2007) is likely due to the transverse cracking data variability.
It is important to note that, in most cases of Figures 4.9 through 4.12, the averages of the
percent differences between the continuous and the sampled transverse cracking data are almost
zero. Yet, the ranges of the percent differences are significant. Hence, it is misleading to
compare the average of the sampled data to the average of the continuous data.
Regardless, in general, the data in Figures 4.9 through 4.12 indicate that as the pavement
ages and the pavement conditions become more variable, sampled data do not accurately
represent the continuous data. Hence, the errors due to sampling increase as the pavement ages
and the pavement surface conditions and distress show higher degrees of variability. Inversely,
after the application of pavement treatment actions, the pavement conditions become more
uniform and the sampled data more accurately represent the continuous data. Therefore, as it has
been stated in previous sections, the accuracy of ten percent sampling is a function of the data
variability along the road.

101

4.2.2 Random Sampling
In the previous section of this thesis, fixed sampling technique was used where the
pavement condition and distress of the first 0.1 mile long segment of each one mile pavement
section were assumed to represent the pavement conditions and distress along the entire one
mile. In this section, random sampling technique was used. Since each one mile of road consists
of ten 0.1 mile pavement segments, for each survey year and for each one mile section along
various roads from the four states, a random number between one and ten was generated. The
random number was then used to select the 0.1 mile pavement segment along each mile that
would be used as the sample. For example, if the random number was four then the pavement
condition and distress data of the fourth 0.1 mile long segment of a given one mile road section
was assumed to represent the pavement condition and distress along that entire mile. Hence, the
randomly selected 0.1 mile long pavement segment may or may not be the same segment from
one data collection cycle to the next.
For each analyzed road, the differences between the ten percent sampled and the
continuous pavement condition and distress data were studied. For each one mile of road, the
randomly sampled data consists of one data point whereas the continuous data provides ten
points. The solid lines shown in Figure 4.13 depict the sampled IRI data while the individual data
points in the figure represent the continuous IRI data for each 0.1 mile segment of the road.
Likewise, the sampled and continuous transverse cracking data along four roads are shown in
Figure 4.14.
The data in Figures 4.13 and 4.14 show similar results to those that have been discussed
in the previous section for the fixed sampling analysis. To avoid redundancy, only four roads
from the CDOT are shown in the figures. Similar results were obtained for the other roads and

102

are shown in Figures B.49 through B.52 of Appendix B. Examination of the data in Figures 4.13
and 4.14 indicate that, for both IRI and transverse cracking, the higher is the variability of the
continuous data, the higher are the differences between the sampled and the continuous data. The
specific observations are stated below.
1.

Except for approximately thirteen 0.1 mile long pavement segments (localized segments),
the continuous IRI data in Figure 4.13a for the thirteen miles long flexible pavement
section along HWY 24 in Colorado are uniform. Consequently, the sampled data
represent the continuous data throughout the thirteen miles section except at localized
segments of the road. At some of these localized areas, the continuous data are more than
four times greater than the sampled data.

2.

The measured IRI data for the twelve miles long rigid pavement section along I-70 shown
in Figure 4.13b are almost perfectly uniform. Thus, except for very few cases, the
sampled data represent the continuous data throughout the length of the road.

3.

The IRI data along the 6 mile long section of HWY 36 in Colorado shown in Figure
4.13c are also uniform. Consequently, except for few localized areas, the sampled data
represent the continuous data.

4.

Figure 4.13d shows high variability of the continuous IRI data of the seven miles long
flexible pavement section along HWY 71 in Colorado. The figure also shows that the
sampled data do not represent the continuous data along a majority of the road section;
some sampled data are twice or half the continuous data.

5.

The transverse cracking data along the twelve miles long rigid pavement section of I-70
in Colorado displayed in Figure 4.14b show no variation. Hence, the sampled data
perfectly represent the measured data.

103

Data sampled per mile

Data per 0.1 mile

200
150
100

Data per 0.1 mile

200
150
100

50

50

0

0
321

323
325
327
329
331
a) Mile point along HWY 24 (flexible)
Year 1999

Data sampled per mile

250

333

290

292

294

296

298

300

302

b) Mile point along I-70 (rigid)
Year 1999
Data sampled per mile

Data per 0.1 mile

Data per 0.1 mile

130

200

IRI (in/mile)

IRI (in/mile)

Data sampled per mile

250
IRI (in/mile)

IRI (in/mile)

250

150
100
50

110
90
70
50
30

0
48

49

50

51

52

53

194

54

c) Mile post along HWY 36 (composite)
Year 2003

196

198

200

d) Mile point along HWY 71 (flexible)
Year 1999

Figure 4.13 Continuous and randomly sampled IRI data per mile along four roads in Colorado

104

321

323

325

327

Transverse crack length (feet) .

Transverse crack length (feet) .

Data sampled per mile

450
400
350
300
250
200
150
100
50
0

Data per 0.1 mile

329

331

333

Data sampled per mile

450
400
350
300
250
200
150
100
50
0
290

Data sampled per mile

450
400
350
300
250
200
150
100
50
0
48

Data per 0.1 mile

50
52
c) Mile point along HWY 36 (composite)
Year 2003

294

296

298

300

302

b) Mile point along I-70 (rigid)
Year 1999

54

Transverse crack length (feet) .

Transverse crack length (feet) .

a) Mile point along HWY 24 (flexible)
Year 1999

292

Data per 0.1 mile

Data sampled per mile

450
400
350
300
250
200
150
100
50
0
194

Data per 0.1 mile

196
198
200
d) Mile point along HWY 71 (flexible)
Year 1999

Figure 4.14 Continuous and randomly sampled transverse cracking data along four roads in Colorado

105

6.

The variability of the continuous transverse cracking data for the other three roads shown
in Figures 4.14a, c, and d is much higher than the IRI data of Figure 4.13 or the
transverse cracking data of Figure 4.14b. As a result, the sampled data for these roads
often misrepresent the continuous data.
The six observations regarding the random sampling of the IRI and transverse cracking

data indicates that, as is the case for fixed sampling:
1.

For uniform pavement condition and distress (such as in a newly constructed or
rehabilitated pavement sections), the sampled data accurately represent the continuous
data. Otherwise, when the pavement condition and distress are highly variable, the
sampled data significantly misrepresent the pavement condition and distress.

2.

In general, ten percent sampling appears to more accurately represent sensor-based data
(IRI) as opposed to image-based data (cracking). This is mainly due to the data collection
methodologies as discussed in section 4.2.1 above.

4.2.3 Sample Size
Given that the results presented in the previous two sections of this thesis indicate that in
most cases, ten percent sampling does not accurately represent variable pavement conditions and
distress, additional analysis was performed to determine the impacts of sample size on the
differences between the sampled and the continuous data. Six sample sizes were used, ten
percent (the results are presented in the previous sections), twenty, thirty, forty, fifty, and sixty
percent. Results of the analysis for two roads in Michigan are shown in Figure 4.15. In the
analysis, it was assumed that for each one mile of pavement, the average distress along the
sampled lengths of 0.2, 0.3, 0.4, 0.5, and 0.6 mile of each mile independently represent the
distress along the entire mile. After calculating the average transverse cracking length along each

106

sample length, the continuous data for each 0.1 mile was divided by the sampled data. The
results for two pavement sections; one along I-94 (Figure 4.15a) and the other along US-31
(Figure 4.15b) in Michigan show similar trends. As it was expected, the differences between the
sampled and the continuous data decreases as the sample size increases. For example, consider
Figure 4.15a for a section of the composite pavement along I-94. The data in the figure indicate
that at 10 percent sample size, the continuous data could be as high as nearly 70 times the
sampled data. In this scenario, the sampled data indicate a transverse crack length of 1 foot while
the sampled data indicate 68.5 feet of transverse cracking. On the other hand, for the 60 percent
sample size, the continuous data could be as high as about ten times the sampled data. The
results for the flexible pavement section along US-31 indicate that the continuous data could be
as much as 17 times higher than the ten percent sampled data and only ten times higher for the
sixty percent sampling.
The sampling of pavement condition and distress data certainly reduces the cost of data
collection. However, the above observations indicate that the sampled data could produce both
accurate and misleading representations of the continuous data. Thus, there is a certain risk
associated with data sampling. The problem herein is the balance between the acceptable level of
risk and the level of cost savings. It is clear, from the data presented above from four SHAs, that
the risk level of data sampling is high when the pavement conditions and distress along the road
are highly variable. On the other hand, the risk level is relatively low for uniform pavement
conditions and distress. Consequently, the problem of data sampling cannot be addressed
accurately and comprehensively unless the impacts of data sampling on the accuracy of the
pavement management decisions can be determined. Knowing such impacts, the hidden cost of
sampling and the cost savings could be calculated and compared. Therefore, the impacts of

107

Maximum, minmum, and average
continuous/sampled transverse cracking
ratio
Maximum, minmum, and average
continuous/sampled transverse cracking
ratio

80

70
60
50
40
30
20
10
0
0

0.2
0.4
0.6
a) Sample size (mile) along I-94 (composite)
BMP 0-18,Year 2005, control section 81104

0

0.2
0.4
0.6
b) Sample size (mile) along US-31 (flexible)
BMP 0-18, Year 1999, control section 61075

18
16
14

12
10
8
6

4
2
0

Figure 4.15 Maximum, minimum, and average continuous/sampled transverse cracking ratio
versus sample size along two roads in Michigan

108

sampling on the accuracy of pavement management decisions are addressed in the next section.
Whereas the hidden cost of sampling is addressed in section 4.5 of this thesis.
4.3

Pavement Performance Data Sampling: Condition State Concept
In the previous sections, the differences between the continuous and the sampled

pavement condition and distress data were addressed. In this section, the effects of sampling the
pavement condition and distress data on the accuracy of pavement management decisions are
analyzed and discussed. The analysis is based on the magnitudes of the pavement condition or
distress and the pavement rates of deterioration. The condition or distress and the rate of
deterioration for each pavement segment in question are combined using the remaining service
life (RSL) concept. Various RSL brackets (ranges) are then used to form the pavement condition
states. The condition states are used to group pavement segments with similar RSL values as
explained in the next section. Please note that detailed discussion of the RSL concept can be
found in section 9.5 of Chapter 2.
For each road included in the analysis from each of the four SHAs, the analysis was
conducted using the same steps presented below.
Step 1 – Pavement Sections Identification – Construction and maintenance records
obtained from the CDOT, the LADOTD, the MDOT, and the WSDOT were examined to
identify a minimum of 6 miles long pavement sections where no maintenance or preservation
actions have been taken during at least three or more consecutive data collection cycles.
Step 2 – Acceptance Criteria – For each pavement section identified in step one, each of
the time series pavement condition and distress data were subjected to the two acceptance criteria
presented below. Note that, for each pavement condition and distress type, any 0.1 mile long
pavement segment that did not pass the two acceptance criteria was excluded from any further

109

analysis. Further, for both acceptance criterion, a 0.1 mile long pavement segment could be
accepted based on the IRI and/or the transverse cracking data and rejected based on other
condition or distress type(s).
1.

First Acceptance Criterion - Three Data Points – For each 0.1 mile long pavement
segment and for each pavement condition and distress type, the time-series data were
independently examined to determine whether or not the database contains a minimum of
three data points. The three data points are required to model the pavement condition and
distress using non-linear functions (any type of curve can be fit to two or one data
points). This acceptance criterion is not redundant to step 1 above because, during any
data collection cycle, the data along certain 0.1 mile long pavement segments may not
have been collected due to equipment malfunctioning, construction zones, traffic flow
and so forth.

2.

Second Acceptance Criterion - Positive Regression Parameters – All pavement
condition and distress data of each 0.1 mile long pavement segment that passed the first
acceptance criteria were subjected to this second acceptance criterion. The criterion
specifies that the time series data of each pavement condition and distress should
independently have positive slope (increasing condition or distress). Positive slope
implies positive regression parameters of the non-linear mathematical functions used to
model the data. Negative regression parameters imply that the pavement is healing itself
over time (improving condition or decreasing distress) without any treatments, which is
not reasonable. Negative slopes could be caused by temperature and/or moisture
variations from one data collection cycle to the next (which affect crack openings in all
pavement types and curling in rigid pavements), equipment calibration, and data

110

variability due to the image digitization processes from one data collection cycle to the
next.
Step 3 – Calculating RSL – For each 0.1 mile long pavement segment of each identified
pavement section in step 1, and for the pavement condition and distress data that passed the two
acceptance criterion, the data were modeled using the proper mathematical function (see Table
4.1). Note that, for cracking, the logistic function listed in Table 4.1 was divided into two parts,
exponential for newly constructed or treated pavement sections and power for older sections. The
main reason is that, in most cases, the four databases used in this study did not contain the
necessary number of time-series data points between two consecutive treatment actions to
support the data modeling using logistic function. Such function requires a minimum of five data
points to estimate the values of the regression parameters with an acceptable confidence level.
Nevertheless, in most cases, the 0.1 mile long pavement segments were newly treated; hence, the
cracking data were modeled using the exponential function. The regression parameters of all
models were calculated using the Microsoft Excel program. Based on the regression parameters,
the RSL of each 0.1 mile pavement section was calculated as the difference in time between the
last available data point and the time when the pavement conditions or distress are expected to
reach the pre-specified threshold value. The pre-specified threshold values used in the
calculation of RSL were 200 in/mile for IRI, 0.25 inch for rutting, and 250 feet of cracks for all
cracking data.
Step 4 – Simulating Sampling Using the Calculated RSL Values – The RSL values of
each 0.1 mile long pavement segment (using the continuous data) along each road included in the
analysis that were calculated in step 3 were used to simulate ten percent sampling. It was
assumed that for each one mile section of the road in question, the RSL of the first 0.1 mile

111

Table 4.1 Mathematical functions used to model the pavement condition and distress data
Pavement condition or
distress type and units

Model form

Generic equation

IRI (inch/mile)

Exponential

IRI   exp t

Rut depth (inch)

Power

Rut   t 

Cracking (feet)

Logistic (sshaped)

Crack 

Max

  exp

  t 







Where, α, β, γ, ω, θ, δ, and μ are regression parameters, t = elapsed time (year), and
Max = the maximum value of cracking (crack saturation threshold)

segment of each one mile represents the RSL of the entire mile For example, if the RSL of
beginning mile point (BMP) 0 was equal to 5 years then the RSL value of mile BMP 0 through
BMP 0.9 was also assumed to be 5 years.
Step 5 – Pavement Condition State Based on RSL Brackets - The calculated RSL
values were grouped into six brackets as listed in Table 4.2. Each of the six brackets is referred
to as a pavement condition state. As indicated in the table, the RSL range of the condition states
increases as the RSL value increases. This is because the accuracy of the calculated RSL values
decreases as the RSL value increases (prediction over long time periods). In addition, Table 4.2
provides a list of possible pavement treatment actions based on the pavement condition state and
RSL range. Explanation of the pavement condition states and the possible pavement treatment
actions listed in the table is provided below.

112

Table 4.2 Pavement condition state, RSL range, and probable pavement treatment actions
Pavement
condition state
1

0-2

2
3
4

3-5
6-10
11-15

5

16-25

6


RSL range (year)

>25

Pavement treatment
actions
Reconstruction or
major rehabilitation
Rehabilitation
Preservation
Preservation
Do nothing or light
maintenance
Do nothing

Pavement condition state one (RSL range 0 to 2 years) - In most cases, the pavement
segments in this condition state have deteriorated to the point that light rehabilitation or
preservation actions are not cost-effective. Hence, reconstruction or major rehabilitation
is the most probable action.



Pavement condition state two (RSL range 3 to 5 years) – Rehabilitation – Pavement
segments in this condition state have experienced significant deterioration and require
some rehabilitation actions.



Pavement condition state three (RSL range 6 to 10 years) – Pavement segments in this
condition state have experienced moderate deterioration and distress. Therefore,
preservation actions would likely extend the life of the pavement in a cost-effective
manner.



Pavement condition state four (RSL range 11 to 15 years) – Pavement segments in this
condition state have experienced minor distress and deterioration and their condition state
could be substantially improved by the application of certain preservation actions. These
actions would likely extend the life of the pavement and decrease its rate of deterioration.

113



Pavement condition states five and six (RSL range 16 to 25 years and greater than 25
years) - Pavement segments within these condition states are in good to excellent
condition and may have minimal distress such as minor cracking. Light maintenance
activities, such as crack sealing, are the most likely cost-effective options.
Nevertheless, the continuous and sampled RSL values were grouped into condition states

listed in Table 4.2. The purpose of such grouping is to determine the effects of sampling on the
accuracy of the pavement management decisions.
Step 6 – Number of 0.1 Mile Long Pavement Segments in Each Condition State –
For each road and each RSL bracket, the number of pavement segments within each condition
state were separately counted for the continuous and sampled data. The same numbers were then
divided by the total number of 0.1 mile long pavement segments along the road section in
question to obtain the percent of each road in the different condition states.
Step 7 – Changes in Condition State Due to Sampling – A change in the condition
state of a pavement segment, with no applied treatment, implies that the pavement segment has
deteriorated from one condition state to the next. For example, if the condition state of one 0.1
mile long pavement segment was 3 in 2005 and 1 in 2007, then the pavement condition state has
changed by 2 states in two years. In this study, for each data collection cycle, the condition state
based on the continuous data was compared to that based on the sampled data. Changes in the
condition states due to sampling imply that sampling affects the accuracy of the pavement
management decisions since project selection is based on the pavement condition state and its
distribution. Nevertheless, for each 0.1 mile pavement segment of each road included in the
analysis, the condition state of the sampled data was subtracted from the condition state of the
continuous data as shown by Equation 4.1. The results (the number of condition states changed)

114

could be negative or positive. For instance, if the condition state based on the continuous data is
1 and the sample indicated a condition state of 5, the number of condition states changed is -4.
On the other hand, if the continuous condition state is 5 and the sample indicates a condition
state of 1, there is a condition state change of + 4.
Changes in condition state = continuous condition state – sampled condition state

Eq. 4.1

Results of the analyses for eight roads, two roads from each of the four SHAs, shown as
the percent of the road that changed a certain number of condition states based on the IRI data
are listed in Table 4.3 and depicted in Figures 4.16 and 4.17.
Table 4.3 Percent of each road changing certain number of condition states based on the IRI data
Percent of each road that changed the stated number of condition states

Length
(mile)

-5

-4

-3

-2

HWY 24

13

0.0

0.0

0.0

3.9

I-70

6

0.0

1.7

US-90

11

2.0

US-80

14

I-94

State

Road

-1

0

1

2

3

4

5

8.5

2.3

0.8

1.6

0.0

5.1

11.9 16.9 22.0 18.6

3.4

8.5

10.2 1.7

0.0

2.0

10.9

8.9

30.7 17.8 14.9

8.9

1.0

3.0

0.0

0.0

1.4

5.1

13.0 34.8 23.9 13.0

5.8

1.4

1.4

18

0.0

0.0

0.0

5.0

12.8 52.8 18.3

6.1

5.0

0.0

0.0

US-131

16

0.0

0.0

0.0

3.8

16.3 53.8 15.6

5.6

5.0

0.0

0.0

SRID 161

9

0.0

0.0

3.8

8.8

21.3 47.5 17.5

1.3

0.0

0.0

0.0

SRID 020

8

1.3

2.5

5.0

2.5

13.8 58.8 10.0

3.8

2.5

0.0

0.0

95

0.1

0.4

1.5

6.0

15.0

6.5

4.3

1.2

0.6

17.1 65.9

CO

LA

MI

WA

Total network

115

47.8

16.7

80.0
Percent of road

Percent of road

80.0
60.0
40.0
20.0

60.0
40.0
20.0
0.0

0.0
-5 -4 -3 -2 -1 0 1 2 3 4
Numbers of condition state change

-5

5

-3 -2 -1 0 1 2 3 4
Numbers of condition state change

5

b) I-70 (flexible), BMP 261-267, CDOT

a) HWY 24 (flexible), BMP 321-334, CDOT

60.0
Percent of road

60.0
Percent of road

-4

40.0
20.0
0.0

40.0
20.0
0.0

-5 -4 -3 -2 -1 0 1 2 3 4
Numbers of condition state change

5

-5

-4

-3 -2 -1 0 1 2 3 4
Numbers of condition state change

5

c) US-90 (flexible), BMP 0-11,control section 0.0031, LADOTD
d) US-80 (flexible),BMP 0-14, control section 0.00107, LADOTD
Figure 4.16 Percent of two roads in Colorado and two in Louisiana versus the numbers of condition state change, IRI data

116

60.0
Percent of road

Percent of road

60.0
40.0
20.0

20.0
0.0

0.0
-5

-4

-3 -2 -1 0 1 2 3 4
Numbers of condition statechange

-5

5

-4

-3 -2 -1 0 1 2 3 4
Numbers of condition state change

5

b) US-31(flexible), BMP 0-18, control section 61075, MDOT

a) I-94 (composite), BMP 0-18, control section 81104, MDOT

80.0
Percent of road

80.0
Percent of road

40.0

60.0

40.0
20.0
0.0

60.0

40.0
20.0
0.0

-5 -4 -3 -2 -1 0 1 2 3 4
Numbers of condition state change

5

-5

-4

-3 -2 -1 0 1 2 3 4
Numbers of condition state change

c) SRID 161(composite), BMP 8.93-17.93, WSDOT
d) SRID 020 (flexible), BMP 32.61 to 40.61,WSDOT
Figure 4.17 Percent of two roads in Michigan and two in Washington versus the numbers of condition state change, IRI data

117

5

Examination of the data listed in Table 4.3 and depicted in Figures 4.16 and 4.17 indicate
that the percent of each road where the sampled and the continuous data produce the same
condition states varies from 24.1 percent for I-70 in Colorado to about 66.1 percent for HWY 24
in Colorado. The percentage for each road is detailed below.


For HWY 24 in Colorado shown in Figure 4.16a, the sampled and continuous data show
no condition state differences for about 66 percent of the pavement segments. That is, ten
percent sampling produces no condition state changes for about 66 percent of the 13 mile
section of HWY 24 whereas 34 percent of the pavement segments change condition
states.



For the 6 miles long section along I-70 in Colorado shown in Figure 4.16b, only 22
percent of the section does not change condition states due to sampling while78 percent
do change condition states as a result of sampling.



For the 11 miles long section along US-90 in Louisiana shown in Figure 4.16c about 26
percent of the pavement segments do not change pavement condition states due to
sampling. However, 74 percent of the pavement section changes condition states.



Figure 4.16d, for US-80 in Louisiana, shows that about 38 percent of the road does not
change pavement condition states due to sampling, whereas 62 percent changes condition
states.



For I-94 and US-31 in Michigan shown in Figures 4.17a and 4.17b, respectively, and for
the eight miles long section along SRID 020 in Washington shown in Figure 4.17d,
approximately 55 percent of the pavement sections do not change condition states from
the sampled to the continuous data. Stated differently, ten percent sampling precipitates

118

differences in the sampled and continuous condition states for about 45 percent of each of
the three roads.


For the nine miles long section along SRID 161 in Washington shown in Figure 4.17c,
approximately 48 percent of the pavement section does not change condition states from
the sampled to the continuous data.
Finally, the eight roads listed in Table 4.3 were combined as one network and the

percentages of the network that changed the indicated number of condition states are listed in the
bottom row of the table and are shown in Figure 4.18. The data listed at the bottom row of Table
4.3 indicate that the effects of ten percent sampling on the condition states are:


About 48 percent of the eight roads (the network) did not change condition states. That is
the condition states based on the sampled data were the same as those based on the
continuous data. Please note that the 48 percent is an average value, the actual percentage
along the network varies from 66.1 to 24.1 percent.



The condition state of about 32 percent of the road network changed one state.



The condition state of about 13 percent of the eight roads changed up or down by 2 states
which is equivalent to approximately 8 years.



The condition states of the remaining 7 percent of the eight roads changes up or down by
3 or more states. This is equivalent to 13 or more years.

In addition, as it was expected, the percent of the network that changed the various condition
state numbers is almost normally distributed amongst all condition states as shown in Figure
4.18. The normal distribution of the differences between the condition states based on the
continuous data and those based on the sampled data may lead some to conclude that on average,
the sampling error is zero. Such conclusion will be unfounded and misleading.

119

60.0

Percent of network

50.0

40.0

30.0

20.0

10.0

0.0
-5

-4

-3

-2

-1

0

1

2

3

4

5

Numbers of condition state change

Figure 4.18 Distribution of the numbers of condition state change based on IRI data for the approximately 97 mile network

120

Indeed, ten percent sampling of the pavement condition data may cause errors in one or all of the
following decisions:


The selection of optimum time and space (project boundaries) for the pavement
preservation and rehabilitation programs since ten percent sampling causes over and/or
underestimation of the condition state (RSL) of certain percentages of the road.



The selection of the pavement treatment type since the sampled pavement condition and
distress data may not represent the actual pavement conditions and distress and their
distribution along the pavement network.



The selection of the pavement treatment strategy since ten percent sampling yields
inaccurate distribution of the pavement condition states before treatment.
Similar condition state analyses were performed on the rut depth and longitudinal

cracking data of the four SHAs. To avoid repetition and facilitate clarity, results of the analyses
along two roads (SRID 020 and SRID 005 from the WSDOT) are presented and discussed.
Figure 4.19 depicts the percent of road versus the numbers of condition states changed based on
the rut depth and longitudinal cracking data. Figures 4.19a and 4.19b show approximately 50
percent of the road along SRID 020 and about 25 percent of SRID 005 did not change condition
states due to sampling. These results were expected and are similar to the IRI results because
both data (rut depth and IRI) are automatically collected by sensors as described previously in
this chapter. The condition states of the remaining 50 percent of SRID 020 and the remaining 75
percent of SRID 005 changed from + 1 to + 4 condition states. Similar to the IRI scenarios
presented above, the condition states changes would result in different pavement management
decisions. Finally, given that the variability of sensor collected data is much lower than the

121

image collected data, it should be expected that the effects of sampling on the image based data
is much higher than the sensor collected data.
Figures 4.19c and 4.19d depict the results of the analyses of the longitudinal cracking
data along sections of SRID 020 and SRID 005. It can be seen that ten percent sampling of the
longitudinal cracking data caused the condition states based on the continuous data to:


Change for about 50 percent of SRID 020 while the condition states of the other 50
percent remained the same.



Change for about 70 percent of SRID 005 while the condition states of the other 30
percent remained the same.



Change by 5 condition states or + 20 years for about 20 percent of SRID 020 and more
than 10 percent of SRID 005.
Relative to the IRI and rut depth data, the higher differences between the RSL brackets

based on the sampled and those based on the continuous data were expected and confirm the
statement made earlier that image based data have higher variability and therefore the sampled
data have higher errors. The high percentages of the two roads changing condition states would
pose significant problems for the SHAs and their decisions regarding the selection of costeffective fix time, project boundaries (discussed in the next section), and fix type. If one is to
examine the bigger picture, such errors force the SHA staff in the various regions to lose
confidence in the PMS data and hence, ignore it. In fact, this could be one of the most damaging
scenarios for any highway agency. Pavement management decisions may be made without any
reference to the data; hence, making the data unnecessary and ineffective.

122

60.0
Percent of road

Percent of road

60.0
40.0
20.0

20.0
0.0

0.0
-5 -4 -3 -2 -1 0 1 2 3 4
Numbers of condition state change

-5 -4 -3 -2 -1

5

0

1

2

3

4

5

Numbers of condition state change

a) SRID 020 (flexible), BMP 32.61 to 40.61, rut depth

b) SRID 005 (composite), BMP 59.7 to 79.7, rut depth

60.0

60.0
Percent of road

Percent of road

40.0

40.0
20.0
0.0

40.0
20.0
0.0

-5

-4

-3

-2

-1

0

1

2

3

4

5

Numbers of condition state change
c) SRID 020 (flexible), BMP 32.61 to 40.61, longitudinal
cracking

-5 -4 -3 -2 -1

0

1

2

3

4

5

Numbers of condition state change
d) SRID 005 (composite), BMP 59.7 to 79.7, longitudinal
cracking

Figure 4.19 Percent of two roads in Washington versus the numbers of condition state change, rut depth and longitudinal cracking data

123

4.4

Pavement Project Boundary Analysis
In this section, the effects of 10, 20, 30, 40, 50, and 60 percent sample sizes on the

selection of project boundaries are analyzed and discussed. The analyses were conducted using:
1.

The continuous and sampled pavement condition and distress data for six pavement
sections; two sections from each of the CDOT, MDOT, and WSDOT.

2.

The RSL values based on the continuous and the sampled data for the six road sections.

3.

The AASHTO unit delineation by cumulative differences method, referred to herein as
the AASHTO unit delineation method, to determine the project boundaries based on
uniform pavement sections. The method consists on the calculation of the various
variables or parameters listed in Table 4.4. The project boundaries are defined by the
locations where the slope of the variable Zx as a function of the distance X along the
project changes sign from positive to negative and vice versa (ARA, Inc. 2004).
Table 4.4 illustrates the equations and solution sequence required to execute the

AASHTO unit delineation method. The table and entries are self-explanatory. In order to
promote clarity and understanding, Table 4.5 illustrates the solution sequence using IRI data
from a two mile long section of the flexible HWY 24 in Colorado. The results (the variable Zx as
a function of X or BMP) are shown in Figure 4.20 where the boundaries of three projects are
defined by the three solid lines in the figure. One project extends from BMP 321 to BMP 322,
one from 322 to 322.7, and the third from 322.7 to 323. In some scenarios and for cost-effective
purposes, some SHAs specify a minimum pavement project length. In this study, a minimum
project length of one mile was used. Hence, the three projects in Figure 4.20 were consolidated
into the two projects shown in Figure 4.21.

124

Table 4.4 Solution sequence of the AASHTO unit delineation method (after AASHTO 1993)
Column
1
i
BMP

Column Column Column
2
3
4
Pavement
condition Interval Interval
or
number length
distress
(n)
(Δxi)
(ri)

Column 5

Column 6

Column 7

Column 8

Column 9

Cumulative
interval length
(CD)

Average
interval
condition or
distress (ri)

(Pavement
condition or
distress)*
(Interval
length) (ai)

Cumulative
area (CA)

Cumulative
difference
variable Zx =
Column 8 F*Column 5

CD1   ΔXi

r1 

1 i
 ri  a1 = r1Δx1
2 i 1

CA1   ai

Zx1 = CA1 -

CD 2   ΔXi

1 i
r2   ri  a2 = r2Δx2
2 i 1

CA 2   ai

Zx2 = CA2 -

1 i
r3   ri  a3 = r3Δx3
2 i 1

CA 3   ai

Zx3 = CA3 –

…

…

n

1

2

3
…

BMP1
BMP2

r1
r2

N1
N2

Δx1
Δx2

i1
n

i1
n

BMP3

r3

N3

Δx3

CD3   ΔXi

…

…

…

…

…

i1



n

n

BMPn

rn

Nn

Δxn

CD n   ΔXi
i1

…

1 i
rn   ri  an = rnΔxn
2 i 1

i

i 1
i

i 1
i

125

F*CD2
F*CD3

i 1
i

Zxn = CAn –

i 1

F*CDn

CA n   ai

F

BMP = Beginning mile point
Interval number = the data point number along the project

F*CD1

CA n
CD n

Table 4.5 Example of the solution sequence of the AASHTO unit delineation method using IRI data for 2 miles of HWY 24 in Colorado
Column 1 Column 2
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Column 3

Column 4

Column 5

Column 6

BMP

IRI
(in/mile)

Interval
number

Interval
length
(mile)

Cumulative
interval length
(mile)

Average
interval IRI
(in/mile)

321
321.1
321.2
321.3
321.4
321.5
321.6
321.7
321.8
321.9
322
322.1
322.2
322.3
322.4
322.5
322.6
322.7
322.8
322.9

163
117
116
128
78
94
88
87
88
110
134
174
212
163
172
213
218
148
130
96

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1

0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0

163
140
116.5
122
103
86
91
87.5
87.5
99
122
154
193
187.5
167.5
192.5
215.5
183
139
113

BMP = Beginning mile point
Interval number = the data point number along the project

Column 7

Column 8

Area =
Cumulative
IRI*(interval
area
length)
16.3
14.0
11.7
12.2
10.3
8.6
9.1
8.7
8.8
9.9
12.2
15.4
19.3
18.8
16.8
19.3
21.6
18.3
13.9
11.3

16.3
30.3
42.0
54.2
64.5
73.1
82.2
90.9
99.7
109.6
121.8
137.2
156.5
175.2
192.0
211.2
232.8
251.1
265.0
276.3
CAn = 276.3
F = 138.125

126

Column 9
Zx value
2.49
2.67
0.51
-1.10
-4.61
-9.83
-14.54
-19.60
-24.66
-28.58
-30.19
-28.60
-23.11
-18.17
-15.24
-9.80
-2.06
2.42
2.51
0.00

5.00
0.00

-5.00

Zx

-10.00
-15.00
-20.00
-25.00
-30.00
-35.00
321

321.5

322
Beginning mile point

322.5

323

Figure 4.20 Cumulative differences versus beginning mile point along the flexible HWY 24 in
Colorado showing three pavement projects
5.00
0.00
-5.00

Zx

-10.00
-15.00
-20.00
-25.00

-30.00
-35.00
321

321.5

322
Beginning mile point

322.5

323

Figure 4.21 Cumulative differences versus beginning mile point along the flexible HWY 24 in
Colorado showing two pavement projects

127

In reality, various scenarios exist for short projects. These scenarios include:
1.

The pavement conditions and distress along the short project do not require any action. In
this case, the short project is a “do-nothing” project.

2.

The pavement conditions and distress along the short project require treatment actions
while the adjacent long project is a “do-nothing” project. In this case, the short project
could be handled by the SHA or by contractor depending on the pavement needs.

3.

The pavement conditions and distress along the short project require treatment actions
similar to those of the adjacent long project. In this case, the two projects could be
combined.

4.

The pavement conditions and distress along the short project require treatment actions
that are substantially different than those along adjacent long projects. In this case, the
two projects can be combined into one contract that specifies the various treatments and
their locations.
As stated earlier, pavement project boundary analyses were completed for six pavement

sections, two from each of the CDOT, MDOT, and WSDOT. The analyses were conducted using
the continuous and sampled pavement condition and distress data and RSL data, coupled with
the AASHTO unit delineation method described above. Results of the analyses are presented and
discussed in the following subsections.
4.4.1 Pavement Project Boundary Analysis: Condition and Distress Data Approach
For each of the six pavement sections, the AASHTO unit delineation method was used to
delineate the continuous and the sampled pavement condition and distress data. The sampled
data for each sample size were obtained by assuming that for each one mile of pavement, the
average condition and distress along the sampled lengths of 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 mile of

128

each mile independently represent the condition and distress along the entire mile. The effects of
10, 20, 30, 40, 50, and 60 percent sample sizes on the identification of pavement project
boundaries were then analyzed by comparing the project boundaries identified using the
continuous condition and distress data to those using the sampled data. The analyses steps
detailed below were used for each pavement section.
Step 1 – Solution Sequence – For the continuous and sampled pavement condition and
distress data along each of the six pavement sections from the three SHAs, the solution sequence
of the AASHTO unit delineation method displayed in Table 4.4 and illustrated in Table 4.5 was
used to calculate the cumulative difference value at each BMP.
Step 2 – Project Boundary Identification – For the continuous and sampled pavement
condition and distress data along each pavement section, the cumulative difference values were
plotted as a function of the distance along the pavement section (the BMP). Example plots for a
portion of HWY 24 in Colorado are shown in Figures 4.22 and 4.23 where the cumulative
differences are based on the continuous and ten percent sampled IRI data, respectively. Plots for
the other sample sizes are similar. Using visual inspection, the project boundaries were defined at
the locations where there are changes in the slope (positive to negative or vice versa) of the
cumulative differences along the length of the pavement section. The black lines in Figures 4.22
and 4.23 indicate the various pavement projects and their boundaries. Note that where the data
indicate a pavement project length of less than one mile, the project was included as a part of a
longer adjacent project. It is important to notice that, for the continuous pavement condition and
distress data, ten cumulative difference values exist for each one mile along the pavement
section. However, for the sampled data, only one cumulative difference value exists for each one

129

mile. This is because the sampled data represent the pavement conditions or distress along the
entire mile.

100
80

Zx

60
40
20
0
-20
320

322

324

326
328
330
Beginning mile point

332

334

Figure 4.22 Project boundaries based on the AASHTO unit delineation method and the
continuous IRI data along 13 miles of the flexible HWY 24 in Colorado
100
80

Zx

60
40
20
0
-20
320

322

324

326
328
330
Beginning mile point

332

334

Figure 4.23 Project boundaries based on the AASHTO unit delineation method and the ten
percent sampled IRI data along 13 miles of the flexible HWY 24 in Colorado

130

Step 3 – Comparison of the Results Based on the Pavement Condition and Distress –
To facilitate clarity and understanding, the project boundaries based on the continuous pavement
condition and distress data (100 percent sampled) and on the 10, 30, and 60 percent sampled data
were combined into one figure. Results of the 20, 40, and 50 percent sample sizes were similar
to the results of the other sample sizes and thus, they are not included in the figure to avoid
congestion. Figures 4.24, 4.25, and 4.26 show the pavement project boundaries based on the
continuous and sampled IRI data along a 13 miles long section of HWY 24 in Colorado, 18 miles
section of I-94 in Michigan, and 8 miles long section of SRID 161 in Washington, respectively.
In each figure, the data points represent the identified pavement project boundaries. Results of
the analysis for the other types of pavement condition and distress data are similar to those
shown for the IRI data and are shown in Figures B.53 through B.55 of Appendix B.

6 projects

6 projects

4 projects

5 projects

Sample size (percent)

10

30

60

100

321

323

325

327

329

331

333

335

Beginning mile point
Figure 4.24 Project boundaries based on the continuous (100 percent sampled) and the sampled
IRI data along a section of the flexible HWY 24 in Colorado

131

4 projects

4 projects

2 projects

2 projects

Sample size (percent)

10
30
60

100

0

2

4

6

8

10

12

14

16

18

Beginning mile point
Figure 4.25 Project boundaries based on the continuous (100 percent sampled) and the
sampled IRI data along a section of the composite I-94 in Michigan

Sample size (percent)

5 projects

4 projects

4 projects

4 projects

10
30
60
100

8

10

12

14

16

18

Beginning mile point
Figure 4.26 Project boundaries based on the continuous (100 percent sampled) and sampled IRI
data along a section of the composite SRID 161 in Washington

132

Examination of the data in Figures 4.24 through 4.26 indicates that:


For HWY 24 in Colorado, shown in Figure 4.24, five pavement projects are identified
based on the continuous IRI data, six on the 10 and 30 percent sampled data and only
four on the 60 percent sampled data. Hence each of the 10, 30, and 60 percent sampled
data produce an absolute 20 percent difference in the number of projects relative to the
continuous data. Further, the first pavement project shown in Figure 4.24 extends from
BMP 321 to BMP 322 based on the continuous IRI data. Whereas the 10 and 30 percent
sampled data show that the same project extends from BMP 321 to BMP 323; a 100
percent difference relative to the continuous data. The 60 percent sampled data show that
the project extends from BMP 321 to BMP 326; a 500 percent difference relative to the
continuous data.



For I-94 in Michigan, shown in Figure 4.25, two pavement projects are identified based
on the continuous and the 60 percent sampled IRI data and four projects based on the 10
and 30 percent sampled data. Thus, the 10 and 30 percent sampled data exhibit 100
percent difference relative to the number of projects identified using the continuous data.
Further, the length of one of the pavement projects identified along I-94 varies from 11.5
miles long based on the continuous data to twelve miles long based on the 60 percent
sampled data and to seven miles long based on the 10 and 30 percent sample sizes. Thus,
depending on the sample size, the sampled data produce an absolute difference between
about 4 and 39 percent relative to the continuous data.



Similarly, the results for SRID 161 in Washington, depicted in Figure 4.26, indicate that
the variation in the number of pavement projects identified based on the continuous and
sampled data varies from 4 based on the continuous and the 30 and 60 percent sampled

133

data to 5 based on the 10 percent sampled data (a 25 percent difference). The identified
pavement project starting at BMP 8.93 varies in length from 4 miles based on the
continuous data to 3 miles based on the 30 and 60 percent sample sizes (a 25 percent
difference) and to 2 miles based on the 10 percent sample size (50 percent difference).
The above discussion indicates that the pavement project boundaries and the project
lengths based on the continuous pavement condition and distress data varies significantly from
those based on the sampled data. These variations are a function of the data variability along the
road. Higher variability produces higher variations in the project boundaries and project length.
These findings have significant implications for SHAs. For instance, if the sampled data indicate
that a pavement treatment project is only one mile long, but in reality, the project is three miles
long, the SHA may only budget one third of the necessary funds to properly treat the pavement.
The opposite scenario is also true; if the sampled data indicate that the pavement project is three
miles long, but in reality, the project is only one mile long, the SHA may budget three times the
necessary funds to properly treat the pavement. However, in most cases, the above scenarios do
not happen. The reason is that most SHAs rely heavily on field inspection before the allocation
of pavement expenditures. The main consequence of the differences between the sampled data
and the reality in the field is that most of the highway agency staff would lose faith in the PMS
data and disregard it. For an ideal PMS scenario, the pavement condition and distress data in the
PMS database should reflect the real scenario in the field. Analysis of the data should produce
the same or similar results that can be obtained through field inspection. Nevertheless, the use of
the sampled data to identify pavement project boundaries may produce significantly different
results from the field inspection and could result in significant misallocation of pavement
expenditures. This topic is discussed in detail in section 4.5.

134

Once again, the author realizes that the current state-of-the-practice for pavement project
boundary identification in most SHAs does not rely solely on the pavement condition and
distress data. Rather, pavement projects are typically identified by employees of the SHAs who
travel the pavement network and identify the boundaries by visual inspection of the pavement
conditions. The short coming of this approach is that the visual inspection does not tell the full
story regarding the pavement condition and distress. The missing element is the pavement rate of
deterioration, which can be obtained from the time series pavement condition and distress data.
However, if the PMS data show significant differences in the pavement condition and distress
than those observed in the field, the employees will lose faith and disregard the PMS data.
Unfortunately, the hidden cost of such loss in faith is very high (to the order of several
magnitudes higher than the savings due to sampling) and cannot be accurately estimated. In
addition, given the current financial situation of many SHAs, some could opt to reduce costs by
choosing to make pavement project boundary decisions based solely on the pavement condition
and distress data. If the SHA chose to further reduce costs by sampling the pavement condition
and distress data, the accuracy and cost-effectiveness of the pavement project boundary
identification could be lost and significant misallocation of pavement expenditures could occur
as explained in section 4.5.
In this section, results of the analyses of the differences between the continuous and the
sampled data in identifying pavement project boundaries based on the pavement condition and
distress data were presented and discussed. In the next section, the RSL concept is utilized in
order to further examine the impacts of data sampling on the identification of pavement project
boundaries. The analysis steps, results, and discussion based on the RSL concept are detailed in
the next subsection.

135

4.4.2 Pavement Project Boundary Analysis: RSL Concept
The AASHTO unit delineation method described in the previous sections was also used
to delineate the continuous and sampled RSL data of six pavement sections, two from each of the
CDOT, MDOT, and WSDOT. The effects of 10, 20, 30, 40, 50, and 60 percent sample sizes on
the identification of pavement project boundaries were analyzed and compared to the project
boundaries identified using the continuous RSL data. For each sample size, it was assumed that
for each one mile of pavement, the average RSL along the sampled lengths of 0.1, 0.2, 0.3, 0.4,
0.5, and 0.6 mile of each mile independently represent the RSL along the entire mile. Note that
the RSL was calculated according to the methods detailed in steps 2 and 3 of section 4.3.1.
Regardless, for each pavement section from the three SHAs, the same analysis steps were used
and they are detailed below.
Step 1 – Solution Sequence – For the continuous and sampled RSL data along each of
the six pavement sections from the three SHAs, the solution sequence of the AASHTO unit
delineation method displayed in Table 4.4 and illustrated in Table 4.5 was used to calculate the
cumulative differences at each BMP.
Step 2 – Project Boundary Identification – For the continuous and sampled RSL data
along each pavement section, the cumulative difference values were plotted as a function of the
distance along the pavement section (the BMP), similar to Figures 4.22 and 4.23. Using visual
inspection, the project boundaries were defined at the locations where there are positive to
negative changes in the slope, or vice versa, of the cumulative differences along the length of the
pavement section. Note that, as was the case for the condition and distress data, where the data
indicate a pavement project length of less than one mile, the project was included as a part of a
longer adjacent project.

136

Step 3 – Comparison of the Results Based on the RSL – To facilitate clarity and
understanding, the project boundaries based on the continuous RSL data (100 percent sampled)
and on the 10, 30, and 60 percent sampled data were combined into one figure. The 20, 40, and
50 percent sample sizes showed similar results that were not included in the figure to avoid
congestion. Figures 4.27, 4.28, and 4.29 show the pavement project boundaries for the
continuous and sampled RSL data based on the IRI along sections of HWY 24 in Colorado, I-94
in Michigan, and SRID 161 in Washington, respectively. In each figure, the data points represent
the identified pavement project boundaries. Results of the analysis for the RSL based on the
other types of pavement condition and distress data are similar to those shown in Figures 4.27
through 4.29 and are shown in Figures B.56 through B.58 of Appendix B.
Examination of the data in Figures 4.27 through 4.29 indicates that:


For HWY 24 in Colorado, shown in Figure 4.27, four pavement projects are identified
based on the continuous and the 10 percent sampled RSL data. Whereas six projects are
identified based on the 30 and 60 percent sampled data. Thus, the 30 and 60 percent
sample sizes have 50 percent difference relative to the number of projects based on the
continuous data. Further, one of the pavement projects shown in Figure 4.27 is six miles
long and extends from BMP 321 to BMP 327 based on the continuous and the10 percent
sampled RSL data. The same project is only two miles long and it extends from BMP 321
to BMP 323 based on the 30 and 60 percent sampled data. Thus, the absolute difference
between the 30 and 60 percent sample sizes and the continuous data is nearly 67 percent.

137

4 projects

6 projects

6 projects

4 projects

Sample size (percent)

10

30
60
100

321

323

325

327

329

331

333

335

Beginning mile point
Figure 4.27 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(IRI) data along a section of the flexible HWY 24 in Colorado
4 projects

4 projects

2 projects

4 projects

Sample size (percent)

10
30
60
100

0

2

4

6

8

10

12

14

16

18

Beginning mile point
Figure 4.28 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(IRI) data along a section of the composite I-94 in Michigan

138

Sample size (percent)

4 projects

5 projects

5 projects

4 projects

10
30
60
100

8

10

12

14

16

18

Beginning mile point
Figure 4.29 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(IRI) data along a section of the composite SRID 161 in Washington


For I-94 in Michigan, shown in Figure 4.28, four pavement projects are identified based
on the continuous, 10 percent, and 30 percent sampled RSL data. However, only two
projects are identified based on the 60 percent sampled data (50 percent absolute
difference). In addition, the four miles long pavement project, which extends from BMP
14 to BMP 18 based on the continuous data is seven miles long based on 10 percent
sampled RSL, 4 miles long based on the 30 percent sampled RSL, and 12 miles long
based on the 60 percent sampled RSL. Thus, depending on the sample size, the length of
a project based on the sampled data could be three times the length of the same project
based on the continuous data.



For the 8 miles long pavement section along SRID 161 in Washington, shown in Figure
4.29, four pavement projects are identified based on the continuous and 10 percent
sampled RSL data while five projects are identified based on the 30 and 60 percent

139

sample size. Stated differently, the 30 and 60 percent sample sizes exhibit 25 percent
difference from the continuous data. Further, the continuous and each of the sample size
data produce one mile long project starting at BMP 9. On the other hand, the continuous
data also produced a 5 mile long project starting at BMP 12. This project is broken into
three different projects based on the 30 and 60 percent sample size and to two and part of
a third project based on the 10 percent sample size. In all cases, there are significant
differences in the various project lengths depending on the sample size and the variability
of the data along the project.
The implications of the above findings are very much similar to those based on the
pavement condition and distress data. The next section details the hidden costs of data sampling
and possible implications for SHAs.
4.5

The Hidden Costs of Pavement Performance Data Sampling
The analyses results presented and discussed in the previous sections showed that

significant differences between the continuous and sampled data sets exist regardless of the data
analysis methods or sample sizes. These differences were shown using the pavement condition
and distress data, condition state concept, and RSL concept, as well as the AASHTO unit
delineation method. Given that the continuous data express the distribution of the pavement
condition and distress along the road more accurately than the sampled data; using sampled data
only may lead to inaccurate pavement management decisions relative to the true pavement needs.
Although data sampling decreases the cost of data collection, its hidden cost may be several folds
higher than the savings.
To illustrate this point, consider the total pavement expenditures and the costs of data
collection in three SHAs listed in Table 4.6. The total pavement expenditures, calculated as the

140

total disbursement less the administration and bridge disbursements for each state, ranges from
22,542 $/lane-mile in Colorado to 13,048 $/lane-mile in Louisiana and to 17,871 $/lane-mile for
Washington (Hartgen et al. 2009). Whereas the data collection cost ranges from 39.75 $/lanemile to 77.67 $/lane-mile and the data digitization cost ranges from 11.25 $/lane-mile to 40.00
$/lane-mile depending on the SHA (Fillastre 2011, Hartgen et al. 2009).
Suppose that the three SHAs listed in Table 4.6 sample the pavement condition and
distress data using a ten percent sample size. This entails obtaining pavement images along the
entire pavement network and digitizing only ten percent of the pavement network. Using the cost
data of each of the three SHAs and the network total lane-miles listed in Table 4.6, the following
calculations were made and the results are listed in Table 4.7:


The total pavement expenditure.



The cost of obtaining pavement images.



The cost of data digitization.



The total data collection costs.
As it was mentioned previously, the total pavement expenditure was estimated as the total

disbursement less the administration and bridge disbursements for each state (Hartgen et al.
2009). The potential total savings due to ten percent sampling were also calculated and are listed
in Table 4.7. For each state, 90 percent of the data digitization costs could be saved as a result of
ten percent sampling. On average, this savings is calculated at about $709,000. However, if ten
percent sampling were to cause a minimum error of only 10 percent, the average potential
misallocation, or the hidden cost of sampling based on the total pavement expenditure would be
greater than $44 million. Stated differently, on average, the potential hidden cost (misallocation
of funds) due to sampling is more than 63 times the savings. Hence, the potential misallocation

141

of funds significantly outweighs the savings in data digitization costs. This scenario becomes
even more dramatic considering that ten percent sampling produces significantly higher errors
than the assumed 10 percent minimum error. It should be noted, though, that the misallocated
expenditures may not be totally lost. Rather, the expenditures could be partially lost due to less
cost-effective treatment timing and types. Still, even if only a portion of the misallocated
expenditures are totally lost, the lost funds significantly outweigh the savings due to ten percent
sampling. The most hidden cost of sampling, though, may be the loss of faith in the PMS due to
inaccurate decisions based on the sampled data.
Table 4.6 Total pavement expenditure, data digitization, and total data collection costs for three
states (Fillastre 2011, Hartgen et al. 2009)

State

Colorado
Louisiana
Washington
Average

Network
(lane-miles)

Total pavement
expenditure
($/lane-mile)

Data
digitization
costs
($/lane-mile)

Total data
collection
cost ($/lanemile)

22,912
38,458
18,392
26,587

22,542

11.25

39.75

13,048

35.59

77.67

17,871

40.00

59.00

17,820

28.95

58.81

142

Table 4.7 Total expenditures, potential savings, and potential misallocation of funds as a result of the use of ten percent sampling for
various pavement networks

State

Colorado
Louisiana
Washington
Average

Network
(lanemiles)

22,912
38,458
18,392
26,587

Total
pavement
expenditure
($)

Data
imaging
cost ($)

516,482,304 652,992
501,799,984 1,618,313
328,683,432 349,448
448,988,573 873,584

Total
Data
data
digitization
collection
cost ($)
cost ($)
257,760
1,368,720
735,680
787,387

143

910,752
2,987,033
1,085,128
1,660,971

Potential
total savings
due to ten
percent
sampling ($)

Potential
misallocation
of expenditures
based on 10
percent error
($)

231,984
1,231,848
662,112
708,648

51,648,230
50,179,998
32,868,343
44,898,857

Ratio of
potential
misallocation
and total
savings for ten
percent
sampling
222.6
40.7
49.6
63.4

4.6

Pavement Analysis Length
Traditionally, the collected pavement condition and distress data are subjected to various

types of analysis. The most popular analysis type includes evaluation of the pavement
performance over time. In the current state-of-the-practice, the length of the pavement section to
be subjected to such performance analysis is constrained by the data collection procedures and
by the analysis details. Specifically, these constraints include:
1.

The pavement survey length along which the pavement condition and distress data are
measured and stored in the database. The length over which the condition and distress
data are analyzed, termed the pavement analysis length, cannot be shorter than the
pavement survey length. However, it can be longer by averaging the data over two or
more adjacent survey lengths. For example, if the pavement survey length is 0.1 mile, the
pavement analysis length is 0.1 mile or longer.

2.

The employed sampling technique and the length of the pavement section where the
collected distress data along the sample size are assumed to represent the pavement
condition and distress along that section. The pavement analysis length cannot be shorter
than that section; it could be longer by averaging the data over two or more adjacent
sections. For example, a SHA could survey one 0.1 mile long pavement segment of each
one mile of road and assume the condition and distress along the one mile are the same as
those along the 0.1 mile. Hence, the data are stored for each one mile of road. The
analysis length cannot be shorter than 1 mile but it can be much longer if the data from
two or more adjacent sections are averaged.

3.

The opinions of the technical staff of the agency. Some believe that data averaging over
longer pavement sections could decrease the data variability and improve data modeling.

144

The effects of data sampling on the variability of the pavement condition data and on the
accuracy of the PMS decisions are discussed in early parts of this chapter. In this section, the
effects of the data analysis length on the variability and modeling of the pavement condition and
distress data along projects are presented and discussed. The impacts of the pavement analysis
length on the accuracy of the PMS decisions are also scrutinized.
4.6.1 The Impacts of Pavement Analysis Length on the Variability and Modeling of
Pavement Performance Data
Recall that the CDOT, LADOTD, and WSDOT collect and store the pavement condition
and distress data for each 0.1 mile long pavement segment along the entire pavement network.
The data from more than 1,632 miles of pavement sections (16,320 0.1 mile long pavement
segments). Thus, for each data collection cycle, 16,320 data points were used to analyze the data
over pavement analysis lengths of 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 mile. The data
analysis steps presented below were used to scrutinize the pavement condition data modeling and
variability for each of the analysis lengths.
Step 1 – Data Mining – Construction and maintenance records obtained from the CDOT,
LADOTD, and WSDOT were examined to identify the boundaries (BMPs and EMPs) of
pavement projects where treatments were conducted in the past. The common treatments that
were considered include:
1.

Thin (< 2.5 inch) HMA overlay of asphalt surfaced pavements.

2.

Thick (> 2.5 inch) HMA overlay of asphalt surfaced pavements.

3.

Single chip seal.

4.

Double chip seal.

5.

Thin (< 2.5 inch) mill and fill of asphalt surfaced pavements.
145

6.

Thick (> 2.5 inch) mill and fill of asphalt surfaced pavements.

For each SHA and for each treatment type, the number of pavement sections or projects that
were identified for analysis, their cumulative length, and the total length of all projects in the
three states are listed in Table 4.8.
Table 4.8 The number of pavement projects and their total length identified for analysis in each state
Number and total length (miles) of pavement projects in
each state

The number of
projects and their
Treatment
length (miles) in all
Colorado
Louisiana
Washington
type
states
Projects Length Projects Length Projects Length Projects
Length
1
70
104.6
18
45.5
48
130.9
136
281
2
59
252
4
22.7
63
274.7
3
69
495.8
46
242.1
7
20.4
122
758.3
4
12
40.5
12
40.5
5
2
9.1
11
36.5
21
93
34
138.6
6
32
139
32
139
Total
141
609.5
178
755.6
80
267
399
1,632.1
Treatment type: 1 = Thin (< 2.5 inch) HMA overlay of asphalt surfaced pavements;
2 = Thick (≥ 2.5 inch) HMA overlay of asphalt surfaced pavements;
3 = Single chip seal;
4 = Double chip seal;
5 = Thin (< 2.5 inch) mill and fill of asphalt surfaced pavements;
6 = Thick (≥ 2.5 inch) mill and fill of asphalt surfaced pavements.
Step 2 – Analysis Lengths – The time series condition and distress data for each 0.1 mile
long pavement segment of each of the 399 pavement projects identified in step one were
downloaded from the PMS databases of each state. Prior to the data analysis, a thorough
examination of the pavement condition and distress data indicated that:
1.

The database has less than three data points for some of the 0.1 mile long pavement
segments and hence, these segments cannot be included in the analysis (see acceptance
criteria 1 in step 4 below).

146

2.

The rate of deterioration of a significant number of 0.1 mile long pavement segments is
negative (self healing) and hence, the data cannot be modeled.

3.

The first data collection cycle after treatment was accomplished a few months to two
years after treatment. Consequently, the first measured pavement condition and distress
data do not correspond to the time immediately after treatment. Although, the initial
pavement condition and distress immediately after treatment are not known, for some
treatments it can be assumed based on common sense and the state-of-the-practice. For
example, for thin and thick HMA overlay treatments and for thin and thick mill and fill
treatments, it can be reasonably assumed that the rut depth immediately after treatment is
0.0 inch. In this study, a rut depth of 0.01 inch rut depth at 0.01 year after treatment was
assumed (0.0 inch rut depth could not be assigned because of power function modeling
requirements). Such assumption increased the number of data points to be included in the
analysis, and increased the number of 0.1 mile long pavement segments that passed the
second acceptance criterion (see step 4 below). The above scenario implies that, in this
study, the rut depth data was modified by adding 0.01 inch rut depth data point
immediately after the treatment was completed.
Depending on the pavement condition and distress types, two methods were used to

calculate the pavement condition and distress data for pavement analysis lengths of 0.2, 0.3, 0.4,
0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 mile. The two methods are enumerated below.
1.

IRI and rut depth – The IRI and rut depth data for each analysis length were calculated as the
respective average IRI or rut depth of the corresponding number of 0.1 mile long segments
making up the analysis length. For example, the IRI and rut depth data for each one mile long
analysis length is the average of the ten data points corresponding to the ten 0.1 mile long
pavement segments along the one mile.

147

2.

Cracking – The cracking data for each analysis length were calculated as the sum of the data of
the corresponding number of 0.1 mile long pavement segments. For example, the cracking data
for each one mile analysis length is the sum of the ten data points corresponding to the ten 0.1
mile pavement segments along the mile.

Step 3 – Number of Analysis Sections - Although the analysis length methodology is
simple in nature, it is necessary to address the analysis technique employed at the end of
pavement projects. To illustrate, consider a 2.2 mile long pavement treatment project. When the
data is analyzed over a length of 0.5 miles, four 0.5 mile analysis lengths were obtained
accounting for the first two miles of the project. The 0.2 mile long left over pavement segment
was analyzed using the data from two 0.1 mile pavement segments and is counted as 0.4 or 40
percent of the 0.5 mile length. Therefore, in this example, the 2.2 mile long project length was
analyzed using 4.4 analysis lengths of 0.5 mile. In more general terms, the remaining length at
the end of a pavement treatment project is analyzed and counted as a fraction of an analyzed
section. For illustrative purposes and for each analysis length, the number of analysis sections for
the 2.2 mile long project is listed in Table 4.9. The same methodology was used for each
pavement treatment project regardless of the pavement or the treatment types.
Note that if the data of a certain 0.1 mile long pavement segment was missing, they were
treated as a blank cell during the analysis. For instance, if an analysis length included one or
more of 0.1 mile pavement segments without data, the value of the pavement condition and
distress for the analysis length was calculated as the average or the sum (depending on the
condition or distress type) of the remaining 0.1 mile long pavement segments with data. If all of
the 0.1 mile long segments did not have data, the analysis length was assigned no data (blank
cell). It is estimated that this method was used to account for blank cells in less than one percent
of the analyzed data.
148

Table 4.9 Number of analysis sections for various analysis lengths along a 2.2 mile long project

0.1
0.2
0.3
0.4
0.5
0.6
0.7

Number of analysis sections for a 2.2 mile long
pavement project
22.00
11.00
7.30
5.50
4.40
3.67
3.14

0.8
0.9
1.0

2.75
2.44
2.20

Analysis length (mile)

Step 4 – Data Acceptance Criteria – For each pavement treatment and analysis length
identified in steps one and two, it is possible that some data elements were not collected along
portions of the project in some years. It is also possible that the collected pavement condition and
distress data show decreasing distress over time without the application of any pavement
treatment. For these reasons, one may not be able to model the pavement condition data.
Therefore, for each pavement project and analysis length, the pavement condition and distress
were subjected to two acceptance criteria tests to determine whether or not the data could be
modeled using non-linear mathematical functions. The two acceptance criteria are:
1.

Acceptance criteria one - Three data points – A minimum of three data points before treatment
(BT) and a minimum of three data points after treatment (AT) are required to fit any non-linear
functions, since any model can be fit to two or one data points. Any pavement segment that did
not meet this criterion was excluded from any further analysis.

2.

Acceptance criteria two - Positive regression parameters – Positive BT and AT regression
parameters of the exponential and power functions are required for time series distress data that
are consistent for pavement sections that did not receive any treatment. Negative regression

149

parameters imply that the pavement is healing itself with time (decreasing distress) without any
treatments, which is not reasonable and would bias the analysis. One of the reasons for negative
regression parameters is the data variability over time.

Step 5 – Percent Acceptance – For each pavement treatment project (treatment type)
and analysis length in each state, and for each condition and distress type, the percent of the
pavement segments that passed the two acceptance criterion was calculated. The results for two
common treatment types (thin HMA overlay and single chip seal) from each state are shown in
Figures 4.30 through 4.35. Figures 4.30 through 4.32 display the results of the thin HMA overlay
treatment in Colorado, Louisiana, and Washington, respectively. Figures 4.33 through 4.35
display the results for the single chip seal treatment in each state. Results of the analysis for the
other treatment types in each state are similar and are shown in Figures C.1 through C.7 of
Appendix C.
It should be noted that an insignificant number of 0.1 mile pavement segments were
rejected based on acceptance criteria one. Most pavement segments had at least three data points
BT and three data points AT. Therefore, most pavement segments were rejected because they did
not satisfy acceptance criteria 2 (positive regression parameters). It is estimated that, of those
pavement segments that were rejected, 90 percent did not exhibit positive time series regression
parameters.
Examination of the data shown in Figures 4.30 through 4.32 for the thin HMA overlay
treatment in Colorado, Louisiana, and Washington indicates that the percent acceptance for most
pavement conditions and distress types fluctuate up and down with increasing analysis length
without following a specific trend. Hence, the results indicate that increasing the pavement
analysis length does not necessarily increase the number of pavement sections that can be
modeled. For instance, the IRI data shown in Figure 4.30 indicates that:
150

IRI

Rut depth

Longitudinal cracking

Alligator cracking

Transverse cracking

Percent acceptance, thin HMA overlay,
1,046 0.1 mile pavement segments

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure 4.30 Percent acceptance versus pavement analysis length, thin HMA overlay, Colorado
IRI

Rut depth

Longitudinal cracking

Alligator cracking

Transverse cracking

Percent acceptance, thin HMA overlay, 455
0.1 mile pavement segments

100.0

80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure 4.31 Percent acceptance versus pavement analysis length, thin HMA overlay, Louisiana

151

IRI

Rut depth

Longitudinal cracking

Alligator cracking

Transverse cracking

Percent acceptance, thin HMA overlay,
1,309 0.1 mile pavement segments

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure 4.32 Percent acceptance versus pavement analysis length, thin HMA overlay, Washington

IRI
Longitudinal cracking

Rut depth
Transverse cracking

Alligator cracking

Percent acceptance, single chip seal, 4,958
0.1 mile pavement segments

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure 4.33 Percent acceptance versus pavement analysis length, single chip seal, Colorado

152

Rut depth

Longitudinal cracking

Percent acceptance, single chip seal, 2,421
0.1 mile pavement segments

IRI

Alligator cracking

Transverse cracking

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure 4.34 Percent acceptance versus pavement analysis length, single chip seal, Louisiana

Rut depth

Longitudinal cracking

Percent acceptance, single chip seal, 204
0.1 mile pavement segments

IRI

Alligator cracking

Transverse cracking

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure 4.35 Percent acceptance versus pavement analysis length, single chip seal, Washington

153

1.

The percent acceptance remains around 60 percent as the analysis lengths increases from
0.1 mile to 0.5 mile.

2.

The percent acceptance increases from about 60 to about 70 percent as the analysis length
increases from 0.5 mile to 0.8 mile.

3.

The percent acceptance decreases from about 70 to about 65 percent as the analysis
length increases from 0.8 to 1.0 mile.

On the other hand, the percent acceptance data, for the rut depth in Figure 4.30 are almost
constant and they do not change as the analysis length increases from 0.1 mile to one mile.
Similar trends can be seen for the cracking data in the figure. Figure 4.31 depicts the analysis
results of the percent acceptance for the thin HMA overlay treatment in Louisiana. It can be seen
that the results are similar to those from the same treatment type in Colorado. Increases in the
analysis length from 0.1 to one mile do not precipitate significant increases in the percent
acceptance.
Similar scenarios can be seen in Figure 4.32 for the IRI and rut depth data of the thin
HMA overlay treatment in Washington. The percent acceptance for the IRI data increases from
slightly less than 20 percent at 0.1 mile analysis length to slightly greater than 20 percent at one
mile analysis length. Furthermore, the percent acceptance for the rut depth data increases from
about 30 percent at 0.1 mile analysis length to slightly greater than 30 percent at one mile
analysis length. However, the percent acceptance for the cracking data is highly variable and
shows no consistent trend with the analysis length.
As mentioned previously, the low percentages of acceptance are mainly due to the second
acceptance criteria of positive regression parameters. This is especially true for the time series
cracking data. That is, a significant percentage of the time series cracking data do not display

154

trends that are consistent with pavements that have received no treatment. This can be attributed
to several different factors, including data variability. Such variability is a function of many things
including the data collection procedures, ambient conditions (temperature and moisture) during the data
collection which vary from one year to the next, improved equipment and so forth. The data collection
procedure has more impact on the cracking data than on sensor collected data such as IRI and rut depth.
The reason is the semi-automated crack data collection technique used to measure and record cracking
data versus the fully automated technique for the sensor based data. In the semi-automated technique, a

data collection vehicle travels along the pavement and obtains electronic images of the pavement
surface. The images are reviewed by trained personnel who digitize the cracking data and record
them in the database. Depending on the personnel, cracks could be rated differently due to the
inherent human subjectivity of the crack rating. Other variables such as the temperature at the
time of the data collection, moisture, lighting, and camera type could also add variability to the
subjective crack rating. Thus the trends in the cracking data are somewhat subjective from one
year to the next and the percent acceptance is highly variable from one pavement analysis length
to another. Unlike the image based data, the IRI and rut depth data are collected and recorded
using fully automated procedures. Lasers mounted on the front of a data collection vehicle
measure and recorded the IRI and rut depth along the pavement. Thus, these pavement
conditions are not subjectively measured and recorded. Hence, compared to the cracking data,
the IRI and rut depth exhibit more consistent trends, and the percent acceptance is not as variable
from one pavement analysis length to another.
Note that the cracking data for the thin HMA overlay treatments in Colorado and
Louisiana, shown in Figures 4.30 and 4.31, respectively, exhibit less variability from one
pavement analysis length to another compared to the cracking data from Washington. This could
be caused by various reasons including the pavement surface age and the methods of data
155

collection (sealed cracks are not counted in Louisiana and Colorado). In summary, the percent
acceptance based on the cracking data varies significantly from one data analysis length to the
next. On the other hand, the percent acceptance based on the IRI and rut depth is almost constant
and it shows no specific relationship to the pavement analysis length.
At the onset of this analysis, it was thought that averaging or summing the pavement
condition and distress data over long pavement segments will decrease the data variability along
the project and over time and would increase the percent of the data that satisfy the two
acceptance criteria. Results of the analysis indicate that:
1.

As it was expected, the data variability along the project decreases as the pavement
analysis length increases. This is evidenced by the fact that, in most cases as the
pavement analysis length increases the coefficient of variation of the data decreases. An
example of such trend is shown in Table 4.10 for the IRI and longitudinal cracking data
along a 9.6 mile portion of US 2 in Washington. For each data collection year shown in
the table, the coefficient of variation generally decreases as the pavement analysis length
increases. Furthermore, the data in this table also support the discussion regarding the
variability of sensor-based data versus image-based data. That is, the data in Table 4.10
indicate that the coefficients of variation of the cracking data are much higher than those
of the IRI data. To illustrate, the ratios of the coefficients of variation of the cracking data
to those of the IRI data were calculated and are shown in Figure 4.36 for three years of
data collection. It can be seen from the figure that the ratio of the coefficient of variation
varies from just above 4 to just above 9.

2.

The percent acceptance is not impacted by the pavement analysis length. That is,
increasing the pavement analysis length does not change the overall trend of the

156

Table 4.10 Coefficients of variation for ten pavement analysis lengths based on three years of IRI
and longitudinal cracking data along US-2 in Washington, BMP 89.3 to 99.0
Pavement
analysis
length
(mile)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0

Coefficient of variation for each distress type and data collection year
IRI
Longitudinal cracking
2003

2004

2005

2003

2004

2005

0.28
0.25
0.22
0.19
0.16
0.16
0.14
0.14
0.13
0.15

0.32
0.28
0.25
0.25
0.22
0.21
0.18
0.17
0.18
0.18

0.27
0.23
0.21
0.20
0.19
0.17
0.14
0.15
0.14
0.15

2.58
1.77
1.40
1.33
1.34
1.06
1.05
0.90
0.99
0.92

1.80
1.58
1.39
1.23
1.05
1.02
1.13
0.87
0.99
0.98

1.90
1.44
1.24
0.94
1.03
0.86
0.68
0.64
0.72
0.73

Ratio of the coefficients of variation for the
longitudinal cracking and IRI data

2003

2004

2005

10
9

8
7
6
5
4
3
2
1
0
0

0.2

0.4
0.6
0.8
Analysis length (mile)

1

1.2

Figure 4.36 Ratio of the coefficients of variation for the longitudinal cracking and IRI data
versus pavement analysis length along US-2 in Washington, BMP 89.3 to 99.0

157

pavement condition and distress data. Stated differently, if the time series data of the 0.1
mile long pavement segments show decreasing trend from one year to the next, averaging
or summing the pavement condition or distress over longer analysis lengths does not, in
most cases, change the overall trend of the data. Hence, the percent acceptance is
unchanged as shown in Figures 4.30 through 4.32.
The same trends described above for the thin HMA overlay treatment can also be seen for
the single chip seal treatment in each of the three states. In every case shown in Figures 4.33 and
4.34, the pavement analysis length does not significantly impact the percent acceptance. The
same can be said for the percent acceptance of the IRI and rut depth data for the single chip seal
treatment in Washington as shown in Figure 4.35. The figure also shows that the percent
acceptance for the cracking data is extremely variable and not consistent from one analysis
length to another. It is important to note, though, that the data in Figure 4.35 consists of only 204
0.1 mile long pavement segments. Thus, some of the variability in the figure may be attributable
to the small number of analyzed pavement segments.
Regardless, the data in Figures 4.30 through 4.35 as well as in Figures C.1 through C.7 in
Appendix C indicate that:
1.

In general, increasing the pavement analysis length does not necessarily increase the
percent acceptance. In other terms, the ability of the data to be analyzed or modeled does
not improve as the analysis length increases.

2.

For sensor collected data (IRI and rut depth), the percent acceptance is almost constant
and independent of the pavement analysis length.

3.

For image based data (cracking), the percent acceptance is variable and not related to the
pavement analysis length.

158

4.6.2 The Impacts of Pavement Analysis Length on PMS Decisions
Although the pavement analysis length does not appear to significantly impact the
percent of pavement segments that can be modeled or analyzed, the analysis length does have
significant impacts on the PMS decisions. Specifically, the pavement analysis length impacts the
PMS in three different scenarios.
1.

The selection of project boundaries which are directly related to the pavement analysis
length. The length over which the pavement condition and distress data are analyzed
dictates the selection of the project boundaries. To illustrate, suppose that a SHA chooses
to analyze the pavement condition and distress data along each one mile of the road
network. This causes the pavement project length to be whole miles such as 1, 2, 3 or
more miles. The selection of a project length of 4.5 mile will be arbitrary and not based
on the results of the data analysis. On the other hand, if the SHA chose to analyze the
data along each 0.1 mile of the road network, the minimum pavement project length
would be 0.1 mile. The above scenarios indicate that the pavement analysis length
impacts the decisions regarding project boundaries. Therefore, the indirect consequence
is that the analysis length also impacts the decisions regarding pavement treatment funds.
Longer analysis lengths result in longer pavement treatment projects that, in turn, require
the allocation of more pavement treatment funds.

2.

The identification of hot spots or areas of localized poor condition or high distress. The
averaging or summing of the pavement condition and distress data along longer analysis
lengths would artificially decrease the variability of the data along the analysis length.
The averaging and summing processes tend to hide areas of localized high distress or
poor condition. Again suppose that a SHA chooses to store the pavement condition and

159

distress data along each one mile of the road network. Such data cannot be used to
identify localized hotspots where the pavement conditions and/or distress along a short
pavement segment (such as 0.2 mile) are very high. Thus, the PMS database will not have
the detailed pavement performance data to identify troubled or highly distressed areas.
3.

The statistical significance of the number of analyzed sections or segments. That is the
longer is the pavement analysis length, the less is the number of pavement sections that
can be subjected to analysis. To illustrate, consider a 7 mile long project. If the analysis
length is 1 mile, there are 7 one mile long pavement sections to be analyzed. This is
statistically insignificant number. On the other hand if the data is stored and analyzed for
each 0.1 mile long pavement segments, there are 70 segments to be analyzed.
Statistically, PMS decisions that are based on 70 data points would have a greater
significance than decisions based on 7 data points. Thus, in general, as the pavement
analysis length increases, the statistical significance or the confidence level in the PMS
decisions decreases as less data points are used to formulate the decisions.
Given the discussion in the previous paragraphs, it is fair to say that the selection of

longer pavement analysis lengths could create multiple problems. In the worst case, longer
pavement analysis lengths could result in longer pavement treatment projects. Within these
longer pavement treatment projects, localized areas of increased distress or poor condition could
be masked. Furthermore, the PMS decisions regarding the distress and condition along these
segments would be based on less data points and the statistical significance or confidence in the
decisions would be lacking. To avoid these problems, and others, it is most beneficial for SHAs
to store and analyze the pavement condition and distress data over short pavement lengths such
as 0.1 mile.

160

4.7

Pavement Performance Data Imputation
For various reasons, the pavement performance data from some data collection cycles

along certain pavement segments or sections may not be documented in the database. These
include equipment malfunctioning, failure to properly record the data, loss of data to human
errors, construction zones and so forth. Missing data may pose serious issues regarding the
modeling and analysis of the time-series pavement performance data especially when less than
three data points are available. Hence, the question herein is what can be done to relatively
accurately substitute the missing data elements?
One possible answer to this question is data imputation. The statistics and various
methodologies supporting the principles of data imputation are well developed and documented
in the literature. However, their applications to the imputation of accurate time dependent
pavement performance data are not clear. Therefore, in this study, various analysis techniques
were used to examine the effects of four different data imputation methodologies on the accuracy
of the imputed pavement performance data. In the analysis, the time dependent IRI data of
flexible, composite, and rigid pavement sections were used. The IRI data were obtained from the
CDOT, the LADOTD, and the WSDOT as well as from cells of the MnROAD experiment. The
four data imputation methods that were analyzed are linear interpolation, regression, moving
regression, and multiple regressions. For each analyzed pavement segment, the same analysis
steps listed below were used.
Step 1 – Data Limitation and Amputation – In general, for each of the 0.1 mile long
pavement segments along the roads in each of the three SHAs that were used in the analysis,
only five time series IRI data points were available from five data collection cycles. In reality,
more data points were available in the database; however, the additional data points were

161

collected either before or after treatments were applied. Pavement treatment actions cause
changes in the pavement condition and distress and in the pavement rate of deterioration and
thus, data imputation cannot be performed using the entire set of data. Regardless, for each
analyzed pavement segment, the second, third, and fourth available IRI data points were
independently removed (amputated) from the time series data. Hence, three amputated data sets
were created; one missing the second data point, one missing the third, and one missing the
fourth data point.
Step 2 – Data Imputation – For each amputated data set created in step 1, the linear
interpolation, regression, moving regression, and multiple regressions imputation methods were
used to independently impute the second, third, and fourth time series IRI data points.
Step 3 – Differences in Imputed and Measured Data – For the second, third, and
fourth data points, the imputed and the measured data were compared using two analysis
techniques:
1.

The percent difference of the imputed data point relative to the measured one.

2.

The differences between the RSL value that was estimated using the measured data set
and a threshold value of 200 inch/mile and the three RSL values estimated using the same
threshold value and each of the imputed data sets. These differences were then compared
to determine the effects of the various data imputation methods on the PMS decisions.
Note that the RSL concept is described in detail in section 2.9 of this thesis.
Detailed descriptions, examples, results, and discussion of each of the analyzed data

imputation method are presented in the next four sections. It should be noted that the name of
each imputation method used in this thesis was selected to promote clarity. The names do not
necessarily reference those stated in the literature.

162

4.7.1 Linear Interpolation Imputation
The linear interpolation imputation method is simple, easy to use, and is based on the
following two assumptions;
1.

The missing data point is located between two available data points.

2.

The two available data points and the missing one can be modeled as a linear function of
time.

Hence, the missing data point is imputed by linearly interpolating between two available data
points. Graphically, this amounts to imputing the missing data point by connecting a straight line
between the two data points on either side of the missing one as stated in Equation 4.1.

IRI(t  1)  IRI(t  1)(t)  (t  1)
IRI(t) 
(t  1)  (t  1)

Equation 4.1

Where IRI(t) = the missing IRI data at time t
IRI(t+1) = the available IRI data at time (t+1)
IRI(t-1) = the available IRI data at time (t-1)
An example of the linear interpolation imputation method is shown in Table 4.11. In this
example, the fourth available time-series IRI data was amputated and imputed. The same
analysis method was used to amputate and consequently impute the second and third data points.
For the three imputed data points (the second, third and fourth), the percent differences
between the measured and the imputed IRI data for five 0.1 mile long pavement segments along
HWY 24 in Colorado are shown in Figure 4.37. It can be seen in the figure that, for these five
BMPs, the percent differences between the imputed and the measured data range from about -30
to +30 percent and that most imputed data are within -15 to +20 percent of the measured data.

163

Table 4.11 Linear interpolation imputation example
Time
Available Amputated Imputed
Data
Elapsed
series
IRI data
IRI data
IRI data
collection
time
data
set
set
set
year
(year)
number
(in/mile)
(in/mile) (in/mile)
1

1999

1

74

74

74

2

2000

2

125

125

125

3

2003

5

131

131

131

4

2005

7

122

5

2007

9

163

Equation

147
163

The difference between the imputed and
measured data in percent of the
measured data

Second available data point

147  131 

(163  131) * (7  5)
(9  5)

163

Third

Fourth

40.0

20.0

0.0

-20.0

-40.0
321

322

323
324
Beginning mile point

325

Figure 4.37 The difference between the imputed and measured data in percent of the measured
data versus the BMP along HWY 24 in Colorado, three data points imputed using the linear
interpolation imputation method

164

As stated earlier, in the second analysis technique, the measured data points were used to
calculate the RSL of each pavement segment. Further, the remaining measured data points and
each of the imputed data points were also used to calculate the RSL of each pavement segment.
The differences in the RSL values based on the measured and the measured and imputed IRI data
were then calculated and are shown in Figure 4.38. The data in the figure indicate that the
maximum difference between the RSL values based on the measured and the imputed and the
measured IRI data for the five 0.1 long pavement segments along HWY 24 in Colorado is only
1.5 years. Further the majority of the differences in the RSL values are less than 0.5 year. For
most cases, such differences in the RSL values would have insignificant impacts on the condition
state (see section 4.3) of the pavement segments and hence, would not affect the PMS decisions.

Second available data point

Third

Fourth

Difference between RSL based on imputed and
that based on measured data (year)

0.5

0.0

-0.5

-1.0

-1.5
321

322

323
Beginning mile point

324

325

Figure 4.38 The difference between the RSL values based on imputed and measured data versus
the BMP along HWY 24 in Colorado, three data points imputed using the linear interpolation
imputation method

165

The above example indicates that although the linear interpolation imputation method
produces + 30 percent difference between the measured and the imputed IRI data, the effect of
the method on RSL (and PMS decisions) is negligible. Nevertheless, Figures D.1 through D.6 of
Appendix D show similar results that were obtained for 15 pavement segments along other roads
located in the other states and the MnROAD experiment.
4.7.2 Regression Imputation
The regression imputation method is used to impute missing data using the proper
regression function, which is obtained based on the available information at the time of
imputation. For example, consider the data shown in Figure 4.39 and listed in Table 4.12, after
amputating the fourth data point (collected in 2005), the remaining three data points (measured
in years 1999, 2000, and 2003) were used to calculate the regression parameters of the
exponential function shown in the figure. The amputated (missing) IRI data point was then
calculated (imputed) using the exponential function and its regression parameters shown in
Figure 4.39 and it is listed in Table 4.12. The same analysis method was used to independently
amputate and consequently impute the second and the third data points. It is important to note
that three data points are required to perform regression imputation using any non-linear
function. This implies that, depending on the year of the missing data point, a SHA has to wait
anywhere from zero to four years to impute the missing data. To illustrate, if the second data
point in a time series data is missing, and if the state collects data every other year, the missing
data point can be imputed using the regression method after four years when two additional data
collection cycles are completed. On the other hand, if the fourth data point is missing (three data
points are available), the missing data point can be imputed immediately using the regression
method presented above.

166

200

IRI (in/mile)

160

120
y = 78.782e0.1134x
R² = 0.5547

80

40

0
0

1

2

3
4
Elapsed time (year)

5

6

7

Figure 4.39 Example regression parameter calculation for regression imputation, missing data at
year 7
Table 4.12 Regression imputation example
Time
Available
Imputed
Data
Elapsed
Amputated
series
IRI data
IRI data
collection
time
IRI data set
data
set
set
year
(year)
(in/mile)
number
(in/mile)
(in/mile)
1

1999

1

74

74

74

2

2000

2

125

125

125

3

2003

5

131

131

131

4

2005

7

122

Equation

174.2

167

174.2  78.782e(.1134*7)

Like the linear interpolation method, for the three imputed data points, the percent
differences between the measured and the imputed IRI data for five 0.1 mile long pavement
segments along HWY 24 in Colorado are shown in Figure 4.40. Note that these are the same five
BMPs that were presented for the linear interpolation imputation method. It can be seen in the
figure that the percent differences between the imputed and measured data range from less than 30 to approximately +50 percent. Most of the imputed data, though, lie within + 20 percent of
the measured data.

The difference between the imputed and
measured data in percent of the
measured data

Second available data point

Third

Fourth

60.0
40.0
20.0
0.0
-20.0
-40.0
321

322

323
324
Beginning mile point

325

Figure 4.40 The difference between the imputed and measured data in percent of the measured
data versus the BMP along HWY 24 in Colorado, three data points imputed using the regression
imputation method

Further, the RSL of each pavement segment was calculated based on a threshold value of
200 inch/mile and the measured and the measured and imputed data points. The differences in
the RSL values based on the measured and the measured and imputed IRI data are shown in
Figure 4.41. The data in the figure indicate that the maximum difference between the RSL values
based on the measured and the imputed and measured IRI data for the five 0.1 mile long
168

segments along HWY 24 in Colorado is nearly 2.5 years. However, the majority of the
differences in the RSL values are less than 0.5 year. Once again, in most scenarios, such
differences in RSL values would have insignificant impacts on the condition state (see section
4.3) of the pavement segments and would not affect PMS decisions.

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0

321

322

323
324
Beginning mile point

325

Figure 4.41 The difference between the RSL values based on imputed and measured data versus
the BMP along HWY 24 in Colorado, three data points imputed using the regression imputation
method

The above example indicates that although the regression imputation method produces, in
general, + 20 percent differences between the measured and imputed IRI data, the effect of the
method on the RSL (and PMS decisions) is negligible. Figures D.7 through D.12 of Appendix D
show similar results that were obtained for 15 pavement segments along other roads located in
the other states and the MnROAD experiment.

169

4.7.3 Moving Regression Imputation
The moving regression method used in this thesis is a modification of the regression
method stated earlier. It uses the proper regression function based on the available information.
In this modified method, the imputed data points are updated every time a new data point is
measured and becomes available. That is, the imputed data are ‘updated’ based on the
recalculated values of the regression parameters of the function after a new data point becomes
available. An example of the moving regression imputation method is shown in Table 4.13. In
this case, the data at year 7 (fourth data point) was amputated and labeled as missing. The
missing data point was then imputed using the regression parameters of the exponential model
based on the first, second, and third data points. This is the same procedure as for the regression
imputation method presented in the previous section. However, when the fifth data point
becomes available, the fourth data point is re-imputed using the regression parameters of the
exponential model based on the first, second, third, and fifth data points. The new imputed value
(moving regression 2) replaces the first imputed value and the cycle will continue when the sixth
data point becomes available. Note that the results of moving regression 1 (the first imputed
value) in Table 4.13 and the imputed value using the regression imputation method (Table 4.12)
are the same.
For the three imputed data points, the percent differences between the measured and
moving regression imputed IRI data for five 0.1 mile long pavement segments along HWY 24 in
Colorado are shown in Figure 4.42. It can be seen in this figure that the percent difference
between the imputed and measured IRI data ranges from slightly less than -30 percent to about
+35 percent with the majority of the imputed data lying within + 20 percent of the measured
data.

170

Table 4.13 Moving regression imputation example
Time
Available
Imputed
Data
Elapsed
Amputated
series
IRI data
IRI data
collection
time
IRI data set
data
set
set
year
(year)
(in/mile)
number
(in/mile)
(in/mile)
1

74

74

74

2

2000

2

125

125

125

3

2003

5

131

131

131

2005

7

122

1

1999

1

74

74

74

2
Moving
regression
number 2

1

4

Moving
regression
number 1

1999

2000

2

125

125

125

3

2003

5

131

131

131

4

2005

7

122

5

2007

9

163

Equation

174.2

146.7
163

171

163

*
174.2  78.782e (.1134 7)

*
146.7  85.313e(.0774 7)

The difference between the imputed and
measured data in percent of the measured data

Second available data point

Third

Fourth

40.0

20.0

0.0

-20.0

-40.0
321

322

323
Beginning mile point

324

325

Figure 4.42 The difference between the imputed and measured data in percent of the measured
data versus the BMP along HWY 24 in Colorado, three data points imputed using the moving
regression imputation method
Similar to the two imputation methods presented previously, the measured and measured
and imputed data points were used to calculate the RSL of each pavement segment based on an
IRI threshold of 200 inch/mile. The differences in the RSL values based on the measured and
measured and imputed IRI data are shown in Figure 4.43. The data in the figure show that the
maximum difference between the RSL values based on the measured and the measured and
imputed IRI is less than 1.5 years. In fact, most of the differences in the RSL values are less than
1 year. Differences of this magnitude would not cause any significant changes in the condition
state (see section 4.3) of the pavement segment. Thus, changes in PMS decisions are not
expected.

172

Second available data point

Third

Fourth

Difference between RSL based on imputed
and that based on measured data (year)

0.5

0.0

-0.5

-1.0

-1.5
321

322

323
Beginning mile point

324

325

Figure 4.43 The difference between the RSL values based on imputed and measured data versus
the BMP along HWY 24 in Colorado, three data points imputed using the moving regression
imputation method
Although the above example indicates that the moving regression imputation method
produces + 20 percent difference between the measured and the imputed IRI data, the effect of
the method on the RSL, and PMS decision, is negligible. Figures D.13 through D.18 in Appendix
D show similar results that were obtained for 15 pavement segments along other roads located in
the other states and the MnROAD experiment.
4.7.4 Multiple Regressions Imputation
The multiple regressions imputation method used in this study is another slight
modification of the regression method. That is the method is slightly different than the regression
and the moving regression methods. It is used to impute missing data using the proper regression
function based on the available information. In the multiple regressions method, the first value of
the missing data point is calculated using at least three available data points. The second value is
173

calculated as the average of the first value and the updated value as one additional data point
becomes available. The third value is calculated as the average of the first, second and the
updated value as another data point becomes available and so forth. Thus, the calculation steps
used in the multiple regressions method are the same as those used in the moving regression and
the added step is for the calculation of the average of multiple values based on the regression
models assumed to represent the missing data. Perhaps this is most easily understood through the
example displayed in Table 4.14. In this case, the data at year 7 (fourth data point) is amputated
and assumed missing. The fourth data point is first imputed using the regression parameters of
the exponential model based on the first, second, and third data points (multiple regression
number 1 in Table 4.14). This is the same procedure as for the regression and the moving
regression imputation methods. However, when the fifth data point becomes available, the
missing fourth data point is calculated using the regression parameters of the exponential model
based on the first, second, third, and fifth data points (multiple regression number 2 in Table
4.14). The difference from the moving regression method is that the final imputed value is the
average of the two calculated values based on the two regression models. In the example shown
in Table 4.14, the multiple regression number 1 produced an IRI value of 174.2 in/mile at year 7.
When the fifth data point is included, the model yields an IRI value of 146.7 inch/mile. The
average of these two values (160.5 in/mile) is the imputed data at year 7 for multiple regression 2
as shown in the table. When the sixth data point becomes available, the parameter of the
exponential function are recalculated using the first, second, third, fifth and sixth data points and
the value of the missing data point (the fourth one in this example) is the average of the three
imputed values. It should be noted that the results of the first regression step (multiple regression
1, moving regression 1 in Table 4.13, and regression imputation in Table 4.12 are the same.

174

Table 4.14 Multiple regressions imputation example
Time
series
data
number

Data
Elapsed
collection
time
year
(year)

Available
Imputed
Amputated
IRI data
IRI data
IRI data set
set
set
(in/mile)
(in/mile)
(in/mile)

1

74

74

74

2

2000

2

125

125

125

3

2003

5

131

131

131

2005

7

122

1

1999

1

74

74

74

2
Multiple
regression
number 2

1

4

Multiple
regression
number 1

1999

2000

2

125

125

125

3

2003

5

131

131

Equation

131

4

2005

7

2007

9

*
174.2  78.782e (.1134 7)

*
146.7  85.313e(.0774 7)

122

5

174.2

163

160.5

163

175

163

160.5 =
Average (174.2, 146.7)

For the three imputed data points, the percent differences between the measured and the
multiple regressions imputed IRI data for five 0.1 mile long pavement segments along HWY 24
in Colorado are shown in Figure 4.44. It can be seen in this figure that the percent difference
between the imputed and the measured IRI data ranges from less than -35 percent to about +35
percent with the majority of the imputed data lying within approximately + 20 percent of the
measured data.

The difference between the imputed and
measured data in percent of the measured
data

Second available data point

Third

Fourth

40.0

20.0

0.0

-20.0

-40.0
321

322

323
324
Beginning mile point

325

Figure 4.44 The difference between the imputed and measured data in percent of the measured
data versus the BMP along HWY 24 in Colorado, three data points imputed using the multiple
regressions imputation method

The measured and the imputed and measured data points were used to calculate the RSL
of each pavement segment based on an IRI threshold value of 200 inch/mile. The differences in
the RSL values based on the measured and the imputed and measured IRI data are shown in
Figure 4.45. The data in the figure show that the maximum difference between the RSL values
based on the measured and the imputed and measured IRI data is less than 2 years. Most of the

176

differences in the RSL values are less than 0.5 year. Differences of this magnitude would not
cause any significant changes in the condition state (see section 4.3) of the pavement segments
and thus, changes in PMS decisions would not be expected.

Difference between RSL based on
imputed and that based on measured data
(year)

Second available data point

Third

Fourth

0.5
0.0
-0.5
-1.0
-1.5
-2.0
321

322

323
324
Beginning mile point

325

Figure 4.45 The difference between the RSL values based on imputed and measured data versus
the BMP along HWY 24 in Colorado, three data points imputed using the multiple regressions
imputation method

Similar to the other imputation methods described previously, the multiple regressions
imputation may produce + 20 percent differences between the measured and the imputed IRI
data, its effect on the RSL is negligible. Hence, the effect of the multiple imputation method on
PMS decisions is also negligible. Figures D.19 through D.24 of Appendix D indicate that similar
results were obtained for 15 pavement segments along other roads in the other states and along
the MnROAD experiment.

177

4.7.5 Discussion
In the previous subsections, four data imputation methods were presented along with
examples using five 0.1 mile long pavement segments along HWY 24 in Colorado. Additional
pavement segments were also analyzed where few data points were amputated and then imputed
using each of the four methods. Although the five 0.1 mile pavement segments do not present a
statistically significant number of segments to support conclusions, the combined analysis results
of the five segments and those reported in Appendix D (15 segments), increase the confidence
level in the results and in the observations and discussion presented in this section. As stated
previously, after imputing the data, the imputed values were compared to the measured ones
using two analysis techniques:
1.

The differences in the values of the imputed and the measured data points.

2.

The differences between the RSL values estimated using the entire measured data set and
the measured and imputed data set.
Results of the two analyses were presented in the previous four sections. Based on

thorough examination of the results of the analysis of the four imputation methods, the following
observations and their associated discussion were made.
1.

The accuracy of the imputed data points is a function of the variability of the measured
data. Low variability data causes the accuracy of the imputed data to be very high. To
illustrate, consider Figures 4.46 and 4.47. In the first figure, three sets of six theoretical
IRI data points are shown having three deterioration rates but no variability over time.
While Figure 4.47 depicts three sets of six time series IRI data points having three
deterioration rates and variability over time. For each set of the six data points in each
figure, the fourth data point was amputated and then imputed using the four methods. The

178

results are listed in Tables 4.15 and 4.16. It can be seen from Table 4.15 that except for
the linear interpolation, the other imputation methods yielded perfect results (no
differences between the theoretical and the imputed data points). The linear interpolation
imputation method yielded slight differences (up to 12.8 percent) between the theoretical
and the imputed data. The results listed in Table 4.16 tell a different story. All imputation
methods produced differences between the imputed and the real data.
700
600

IRI (inch/mile)

500
400
300
200
100
0
0

2

4

6
Elapsed time (year)

8

10

Figure 4.46 IRI data having three deterioration rates and no variability

179

12

700
600

IRI (inch/mile)

500
400
300
200
100
0
0

2

4

6
Elapsed time (year)

8

10

12

Figure 4.47 Variable IRI data having three deterioration rates
2.

The accuracy of the imputed data points is a function of the pavement rate of
deterioration. This functionality varies from one imputation method to the next. The
results listed in Table 4.16 indicate that:
a)

For the linear imputation method, the percent difference between the imputed and
the actual data increases as the rate of deterioration increases. This was expected
because the data follow an exponential function while the imputation method is
based on a linear relationship.

b)

For the other three imputation methods, the percent differences between the
imputed and the actual data fluctuate up and down as the rate of deterioration

180

Table 4.15 Differences and percent differences between the imputed and the actual IRI data for four imputation methods (three rates of
deterioration and no variability)
Deterioration rate

Elapsed
time
(year)

Low

Medium

High

0.02
2
4
6
8
10

50
55
61
67
75
82

50
67
91
123
166
224

50
82
136
224
369
609

Deterioration
rate
Low
Medium
High

Differences and percent differences between the imputed and the actual IRI
data for four imputation methods
Linear
Moving
Multiple
Regression
interpolation
regression
regressions
Difference (%) Difference (%) Difference (%) Difference (%)
0.3
0.5
0
0
0
0
0
0
6
4.5
0
0
0
0
0
0
9
12.8
0
0
0
0
0
0

Table 4.16 Differences and percent differences between the imputed and the actual IRI data for four imputation methods (three rates of
deterioration and variable data)
Deterioration rate

Elapsed
time
(year)

Low

Medium

High

0.02
2
4
6
8
10

50
53
60
67
76
80

45
52
68
123
133
215

42
62
155
224
380
609

Deterioration
rate
Low
Medium
High

Differences and percent differences between the imputed and the actual IRI
data for four imputation methods
Linear
Moving
Multiple
Regression
interpolation
regression
regressions
Difference (%) Difference (%) Difference (%) Difference (%)
1
1
-2
-3
-0.4
-1
-1
-1
-22
-18
-41
-33
-20
-16
-29
-24
43
19
50
22
7
-13
15
7

181

increases. It appears that the accuracy of the three imputation methods is a
function of the interaction between data variability and the rate of deterioration.
c)

The ranges of the differences and the percent differences appear to be the smallest
for the moving imputation method amongst the four methods. This is similar to
the findings presented in the previous sections based on the five 0.1 mile long
pavement segments along HWY 24 in Colorado.

d)

The accuracy of the imputation method is a function of the number of available
data points. Higher number of data points produces more accurate imputation.
This was expected because higher number of data points defines the trend of the
IRI better than fewer data points. The implication of this is that the accuracy of
the imputed data is a function of the data collection frequency.

After a thorough examination of the results of the various imputation methods, one
question arises; what if no imputation action is taken and the missing data remain missing? This
issue is addressed in the next section.
4.7.6 The No-Action (No Imputation) Approach
For various reasons, including time and technological restraints, some SHAs may choose
not to impute missing pavement performance data. This is referred to as the no-action approach.
That is, the missing data remains missing and the available time series pavement performance
data are used for pavement performance modeling. This implies that the number of available
time series data points may be limited if, for some reason, the data are not collected along a
pavement segment during a data collection cycle. Results of the no-action approach and
comparison of the results with the four imputation methods are presented in the next section.

182

4.7.7 Comparison of the Four Imputation Methods and the No-Action Approach
In the previous sections, the impacts of each of four imputation methods on the
differences between the measured and the imputed IRI data and the impacts of each method on
the calculated RSL values were presented and discussed for five BMPs along the same road in
Colorado. The impacts of data variability, the pavement rate of deterioration and the data
collection frequency on the accuracy of the imputed data using the four imputation methods were
also addressed. In this section, the four imputation methods and the no-action approach are
compared.
For each imputation method, the differences between the measured and the imputed IRI
data for the five 0.1 mile pavement segments along HWY 24 in Colorado shown in Figures 4.37,
4.40, 4.42, and 4.44 were combined to determine the maximum, minimum, and the average
percent differences between the imputed and the measured data. The results of this combination
are shown in Figure 4.48. It can be seen in the figure that the moving regression imputation
method produces the smallest percent differences range (slightly less than -30 percent to about
+20 percent). The next widest percent differences belongs to the linear interpolation method (-30
to about +30 percent). The range in the differences between the measured and the imputed data
for the multiple regressions imputation method varies from about -30 to +35 percent, whereas
for the regression imputation method from about -30 to about +50 percent. For all four methods,
the average percent difference between the imputed and the measured data is near zero. The
misleading average was expected and is mainly due to the positive and negative percent
differences between the measured and the imputed data. Keep in mind that the distributions of
the percent differences for the five BMPs along HWY 24 in Colorado are shown in Figures 4.37,
4.40, 4.42, and 4.44. It can be seen that most of the percent differences for the five BMPs fall

183

within a much smaller range than is depicted by the maximum and minimum percent errors
shown in Figure 4.48. Note that the no-action approach is not shown in Figure 4.48. The reason
is that it is not possible to calculate the percent differences between the imputed and the

Maximum, minimum, and average percent
difference between imputed and measured
data

measured data given that no data are imputed.
60.0

40.0
20.0
0.0
-20.0
-40.0
0

1

2
3
Imputation methods

4

5

1 = linear interpolation, 2 = regression,
3 = moving regression, 4 = multiple regression
Figure 4.48 Maximum, minimum, and average percent difference between imputed and
measured data at BMPs 321, 322, 323, 324, and 325 along HWY 24 in Colorado, using four
imputation methods
On the other hand the differences between the RSL values based on the four imputation
methods, the no-action approach, and on the complete measured data sets are shown in Figures
4.49 through 4.51. Figures 4.49 through 4.51 display the results from amputating and imputing
the second, third, and fourth available data point, respectively. It can be seen that, for each of the
imputed data points, the differences in the RSL based on each imputation method and the noaction are not significant. Furthermore, these differences would not have measurable impacts on
the PMS decisions.

184

Differences between the RSL based on
the stated imputation method and that
based on the complete measured data
set (year)

Linear interpolation
Moving regression
No-action (no imputation)

Regression
Mutiple regressions

0.2
0.0
-0.2
-0.4
-0.6

-0.8
-1.0
-1.2

320

321

322
323
324
Beginning mile point

325

326

Differences between the RSL based on
the stated imputation method and that
based on the complete measured data
set (year)

Figure 4.49 Differences between the RSL based on the stated imputation method (second
available data point imputed) and that based on the complete measured data at BMPs 321, 322,
323, 324, and 325 along HWY 24 in Colorado
Linear interpolation
Moving regression
No-action (no imputation)

Regression
Mutiple regressions

0.6
0.5
0.4
0.3
0.2

0.1
0.0
320

321

322
323
324
Beginning mile point

325

326

Figure 4.50 Differences between the RSL based on the stated imputation method (third
available data point imputed) and that based on the complete measured data at BMPs 321, 322,
323, 324, and 325 along HWY 24 in Colorado

185

Differences between the RSL based on
the stated imputation method and that
based on the complete measured data
set (year)

Linear interpolation
Moving regression
No-action (no imputation)

Regression
Mutiple regressions

0.0
-0.5
-1.0
-1.5
-2.0

-2.5
-3.0
320

321

322
323
324
Beginning mile point

325

326

Figure 4.51 Differences between the RSL based on the stated imputation method (fourth
available data point imputed) and that based on the complete measured data at BMPs 321, 322,
323, 324, and 325 along HWY 24 in Colorado
The differences between the RSL values based on the measured and those based on the
imputed and measured IRI data shown in Figures 4.38, 4.41, 4.43, and 4.45 were combined to
determine the maximum, minimum, and average RSL differences shown in Figure 4.52. The
range in the differences of the no-action approach relative to the full set of the measured data is
also shown in Figure 4.52. It can be seen from the figure that the no-action approach and the
moving regression imputation method produces the smallest range of RSL differences (slightly
less than 1.5 years) followed by the linear interpolation method (about 1.5 years), the multiple
regressions imputation method (slightly less than 2 years), and by the regression imputation
method (about 2.5 years). In any case, these differences would not have significant effects on the
condition state of the pavement segments (see section 4.3). Similar results were obtained for the
pavement segments along other roads in the other states and the MnROAD experiment and are
shown in Figures D.25 through D.30 in Appendix D.

186

Maximum, minimum, and average RSL
difference between imputed and measured
data (year)

0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
0

1

2

3
4
5
6
Imputation methods
1 = linear interpolation, 2 = regression,
3 = moving regression, 4 = multiple regression, 5 = no-action (no
imputation)

Figure 4.52 Maximum, minimum, and average difference between RSL values based on imputed
and measured data at BMPs 321, 322, 323, 324, and 325 along HWY 24 in Colorado, using four
imputation methods
It should be noted that, although the no-action approach produces small RSL differences
relative to the complete measured data, in some cases, data imputation is desirable. The decision
to impute or not to impute, as well as the imputation method to be used, depends on several
factors including:
1.

The agency’s desire to impute missing data.

2.

The number of missing and available data points. For example, if the missing data point
causes the number of available data points to decrease below three, the only available
imputation option is linear interpolation. However, the imputed data point will add no
more information and the linear model based on the two available data points will be
exactly the same as that based on the two available data points and the imputed data.

187

If there are three or more data points available in the database, the missing data point or
points can be neglected (no-action), or imputed using either the multiple or the moving
regression method. These imputation methods generally generate the smallest errors.
One important point that should be noted is that some SHAs employees may lose
confidence in the data analyses results if the analyses are based on time series data sets having
missing data elements. Imputing the data bridges the gaps reasonably, which may increase the
confidence in the analyses results increased. Thus, for various reasons, it may be beneficial to
impute the missing data points.
4.7.8 Advantages and Disadvantages of the Four Imputation Methods
Given that the analysis results show that the impacts of each of the four data imputation
methods on the calculated RSL values are insignificant, it is fair to say that a SHA could use any
of the four methods without expecting any significant changes in the PMS decisions. However,
each of the four imputation methods has advantages and disadvantages that should be evaluated
before a data imputation method is selected to impute missing pavement condition and distress
data points. The advantages and disadvantages of each imputation method include those listed in
Table 4.17 below.
The most simple of the four imputation methods that was analyzed is the linear
interpolation method. In general, the application of this method is simple, easily understood, and
only requires two data points. However, the missing data point that requires imputation must be
between two existing data points. Stated differently, linear interpolation imputation cannot be
used to impute any data points at the end of a time series data set by extrapolation. Furthermore,
because this method assumes a linear rate of pavement deterioration, the results of the imputation
could be significantly impacted by localized data variability. If the two data points used in the

188

Table 4.17 Advantages and disadvantages of four data imputation methods
Imputation
method

Linear
interpolation

Regression

Moving
regression

Multiple
regressions

Advantages

Disadvantages

 Easy to calculate and understand  Missing data must be between two
measured data points and hence it
 Expresses pavement deterioration
cannot be used to impute any end
using simple linear model
data (extrapolation)
 Requires only two data points
 Assumes linear pavement rate of
deterioration
 Could be significantly impacted by
localized data variability
 Based on the available time-series  Requires modeling of the time
data (distress versus time) and the
series data
non-linear pavement rate of
 Cannot be used if less than three
deterioration.
data points are available
 Could be significantly impacted by
localized data variability
 Based on the available time-series  Requires modeling of the time
data (distress versus time) and the
series data
non-linear pavement rate of
 Cannot be used if less than three
deterioration.
data points are available
 The imputed values are ‘updated’
as more data are collected
 Based on the available time-series  Requires modeling of the time
data (distress versus time) and the
series data
non-linear pavement rate of
 Cannot be used if less than three
deterioration.
data points are available
 The imputed values are ‘updated’
as more data are collected
 The averaging of the multiple
imputed values mitigates the
effects of significant data
variability

imputation method have significant localized variability, the imputed data between these two
points will also be affected by the localized variability. This can be seen clearly by comparing
the data shown in Tables 4.15 and 4.16.The advantages of simplicity and understandability are
countered by the impacts of localized data variability and the ability to only impute data between
two existing data points. Extrapolation may produce significant error in the imputed data.
189

In comparison, the mathematical modeling requirements of the regression, moving
regression, and multiple regressions methods cause these methods to be more time-consuming
and laborious than the linear interpolation method. Without modeling software, the application of
these methods to the pavement condition and distress data becomes problematic. This, however,
could be easily solved by using the proper available software, which can be automated to analyze
each pavement project along the entire database. In addition, similar to linear interpolation, these
methods are impacted by localized data variability. The data variability decreases the accuracy of
the non-linear regression models and impacts the differences between the imputed and the
measured data. However, the moving regression and multiple regressions methods mitigate the
effects of localized data variability because the data are re-imputed as more data become
available. Examples of such mitigation are shown in Table 4.16. For the same deterioration rate,
the moving and multiple regressions imputation methods produce lower percent differences than
the regression imputation method. Hence, the imputed data are not as susceptible to the effect of
localized data variability from one year to the next.
Regardless, it is the opinion of the author that, since the impacts of the linear
interpolation and regression methods (regression, moving, and multiple regressions imputation)
on the RSL (and hence, PMS decisions) are similar, the linear interpolation imputation method
could prove more useful for implementation in SHAs. For extremely large pavement networks,
the time and modeling requirements for the regression imputation methods could become
overwhelming. The linear interpolation imputation method could be implemented in a much
more timely manner while producing results that are reasonable and do not change the condition
state (or PMS decision) for the pavement segments. However, if the SHA wishes to computerize
the data imputation process, the moving regression or multiple regressions imputation methods
could be used to better account for the pavement deterioration rates and mitigate the effects of
190

localized data variability from one year to the next. This would also allow for imputation of
missing data that are not between two measured data points. Therefore, depending on the
available technological resources, time constraints, and imputation preferences of different
SHAs, the moving and multiple regressions imputation methods could also be selected to impute
missing data points that are reasonable and do not affect the PMS decisions.

191

CHAPTER 5
SUMMARY, CONCLUSIONS, & RECOMMENDATIONS
5.1

Summary
Some SHAs collect pavement performance data along the entire road network whereas

others use sampling techniques. The long-term economic climate has caused some highway
administrators to consider pavement performance data sampling as an alternative to reduce data
collection costs. The problem is that the effects of data sampling on the accuracy of the PMS
decisions are not well documented. It is not clear that data sampling ultimately reduces the
overall PMS costs. The problem is compounded in that data sampling affects the pavement
length for which the performance data are stored and analyzed. Long analysis lengths may not
improve the data analysis results and may artificially decrease the data variability. In addition,
some pavement performance data from one or more data collection cycles along certain
pavement segments may not be documented or are missing, which makes it difficult or
impossible to model and analyze the data.
To address these issues, pavement management system (PMS) databases were obtained
from four State Highway Agencies; the Colorado Department of Transportation (CDOT), the
Louisiana Department of Transportation and Development (LADOTD), the Michigan
Department of Transportation (MDOT), and the Washington State Department of Transportation
(WSDOT). In addition, the pavement performance data from the Minnesota Road Research
Project (MnROAD) were also obtained. The four SHAs collect and store the pavement
condition and distress data for each 0.1 mile long pavement segment along their entire road
network (no sampling) on an annual or bi-annual basis. The pavement condition and distress data

192

from the four databases were used to simulate various sampling techniques and to study the
impacts of sampling on:
1.

The differences between the continuously measured and the sampled pavement condition
and distress data.

2.

The variability of the pavement condition and distress data along various pavement
projects.

3.

The remaining service life (RSL) and the condition state of each 0.1 mile long pavement
segment along various pavement projects.

4.

The accuracy of the pavement management decisions regarding the selection of project
boundaries and time of treatment.
The results from the various sampling analyses were combined to quantify the potential

savings and the hidden cost of sampling pavement performance data and its potential impacts on
the SHAs.
Additionally, in the current state-of-the-practice, the length of pavement sections
subjected to performance analysis is constrained by the data collection procedures, such as the
sampling technique, and by the analysis details. To address the issue of pavement analysis
length, pavement condition and distress data from each of the four SHAs were analyzed (the IRI
data were averaged and the cracking data summed) over 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,
and 1.0 mile pavement lengths. The data for each analysis length were scrutinized to determine
whether or not the data could be modeled using the proper non-linear mathematical function.
Based on the results, the impacts of the pavement analysis length on the PMS decisions were
estimated and discussed in detail.

193

Finally, for various reasons, the pavement performance data from some data collection
cycles along certain pavement segments or sections may not be documented in the database.
Missing data may pose serious issues regarding the modeling and analysis of the time series
pavement performance data especially when the missing data decrease the number of available
data points to less than three. To help solve these issues, some of the measured pavement
performance data from the four SHAs and the MnROAD databases were amputated to simulate
missing data points. These data were consequently imputed using four data imputation
techniques. The differences between the imputed and the measured data were then analyzed and
their impacts on the pavement management decisions were documented and discussed.
5.2

Conclusions
Based on the results of the analyses conducted in this study, conclusions regarding

general issues, data sampling, pavement analysis length, and data imputation were drawn and are
presented below.
General Issues


Certain data elements such as pavement treatment costs, location, and pavement surface
age are currently not included in the PMS database.



The use of linear location referencing systems, such as beginning and ending mile points,
cause significant errors in the location of a pavement segment from one data collection
cycle to the next.



Robust quality assurance and quality control procedures for the pavement performance
data should be developed and implemented to increase the overall reliability of the data.
This is especially important for the cracking data.

194

Data Sampling


For uniform pavement condition and distress along given pavement projects, such as in
newly constructed or rehabilitated pavement sections, the sampled pavement performance
data accurately represent the continuous data.



As the pavement ages and/or the pavement conditions and distress become more variable,
sampled data do not accurately represent the continuous data. Hence, the errors caused by
data sampling increase as the pavement ages and/or the pavement conditions and
distresses become more variable.



Pavement performance data sampling causes various degrees of errors in one or all of the
following decisions:
o

The assessment of the true variability of the pavement performance data along a
project and along the road network.

o

The selection of optimum time and space (project boundaries).

o

The selection of pavement treatment type.

o

The selection of pavement treatment strategy.

o

The allocation of pavement treatment funds.

Pavement Analysis Length


Longer pavement analysis lengths artificially decrease the variability of the pavement
performance data along given projects and along the network.



In general, increasing the length over which the pavement performance data are collected,
stored, and analyzed does not necessarily improve or increase the percent of pavement
segments that can be modeled and analyzed. Specifically, the pavement analysis length

195

has different effects on the pavement performance data depending on the data collection
procedures as detailed below.
o

For sensor collected data, the percent of pavement segments that can be modeled
and analyzed is almost constant and independent of the pavement analysis length.

o

For image based data, the percent of pavement segments that can be modeled and
analyzed is variable and not related to the pavement analysis length.



The pavement analysis length has significant adverse impacts on various PMS decisions
including:
o

The selection of project boundaries.

o

The identification of hot spots or areas of localized poor condition or increased
distress.

o

The statistical significance of the number of pavement segments or sections that
can be subjected to analysis. That is, longer pavement analysis lengths decrease
the sample size.

Data Imputation


All available imputation techniques produce differences between the imputed and the
measured data. These differences are a function of several factors including:
o

The variability of the measured data. Low data variability causes the accuracy of
the imputed data to be very high.

o

The pavement rate of deterioration. Higher pavement deterioration rates decrease
the accuracy of the imputed data.



The impacts of each of the four data imputation methods analyzed in this study (linear
interpolation, regression, moving regression, and multiple regressions) on the calculated

196

RSL values, and PMS decisions, are insignificant and similar to that if not action is taken.
Differences between the imputed and the measured data do not necessarily produce
differences in PMS decisions.
5.3

Recommendations
Based on the results of the analyses and conclusions, it is recommended that State

Highway Agencies:


Expand the PMS databases to an integrated database that includes detailed data regarding
pavement treatment, maintenance, preservation, rehabilitation and reconstruction types
and costs, location, pavement surface age, material properties, traffic, incentive and
disincentive payments, and all other pavement related data.



Use a global positioning system (GPS) as a location reference system in order to provide
more consistent location of pavement segments and treatment locations from one data
collection cycle to the next.



Collect pavement condition and distress data on continuous basis along the entire road
network.



Store the pavement performance data in the database for each 0.1 mile long pavement
segment.



Analyze the pavement condition and distress data for each 0.1 mile long pavement
segment along projects or along the road network. The 0.1 mile analysis length provides
more flexibility and accuracy in the selection of pavement project boundaries, the
identification of hot spots or areas of localized poor condition or increased distress, and
improves the statistical significance of decisions based on the data.

197



Select, if needed, the data imputation methods (i.e. linear interpolation, regression,
moving regression, or multiple regressions) based on the technological resources, time
constraints, and imputation preferences of the SHA. Each method has advantages and
disadvantages depending on the situation, although all methods cause insignificant
differences in the PMS decisions.

198

APPENDICES

199

APPENDIX A

PMS DATA

200

The PMS databases collected for this study are extremely large and would take many
thousands of pages to include on paper. Hence, the databases are available, by request, from the
Department of Civil & Environmental Engineering at Michigan State University. To request the
data, please contact:
Department of Civil & Environmental Engineering
C/O Dr. Gilbert Baladi
Michigan State University
Engineering Building
428 S. Shaw Lane, Room 3546
East Lansing, MI 48824
Tel: (517) 355-5107 Fax: (517) 432-1827 E-mail: cee@egr.msu.edu
For convenience, examples of the pavement condition and distress data are included
below. Tables A.1 and A.2 contain the measured and formatted condition and distress data for a
section of I-70 from the Colorado Department of Transportation (CDOT). Similar examples of
the formatted condition and distress data are listed in Tables A.3 through A.6 for the Louisiana
Department of Transportation and Development (LADOTD), the Michigan Department of
Transportation (MDOT), the Washington State Department of Transportation (WSDOT), and the
Minnesota Road Research Project (MnROAD).

201

Table A.1 Measured pavement condition data along I-70 in Colorado
Mile points

Route

Control
section

Beginning

I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70

070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A

4.8
4.9
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3

Ending

Direction
to survey

Year

IRI
(in/mi)

4.9
5
5.1
5.2
5.3
5.4
5.5.
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998

98
114
94
99
98
78
80
89
100
104
95
86
112
81
85
85
103
78
93
86
71
92
95
90
76
93

202

Rut
depth
(in)
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.3

Alligator
cracking
2
(ft )
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
100
0
0
0
2
0
0
0

Longitudinal
cracking (ft)
3
1
8
1
0
7
0
0
0
0
0
0
0
3
0
0
2
2
14
0
0
0
0
0
0
0

Transverse
cracking
(count)
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0

Table A.2 Formatted pavement condition data along I-70 in Colorado
Mile points

Route

Control
section

Beginning

I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70
I-70

070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A
070A

4.8
4.9
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3

Ending

Direction
to survey

Year

IRI
(in/mi)

4.9
5
5.1
5.2
5.3
5.4
5.5.
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998

98
114
94
99
98
78
80
89
100
104
95
86
112
81
85
85
103
78
93
86
71
92
95
90
76
93

203

Rut
depth
(in)
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.3

Alligator
cracking
(ft)
0
0
0
0
0
0
0
0
0
0
2.6
0
0
0
0
0
0
0
8.3
0
0
0
0.3
0
0
0

Longitudinal
cracking (ft)

Transverse
cracking (ft)

3
1
8
1
0
7
0
0
0
0
0
0
0
3
0
0
2
2
14
0
0
0
0
0
0
0

12
12
24
0
0
0
12
0
0
0
0
0
0
0
0
12
0
0
0
12
0
12
0
0
0
0

Table A.3 Formatted pavement condition data along US-80 in Louisiana
Mile points

Route

Control
section

Beginning

US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80
US-80

001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05
001-05

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5

Ending

Direction
to survey

Year

IRI
(in/mi)

0.1
0.2
0.3
0.4
0.
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005

172
171
138
136
241
105
127
135
136
74
105
109
119
120
107
102
118
114
140
192
163
217
194
191
244

204

Rut
depth
(in)
0.11
0.1
0.08
0.06
0.15
0.07
0.11
0.21
0.14
0.21
0.25
0.14
0.15
0.15
0.12
0.08
0.12
0.22
0.32
0.23
0.21
0.3
0.41
0.35
0.31
0.24

Alligator
cracking
(ft)
69
120
110
51
43
349
381
35
86
7
55
29
54
4
0
13
134
102
12
216
49
62
48
72
0
0

Longitudinal
cracking (ft)

Transverse
cracking (ft)

100
140
87
148
194
56
0
71
38
9
0
0
38
13
16
0
35
161
86
125
0
0
0
0
0
0

404
470
345
278
400
304
330
120
56
59
31
33
81
77
79
28
93
204
64
176
24
0
8
33
0
0

Table A.4 Formatted pavement condition data along I-69BL in Michigan
Mile points

Route

Control
section

Beginning

I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL
I69BL

33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043
33043

0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
1.100
1.200
1.300
1.400
1.500
1.600
1.700
1.800
1.900
2.000
2.100
2.200
2.300
2.458
2.558

Ending

Direction
to survey

Year

IRI
(in/mi)

0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
1.100
1.200
1.300
1.400
1.500
1.600
1.700
1.800
1.900
2.000
2.100
2.200
2.300
2.458
2.558
2.658

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000

202
143
175
258
182
188
170
112
144
189
207
166
232
173
174
89
307
243
200
100
74
116
67
61
202
143

205

Rut
depth
(in)
0.94
0.59
0.59
0.58
0.67
0.65
0.69
0.36
0.42
0.61
0.86
0.67
0.30
0.52
0.61
0.33
1.30
1.23
0.76
0.18
0.15
0.16
0.20
0.43
0.94
0.59

Alligator
cracking
(ft)
-

Longitudinal
cracking (ft)

Transverse
cracking (ft)

25
41
68
80
76
81
74
76
103
106
106
34
99
59
64
57
74
73
54
35
32
61
54
107
2
25

22
18
37
36
29
33
47
38
30
56
35
35
45
9
1
1
34
27
4
16
3
14
22
18

Table A.5 Formatted pavement condition data along I-5 in Washington
Mile points

Route

Control
section

Beginning

I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5
I-5

-

5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8

Ending

Direction
to survey

Year

IRI
(in/mi)

5.4
5.5
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003

94
123
67
68
95
77
75
81
85
91
131
89
68
67
78
73
74
95
67
85
81
106
84
85
80
68

206

Rut
depth
(in)
0.04
0.04
0.16
0.31
0.35
0.31
0.20
0.31
0.31
0.46
0.41
0.24
0.28
0.24
0.35
0.28
0.20
0.12
0.12
0.12
0.20
0.31
0.35
0.24
0.16
0.04

Alligator
cracking
(ft)
0
0
0
0
0
0
0
137.28
42.24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10.56
0
0

Longitudinal
cracking (ft)

Transverse
cracking (ft)

0
132
359.04
73.92
0
0
21.12
15.84
0
42.24
21.12
163.68
68.64
63.36
52.8
0
52.8
132
0
0
0
0
0
42.24
5.28
0

0
0
0
0
0
0
0
0
0
0
48
12
0
0
0
0
0
0
12
0
0
12
24
48
12
0

Table A.6 Formatted pavement condition data along cell 1 at MnROAD
Cell

Date

IRI
(in/mi)

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

11-FEB-94
21-OCT-94
20-APR-95
04-NOV-95
13-FEB-96
01-MAR-96
13-MAR-96
18-APR-96
13-NOV-96
30-APR-97
15-NOV-97
29-APR-98
02-OCT-98
20-APR-99
22-OCT-99
16-MAY-00
04-JAN-01
30-APR-01
23-OCT-01
20-APR-02
08-OCT-02
18-APR-03
15-OCT-03
21-APR-04
14-APR-05

94
123
67
68
95
77
75
81
85
91
131
89
68
67
78
73
74
95
67
85
81
106
84
85
80

Rut
depth
(in)
0.04
0.04
0.16
0.31
0.35
0.31
0.20
0.31
0.31
0.46
0.41
0.24
0.28
0.24
0.35
0.28
0.20
0.12
0.12
0.12
0.20
0.31
0.35
0.24
0.16

Alligator cracking (ft)

Longitudinal cracking
(ft)

Transverse cracking (ft)

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40
20
20
5

0
0
0
0
170
184
184
190
190
190
190
191
2
2
2
2
2
2
2
14
14
38
38
160
204

207

APPENDIX B

PAVEMENT PERFORMANCE DATA SAMPLING FIGURES

208

Data per 0.1 mile

330
280
230
180
130
80
30

321

323

290

325
327
329
331
333
a) Mile point along HWY 24 (flexible)
Year 1999

Data sampled per mile

330

292

294

296

298

300

302

b) Mile point along I-70 (rigid)
Year 2000

Data per 0.1 mile

Data sampled per mile

330

280

IRI (in/mile) .

IRI (in/mile) .

Data sampled per mile

Data per 0.1 mile
IRI (in/mile)

IRI (in/mile)

Data sampled per mile

350
300
250
200
150
100
50
0

230
180
130

Data per 0.1 mile

280
230
180
130
80

80

30

30

48

49
50
51
52
53
c) Mile point along HWY 36 (composite)
Year 2004

194

54

196
198
200
d) Mile point along HWY 71 (flexible)
Year 2000

Figure B.1 Continuous and sampled IRI data along four roads in Colorado

209

202

Data sampled per mile

Data per 0.1 mile

280

IRI (in/mile) .

IRI (in/mile) .

330

230
180
130
80
30
0

2

4

6

8

Data sampled per mile

330
280
230
180
130
80
30
0

10

2

a) Mile point along LA-34 (flexible)
Year 1999
Data sampled per mile

6

8

10

12

14

b) Mile point along LA-83 (rigid)
Year 1997

Data per 0.1 mile

280

Data sampled per mile

330

Data per 0.1 mile

280
IRI (in/mile) .

330
IRI (in/mile) .

4

Data per 0.1 mile

230
180
130

230
180
130

80

80

30

30
0

2

4
6
8
10
12
c) Mile point along LA-1 (composite)
Year 2000

0

2

4

6

8

10

d) Mile point along LA-526 (rigid)
Year 1995

Figure B.2 Continuous and sampled IRI data along four roads in Louisiana

210

12

Data sampled per mile

Data per 0.1 mile

Data sampled per mile

200
150
100
50
0

200
150
100
50
0

0

2

4

6

8

10

12

14

16

18

0

a) Mile point along I-94 (composite)
Year 2001

Data sampled per mile

2

4

6

8

10

12

b) Mile point along I-69, control section 12033
(rigid) Year 2001

Data per 0.1 mile

200

Data sampled per mile

250

Data per 0.1 mile

200

IRI (in/mile) .

250
IRI (in/mile) .

Data per 0.1 mile

250

IRI (in/mile) .

IRI (in/mile) .

250

150
100
50
0

150
100
50
0

0

2

4

6

8

10

12

14

16

18

0

c) Mile point along US-31 (flexible)
Year 2001

2

4

6

8

10

d) Mile Point along I-69, control section 77024
(rigid) Year 2001

Figure B.3 Continuous and sampled IRI data per mile along four roads in Michigan

211

12

Data sampled per mile

Data sampled per mile

Data per 0.1 mile

IRI (in/mile)

IRI (in/mile)

400
300
200

400
300
200

100

100

0

0
58

60

62

64

66

68

70

72

74

76

78

80

8

a) Mile point along SRID 005 (composite)
Year 2002

Data sampled per mile

10
12
14
16
18
b) Mile point along SRID 161 (composite)
Year 2002

Data sampled per mile

Data per 0.1 mile

IRI (in/mile)

400
IRI (in/mile)

Data per 0.1 mile

300
200

Data per 0.1 mile

400
300
200

100

100

0

0
263

265

267

269

271

273

275

100

104

108

112

116

120

d) Mile point along SRID 082 (rigid)
Year 2000

c) Mile point along SRID 005 (flexible)
Year 2000

Figure B.4 Continuous and sampled IRI data per mile along four roads in Washington

212

124

Transverse crack length (feet) .

321

Transverse crack length (feet) .

Data per 0.1 mile

323
325
327
329
331
333
a) Mile point along HWY 24 (flexible)
Year 1999
Data sampled per mile

Transverse crack length (feet) .

Transverse crack length (feet)

Data sampled per mile

350
300
250
200
150
100
50
0

Data per 0.1 mile

350
300
250
200
150
100
50
0
48

49
50
51
52
53
c) Mile point along HWY 36 (composite)
Year 2003

54

Data sampled per mile

Data per 0.1 mile

350
300
250
200
150
100
50
0
290

295
300
b) Mile point along I-70 (rigid)
Year 2003
Data sampled per mile

Data per 0.1 mile

350
300
250
200
150
100
50
0
194

196

198

200

d) Mile point along HWY 71 (flexible)
Year 2000

Figure B.5 Continuous and sampled transverse crack data along four roads in Colorado

213

Transverse crack length (feet) .

Data per 0.1 mile

1000

800
600

400
200
0
0

2
4
6
8
a) Mile point along LA-34 (flexible)
Year 1995
Data sampled per mile

10

Transverse crack length (feet) .

Transverse crack length (feet) .
Transverse crack length (feet) .

Data sampled per mile

Data per 0.1 mile

1000
800
600
400
200
0
0

2
4
6
8
10
c) Mile point along LA-1 (composite)
Year 1995

12

Data sampled per mile

Data per 0.1 mile

1000
800
600
400
200
0
0

2

4
6
8
10
12
b) Mile point along LA-83 (rigid)
Year 1995

Data sampled per mile

Data per 0.1 mile

1000
800
600
400
200
0
0

2

4

6

8

10

d) Mile point along LA-526 (rigid)
Year 1995

Figure B.6 Continuous and sampled transverse crack data per mile along four roads in Louisiana

214

14

12

80
60
40
20
0
0

2

4
6
8
10 12 14 16
a) Mile point along I-94 (composite)
Year 1993
Data sampled per mile

18

Transverse crack length (feet) .

Data per 0.1 mile

Transverse crack length (feet)

Transverse crack length (feet)
.
Transverse crack length (feet) .

Data sampled per mile

100

Data per 0.1 mile

100
80
60
40
20
0
0

2

4
6
8
10 12 14 16
c) Mile point along US-31 (flexible)
Year 1993

18

Data sampled per mile

100

Data per 0.1 mile

80
60
40
20
0
0

2
4
6
8
10
12
b) Mile point along I-69, control section 12033
(rigid) Year 1993
Data sampled per mile

100

Data per 0.1 mile

80
60
40
20
0
0

2

4

6

8

10

d) Mile point along I-69, control section 77024
(rigid) Year 2001

Figure B.7 Continuous and sampled transverse crack data per mile along four roads in Michigan

215

12

60

62 64 66 68 70 72 74 76 78
a) Mile point along SRID 005 (composite)
Year 2008
Data sampled per mile

350

80

Data per 0.1 mile

300
250
200
150
100
50
0
263

265

267

269

271

273

Transverse crack length (feet)

58

Data per 0.1 mile

Tramsverse crack length (feet)

Transverse crack length (feet)

Transverse crack length (feet)

Data sampled per mile

350
300
250
200
150
100
50
0

275

c) Mile point along SRID 005 (flexible)
Year 2006

Data sampled per mile

Data per 0.1 mile

350
300
250
200
150
100
50
0
8

10
12
14
16
b) Mile point along SRID 161 (composite)
Year 2002
Data sampled per mile

350

Data per 0.1 mile

300
250
200

150
100
50
0
100

104
108
112
116
120
d) Mile point along SRID 082 (rigid)
Year 2008

Figure B.8 Continuous and sampled transverse crack data per mile along four roads in Washington

216

18

124

300
IRI (in/mile) .

IRI (in/mile) .

300
200
100
0

200
100
0

321

323

325

327

329

331

333

290

a) Mile point along HWY 24 (flexible)
Year 1999

294

296

298

300

b) Mile point along I-70 (rigid)
Year 1999

300

300

IRI (in/mile) .

IRI (in/mile)

292

200
100
0
48

49

50

51

52

200
100
0

53

194

196

198

200

d) Mile point along HWY 71 (flexible)
Year 2002

c) Mile point along HWY 36 (composite)
Year 2003

Figure B.9 Sampled (squares) and continuous IRI data per mile along four roads in Colorado

217

400
IRI (in/mile)

IRI (in/mile)

400
300
200
100

200

100
0

0
0

2
4
6
8
a) Mile point along LA-34 (flexible)
Year 1997

0

10

2

4

6

8

10

12

b) Mile point along LA-83 (rigid)
Year 2005

400

400
IRI (in/mile) .

IRI (in/mile)

300

300
200
100

300
200
100
0

0
0

2

4

6

8

0

10

2

4

6

8

10

d) Mile point along LA-526 (rigid)
Year 2003

c) Mile point along LA-1 (composite)
Year 1995

Figure B.10 Sampled (squares) and continuous IRI data per mile along four roads in Louisiana

218

250

200

200

IRI (in/mile)

IRI (in/mile)

250

150
100

150
100

50

50

0

0
0

2

4

6

8

10

12

14

0

16

a) Mile point along I-94 (composite)
Year 2001

4

6

8

10

b) Mile point along I-69, control section 12033 (rigid)
Year 2001
250

200

200

IRI (in/mile)

250
IRI (in/mile)

2

150
100
50
0

150
100

50
0

0

2

4

6

8

10

12

14

16

0

c) Mile point along US-31 (flexible)
Year 2001

2

4

6

8

10

d) Mile point along I-69, control section 77024 (rigid)
Year 2001

Figure B.11 Sampled (squares) and continuous IRI data per mile along four roads in Michigan

219

200

IRI (in/mile)

250

200
IRI (in/mile)

250

150
100

150
100

50

50

0

0
8

58 60 62 64 66 68 70 72 74 76 78 80
a) Mile point along SRID 005 (composite)
Year 1999

200

IRI (in/mile) .

250

200
IRI (in/mile)

250

10
12
14
16
b) Mile point along SRID 161 (composite)
Year 1999

150
100

150
100

50

50

0

0
263

100

265
267
269
271
273
c) Mile point along SRID 005 (flexible)
Year 1999

104
108
112
116
120
d) Mile point along SRID 082 (rigid)
Year 1999

Figure B.12 Sampled (squares) and continuous IRI data per mile along four roads in Washington

220

Transverse crack length (feet) .

300
200
100
0
321

323

325

327

329

331

333

400
300
200
100
0
290

a) Mile point along HWY 24 (flexible)
Year 1999
400
300
200
100
0
48

49

50

51

52

292

294

296

298

300

b) Mile point along I-70 (rigid)
Year 2000
Transverse crack length (feet)

Transverse crack length (feet) .
Transverse crack length (feet) .

400

53

c) Mile point along HWY 36 (composite)
Year 2003

400
300
200
100
0
194

196

198

200

d) Mile point along HWY 71 (flexible)
Year 2002

Figure B.13 Sampled (squares) and continuous transverse crack data per mile along four roads in Colorado

221

Transverse crack length (feet) .

Transverse crack length (feet) .

2500
2000
1500
1000
500
0

0

2

4

6

8

10

2500
2000
1500
1000
500
0
0

2

Transverse crack length (feet) .

Transverse crack length (feet)

2500
2000
1500
1000
500
0
2

4

6

8

6

8

10

12

b) Mile point along LA-83 (rigid)
Year 1995

a) Mile point along LA-34 (flexible)
Year 1995

0

4

10

c) Mile point along LA-1 (composite)
Year 1997

2500
2000

1500
1000
500
0
0

2

4

6

8

10

d) Mile point along LA-526 (rigid)
Year 1995

Figure B.14 Sampled (squares) and continuous transverse crack data per mile four roads in Louisiana

222

12

Transverse crack length (feet) .

Transverse crack length (feet)

100

80
60
40
20
0
0

2

4

6

8

10

12

14

16

100
80
60
40
20
0
0

100
80
60
40
20
0
0

2

4

6

8

10

12

14

4

6

8

10

b) Mile point along I-69, control section 12033 (rigid)
Year 1993

Transverse crack length (feet) .

Transverse crack length (feet)

a) Mile point along I-94 (composite)
Year 1993

2

16

c) Mile point along US-31 (flexible)
Year 1993

100

80
60
40
20
0
0

2

4

6

8

10

d) Mile point along I-69, control section 77024 (rigid)
Year 2001

Figure B.15 Sampled (squares) and continuous transverse crack data per mile along four roads in Michigan

223

350
Transverse crack length (feet)

Transverse crack length (feet)

350
300
250
200
150
100
50
0

300
250
200
150
100
50
0

8

350
300
250
200
150
100
50
0
263

Transverse crack length (feet)

Transverse crack length (feet)

58 60 62 64 66 68 70 72 74 76 78 80
a) Mile point along SRID 005 (composite)
Year 2008

265
267
269
271
273
c) Mile point along SRID 005 (flexible)
Year 2006

10
12
14
16
b) Mile point along SRID 161 (composite)
Year 2002

350
300
250
200
150
100
50
0
100

104

108

112

116

120

d) Mile point along SRID 082 (rigid)
Year 2008

Figure B.16 Sampled (squares) and continuous transverse crack data per mile along four roads in Washington

224

Continuous IRI data as a percent of the sampled data .

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

300

250

200

150

100

50

0
100

105

110

115

120

Mile point
Figure B.17 Continuous time series IRI data as percent of the sampled data along HWY 24 (flexible) in Colorado

225

125

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

Continuous IRI data as percent of the sampled data .

260
240

220
200
180
160
140
120
100
80
60
40
290

292

294

296

298

300

Mile point
Figure B.18 Continuous time series IRI data as percent of the sampled data along I-70 (rigid) in Colroado

226

302

Sampled

2003

2004

2005

2006

2007

2008

Continuous IRI data a percent of the sampled data .

260
240
220
200
180
160
140
120
100
80
60

40
48

49

50

51

52

53

54

Mile point
Figure B.19 Continuous time series IRI data as percent of the sampled data along HWY 36 (composite) in Colorado

227

55

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

Continuous IRI data as percent of the sampled data .

260
240
220
200
180
160
140
120
100
80
60
40
20
0
194

195

196

197

198

199

200

201

Mile point
Figure B.20 Continuous time series IRI data as percent of the sampled data along HWY 71 (flexible) in Colorado

228

202

Sampled

1997

2000

2003

2005

Continuous IRI data as percent of the sampled data .

450
400
350
300
250
200
150
100
50
0
0

2

4

6

8

10

Mile point
Figure B.21 Continuous time series IRI data as percent of the sampled data along LA-34 (flexible) in Louisiana

229

Sampled

1995

1997

2000

2003

2005

Continuous IRI data as a percent of the sampled data .

250

200

150

100

50

0
0

2

4

6

8

10

12

Mile point
Figure B.22 Continuous time series IRI data as percent of the sampled data along LA-83 (rigid) in Louisiana

230

14

Sampled

1995

1997

2000

2003

2005

Continuous IRI data as percent of the sampled data .

200
180
160
140
120
100
80
60

40
20
0
0

2

4

6

8

10

Mile point
Figure B.23 Continuous time series IRI data as percent of the sampled data along LA-1 (composite) in Louisiana

231

12

Sampled

1995

1997

2000

2003

2005

Continuous IRI data as percent of the sampled data .

350

300

250

200

150

100

50

0
0

2

4

6

8

10

Mile point
Figure B.24 Continuous time series IRI data as percent of the sampled data along LA-526 (rigid) in Louisiana

232

12

Sampled

Continuous IRI data as percent of the sampled data .

400

2001

2003

2005

2007

300

200

100

0
0

2

4

6

8

10

12

14

16

Mile point

Figure B.25 Continuous time series IRI data as percent of the sampled data along I-94 (composite) in Michigan

233

18

Sampled

Continuous IRI data as percent of the sampled data .

200

2001

2003

2005

2007

100

0
0

2

4

6

8

10

Mile point, control section 12033

Figure B.26 Continuous time series IRI data as percent of the sampled data along I-69 (CS 12033, rigid) in Michigan

234

12

Sampled

2001

2003

2005

2007

Continuous IRI data as percent of the sampled data .

600

500

400

300

200

100

0
0

2

4

6

8

10

12

14

16

Mile point

Figure B.27 Continuous time series IRI data as percent of the sampled data along US-31 (flexible) in Michigan

235

18

Sampled

2001

2003

2005

2007

Continuous IRI data as percent of the sampled data .

260

240
220
200
180
160
140
120
100
80

60
40
20
0
0

2

4

6

8

10

Mile point, control section 77024

Figure B.28 Continuous time series IRI data as percent of the sampled data along I-69 (CS 77024, rigid) in Michigan

236

12

Continuous IRI data as a percent of sampled data

Sampled

1999

2000

2001

62

64

66

2002

2003

2004

68

70

72

2005

2006

2007

2008

6000

5000

4000

3000

2000

1000

0
58

60

74

76

78

80

Mile point

Figure B.29 Continuous time series IRI data as a percent of the sampled data along SRID 005 (composite) in Washington

237

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

Continuous IRI data as a percent of sampled data

300

250

200

150

100

50

0
8

10

12

14

16

Mile point

Figure B.30 Continuous time series IRI data as a percent of the sampled data along SRID 161 (composite) in Washington

238

18

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

Continuous IRI data as percent of the sampled data

300

250

200

150

100

50

0
263

265

267

269

271

273

275

Mile point
Figure B.31 Continuous time series IRI data as a percent of the sampled data along SRID 005 (flexible) in Washington

239

Continuous IRI data as a percent of the sampled data .

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

300

250

200

150

100

50

0
100

105

110

115

120

Mile point
Figure B.32 Continuous time series IRI data as a percent of the sampled data along SRID 082 (rigid) in Washington

240

125

Continuous transverse crack data as a percent of the sampled
data

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

350
300
250
200
150
100
50
0
100

105

110

115

120

125

Mile point

Figure B.33 Continuous time series transverse crack data as percent of the sampled data along HWY 24 (flexible) in Colorado

241

Continuous transverse crack data as percent of the sampled data
.

Sampled

1999

2000

2001

2002

2003

10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
290

292

294

296

298

300

Mile point
Figure B.34 Continuous time series transverse crack data as percent of the sampled data along I-70 (rigid) in Colorado

242

302

Continuous transverse crack data as percent of the sampled data
.

Sampled

2003

2004

260
240
220
200
180
160
140
120
100
80
60
40
48

49

50

51

52

53

54

Mile point
Figure B.35 Continuous time series transverse crack data as percent of the sampled data along HWY 36 (composite) in Colorado

243

Continuous transverse crack data as percent of the sampled data
.

Sampled

1999

2000

2001

2002

2003

260
240
220
200
180
160
140
120
100
80
60
40
20
0
194

195

196

197

198

199

200

Mile point
Figure B.36 Continuous time series transverse crack data as percent of the sampled data along HWY 71 (flexible) in Colorado

244

201

Continuous transverse crack data as percent of the sampled data
.

Sampled

1995

1997

2000

2003

2005

160000
140000
120000
100000
80000
60000

40000
20000
0
0

2

4

6

8

10

Mile point
Figure B.37 Continuous time series transverse crack data as percent of the sampled data along LA-34 (flexible) in Louisiana

245

Continuous transverse crack data as percent of the sampled data .

Sampled

1995

1997

2000

2003

2005

1800
1600
1400
1200
1000
800
600
400

200
0
0

2

4

6

8

10

12

Mile point
Figure B.38 Continuous time series transverse crack data as percent of the sampled data along LA-83 (rigid) in Louisiana

246

14

Continuous transverse crack data as percent of the sampled
data .

Sampled

1995

1997

2000

2003

2005

1600
1400
1200
1000
800
600
400
200
0
0

2

4

6

8

10

Mile point
Figure B.39 Continuous time series transverse crack data as percent of the sampled data along LA-1 (composite) in Louisiana

247

12

Continuous transverse crack data as a percent of the sampled
data .

Sampled

1995

1997

2000

2003

2005

2500

2000

1500

1000

500

0
0

2

4

6

8

10

12

Mile point
Figure B.40 Continuous time series transverse crack data as percent of the sampled data along LA-526 (rigid) in Louisiana

248

14

Continuous transverse crack data as percent of the sampled data
.

Sampled

1993

1995

1997

1999

2001

2003

2005

2007

14000

12000

10000

8000

6000

4000

2000

0
0

2

4

6

8

10

12

14

16

Mile point

Figure B.41 Continuous time series transverse crack data as percent of the sampled data along I-94 (composite) in Michigan

249

18

Sampled

Continuous IRI data as percent of the sampled data .

5000

2001

2003

2005

2007

4000

3000

2000

1000

0
0

2

4

6

8

10

12

Mile point, control section 12033
Figure B.42 Continuous time series transverse crack data as percent of the sampled data long I-69 (CS 12033, rigid) in Michigan

250

Continuous transverse crack data as percent of the sampled data
.

Sampled

1993

1995

1997

1999

2001

2003

2005

2007

25000

20000

15000

10000

5000

0
0

2

4

6

8

10

12

14

16

Mile point
Figure B.43 Continuous time series transverse crack data as percent of the sampled data along US-31 (flexible) in Michigan

251

18

Continuous transverse crack data as percent of the sampled .
data

Sampled

10000

1997

1999

2001

2005

2007

9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0

2

4

6

8

10

12

Mile point, control section 77024

Figure B.44 Continuous time series transverse crack data as percent of the sampled data along I-69 (CS 77024, rigid) in Michigan

252

Continuous transverse crack data as a percent of sampled
data

Sampled

1999

2000

2001

2002

2003

2004

2005

62

64

66

68

70

72

74

2006

2007

2008

4000
3500
3000
2500
2000
1500
1000
500

0
58

60

76

78

80

Mile point
Figure B.45 Continuous time series transverse crack data as percent of the sampled data along SRID 005 (composite) in Washington

253

Continuous transverse cracking data as a percent of sampled
data

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

1200

1000

800

600

400

200

0
8

10

12

14

16

18

Mile point
Figure B.46 Continuous time series transverse crack data as percent of the sampled data along SRID 161 (composite) in Washington

254

Continuous transverse crack data as percent of the sampled data

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

400

350

300

250

200

150

100

50

0
263

265

267

269

271

273

275

Mile point

Figure B.47 Continuous time series transverse crack data as percent of the sampled data along SRID 005 (flexible) in Washington

255

Continuous transverse crack data as a percent of the sampled
data

Sampled

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

350
300
250
200
150
100
50
0
100

105

110

115

120

125

Mile point
Figure B.48 Continuous time series transverse crack data as percent of the sampled data along SRID 082 (rigid) in Washington

256

0

2
4
6
8
a) Mile point along LA-34 (flexible)
Year 1999
Data sampled per mile

0

1

2

4

6

8

10

12

b) Mile point along LA-83 (rigid)
Year 1995

Data per 0.1 mile

Data sampled per mile

430
380
330
280
230
180
130
80
30
0

Data per 0.1 mile

430
380
330
280
230
180
130
80
30

10

IRI (in/mile)

IRI (in/mile)

Data sampled per mile

Data per 0.1 mile

IRI (in/mile)

IRI (in/mile)

Data sampled per mile

430
380
330
280
230
180
130
80
30

0

2
3
4
5
6
c) Mile point along LA-1 (composite)
Year 1995

2

4
6
8
10
12
d) Mile point along LA-526 (rigid)
Year 1999

Figure B.49 Continuous and randomly sampled IRI data per mile along four roads in Louisiana

257

Data per 0.1 mile

430
380
330
280
230
180
130
80
30

14

Data per 0.1 mile

IRI (in/mile)

IRI (in/mile)

Data sampled per mile

330
280
230
180
130
80
30
0

2

4
6
8
10 12 14
a) Mile point along I-94 (composite)
Year 2001

Data sampled per mile

330

16

0

18

2

4

6

Data per 0.1 mile

8

10

12

b) Mile point along I-69, control section 12033
(rigid) Year 2001

Data per 0.1 mile

Data sampled per mile

Data per 0.1 mile

330
IRI (inch/mile)

280
IRI (in/mile)

Data sampled per mile

330
280
230
180
130
80
30

230
180
130
80

280
230
180
130
80
30

30
0

2

4

6
8
10 12 14
c) Mile point along US-31
Year 2001

16

0

18

2
4
6
8
10
d) Mile Point along I-69, control section 77024
(rigid) Year 2001

Figure B.50 Continuous and randomly sampled IRI data per mile along four roads in Michigan

258

12

Transverse crack length (feet)

Data per 0.1 mile

2000
1500
1000
500
0
0

2
4
c ) Mile point along LA-1 (composite)
Year 1997
Data sampled per mile

2500

Data per 0.1 mile

2000
1500
1000
500
0
0

6

Data sampled per mile

2500

Data per 0.1 mile

2000
1500
1000
500
0
0

2

4

6

8

10

12

14

d) Mile point along LA-526 (rigid)
Year 1995
Transverse crack length (feet)

Transverse crack length (feet)
Transverse crack length (feet)

Data sampled per mile

2500

2
4
6
8
10
a) Mile point along LA-34 (flexible)
Year 1995

Data sampled per mile

Data per 0.1 mile

2500
2000
1500
1000
500
0
0

2

4

6

8

10

12

14

b) Mile point along LA-83 (rigid)
Year 1995

Figure B.51 Continuous and randomly sampled transverse crack data along four roads in Louisiana

259

16

Transverse crack length (feet)
.

Data per 0.1 mile

Data sampled per mile

Data per 0.1 mile

150

100

100

50
0
0

2
4
6
8
10 12 14 16
a) Mile point along I-94 (composite)
Year 1993
Data sampled per mile

150

18

Data per 0.1 mile

100
50
0
0

2

4

6

8

10

12

14

16

50
0
0

2

4

6

8

10

12

b) Mile point along I-69, control section 12033
(rigid) Year 1993

18

Transverse crack length (feet)

Transverse crack length (feet)
Transverse crack length (feet) .

Data sampled per mile

150

c) Mile point along US-31 (flexible)
Year 1993

Data sampled per mile

150

Data per 0.1 mile

100
50
0
0

2
4
6
8
10
12
d) Mile point along I-69, control section 77024
(rigid) Year 1997

Figure B.52 Continuous and randomly sampled transverse crack data along four roads in Michigan

260

4 projects

2 projects

4 projects

2 projects

Sample size (percent)

10
30
60
100

321

323

325

327

329

331

333

335

Beginning mile point
Figure B.53 Project boundaries based on the continuous (100 percent sampled) and the sampled
rut depth data along a section of the flexible HWY 24 in Colorado
7 projects

8 projects

7 projects

5 projects

Sample size (percent)

10
30
60
100

321

323

325

327

329

331

333

335

Beginning mile point
Figure B.54 Project boundaries based on the continuous (100 percent sampled) and the sampled
transverse cracking data along a section of the flexible HWY 24 in Colorado

261

3 projects

4 projects

3 projects

5 projects

Sample size (percent)

10
30
60
100

8

10

12

14

16

18

Beginning mile point
Figure B.55 Project boundaries based on the continuous (100 percent sampled) and the sampled
rut depth data along a section of the composite SRID 161 in Washington
4 projects

4 projects

4 projects

4 projects

Sample size (percent)

10
30
60
100

321

323

325

327

329

331

333

335

Beginning mile point
Figure B.56 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(rut depth) data along a section of the flexible HWY 24 in Colorado

262

3 projects

7 projects

3 projects

5 projects

Sample size (percent)

10
30
60
100

321

323

325

327

329

331

333

335

Beginning mile point
Figure B.57 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(transverse cracking) data along a section of the flexible HWY 24 in Colorado
4 projects

3 projects

3 projects

5 projects

Sample size (percent)

10
30
60
100

8

10

12

14

16

18

Beginning mile point
Figure B.58 Project boundaries based on the continuous (100 percent sampled) and sampled RSL
(rut depth) data along a section of the composite SRID 161 in Washington

263

APPENDIX C

PAVEMENT ANALYSIS LENGTH FIGURES

264

Rut depth

Longitudinal cracking

Percent acceptance, thin mill and fill, 91
0.1 mile pavement segments

IRI

Alligator cracking

Transverse cracking

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure C.1 Percent acceptance versus pavement analysis length, thin mill and fill, Colorado
IRI
Longitudinal cracking

Rut depth
Transverse cracking

Alligator cracking

Percent acceptance, thick HMA overlay,
2520 0.1 mile pavement segments

100.0
80.0

60.0
40.0
20.0

0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure C.2 Percent acceptance versus pavement analysis length, thick HMA overlay, Louisiana

265

IRI
Longitudinal cracking

Rut depth
Transverse cracking

Alliagator cracking

Percent acceptance, double chip seal, 405
0.1 mile pavement segments

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure C.3 Percent acceptance versus pavement analysis length, double chip seal, Louisiana
Rut depth

Longitudinal cracking

Percent acceptance, thin mill and fill, 365
0.1 mile pavement segments

IRI

Alligator cracking

Transverse cracking

100.0
80.0

60.0
40.0
20.0

0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure C.4 Percent acceptance versus pavement analysis length, thin mill and fill, Louisiana

266

Percent acceptance, thick mill and fill,
1,390 0.1 mile pavement segments

IRI
Longitudinal cracking

Rut depth
Transverse cracking

Alligator cracking

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure C.5 Percent acceptance versus pavement analysis length, thick mill and fill, Louisiana
IRI
Longitudinal cracking

Rut depth
Transverse cracking

Alligator cracking

Percent acceptance, thick HMA overlay,
227 0.1 mile pavement segments

100.0
80.0

60.0
40.0
20.0

0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure C.6 Percent acceptance versus pavement analysis length, thick HMA overlay, Washington

267

Percent acceptance, thin mill and fill, 930
0.1 mile pavement segments

IRI
Longitudinal cracking

Rut depth
Transverse cracking

Alligator cracking

100.0
80.0
60.0
40.0
20.0
0.0
0

0.1

0.2

0.3

0.4
0.5
0.6
0.7
Analysis length (mile)

0.8

0.9

1

Figure C.7 Percent acceptance versus pavement analysis length, thin mill and fill, Washington

268

APPENDIX D

PAVEMENT PERFORMANCE DATA IMPUTATION FIGURES

269

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

40.0
20.0
0.0
-20.0
-40.0
3

4

5
Beginning mile point

6

7

Figure D.1 The difference between the imputed and measured data in percent of the measured
data versus the BMP along LA 21 (control section 0.02902) in Louisiana, three data points
imputed using the linear interpolation method

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

5

14

40.0
20.0
0.0
-20.0
-40.0
1

2

3
Cell number

Figure D.2 The difference between the imputed and measured data in percent of the measured
data versus cells 1, 2, 3, 5, and 14 at MnROAD, three data points imputed using the linear
interpolation method

270

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

40.0
20.0
0.0
-20.0
-40.0
10.5

10.6

11.2
11.6
Beginning mile point

11.7

Figure D.3 The difference between the imputed and measured data in percent of the measured
data versus the BMP along SRID 099 in Washington, three data points imputed using the linear
interpolation method

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

6.5
4.5
2.5
0.5
-1.5

3

4

5
Beginning mile point

6

7

Figure D.4 The difference between the RSL values based on imputed and measured data versus
the BMP along LA 21 (CS 0.02902) in Louisiana, three data points imputed using the linear
interpolation method

271

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

5

14

1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1

2

3
Cell number

Difference between RSL based on
imputed and that based on measured
data (year)

Figure D.5 The difference between the RSL values based on imputed and measured data versus
the cell number at MnROAD, three data points imputed using the linear interpolation method
Second available data point

Third

Fourth

0.5
0.0
-0.5
-1.0
-1.5
10.5

10.6

11.2
11.6
Beginning mile point

11.7

Figure D.6 The difference between the RSL values based on imputed and measured data versus
the BMP along SRID 099 in Washington, three data points imputed using the linear interpolation
method

272

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

40.0
20.0
0.0
-20.0
-40.0
3

4

5
Beginning mile point

6

7

Figure D.7 The difference between the imputed and measured data in percent of the measured
data versus the BMP along LA 21 (control section 0.02902) in Louisiana, three data points
imputed using the regression method

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

5

14

40.0
20.0
0.0
-20.0
-40.0
1

2

3
Cell number

Figure D.8 The difference between the imputed and measured data in percent of the measured
data versus cells 1, 2, 3, 5, and 14 at MnROAD, three data points imputed using the regression
method

273

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

40.0
20.0
0.0
-20.0
-40.0
10.5

10.6

11.2
11.6
Beginning mile point

11.7

Figure D.9 The difference between the imputed and measured data in percent of the measured
data versus the BMP along SRID 099 in Washington, three data points imputed using the
regression method

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

8.0
6.0
4.0
2.0
0.0
-2.0
3

4

5
6
Beginning mile point

7

Figure D.10 The difference between the RSL values based on imputed and measured data versus
the BMP along LA 21 (CS 0.02902) in Louisiana, three data points imputed using the regression
method

274

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

5

14

4.0
3.0
2.0
1.0
0.0
-1.0
1

2

3
Cell number

Figure D.11 The difference between the RSL values based on imputed and measured data versus
the cell number at MnROAD, three data points imputed using the regression method

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

0.5

0.0

-0.5

-1.0
10.5

10.6

11.2
11.6
Beginning mile point

11.7

Figure D.12 The difference between the RSL values based on imputed and measured data versus
the BMP along SRID 099 in Washington, three data points imputed using the regression method

275

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

40.0
20.0
0.0
-20.0
-40.0
3

4

5
Beginning mile point

6

7

Figure D.13 The difference between the imputed and measured data in percent of the measured
data versus the BMP along LA 21 (control section 0.02902) in Louisiana, three data points
imputed using the moving regression method

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

5

14

20.0
10.0
0.0
-10.0
-20.0
1

2

3
Cell number

Figure D.14 The difference between the imputed and measured data in percent of the measured
data versus cells 1, 2, 3, 5, and 14 at MnROAD, three data points imputed using the moving
regression method

276

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

40.0

20.0

0.0

-20.0
10.5

10.6

11.2
11.6
Beginning mile point

11.7

Figure D.15 The difference between the imputed and measured data in percent of the measured
data versus the BMP along SRID 099 in Washington, three data points imputed using the moving
regression method

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

6.0
4.0
2.0
0.0
-2.0
3

4

5
Beginning mile point

6

7

Figure D.16 The difference between the RSL values based on imputed and measured data versus
the BMP along LA 21 (CS 0.02902) in Louisiana, three data points imputed using the moving
regression method

277

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

5

14

2.0
1.5
1.0
0.5
0.0
-0.5
1

2

3
Cell number

Figure D.17 The difference between the RSL values based on imputed and measured data versus
the cell number at MnROAD, three data points imputed using the moving regression method

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

0.5
0.0
-0.5
-1.0
-1.5
10.5

10.6

11.2
11.6
Beginning mile point

11.7

Figure D.18 The difference between the RSL values based on imputed and measured data versus
the BMP along SRID 099 in Washington, three data points imputed using the moving regression
method

278

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

40.0
20.0
0.0
-20.0
-40.0
3

4

5
Beginning mile point

6

7

Figure D.19 The difference between the imputed and measured data in percent of the measured
data versus the BMP along LA 21 (control section 0.02902) in Louisiana, three data points
imputed using the multiple regressions method

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

5

14

20.0

0.0

-20.0

-40.0
1

2

3
Cell number

Figure D.20 The difference between the imputed and measured data in percent of the measured
data versus cells 1, 2, 3, 5, and 14 at MnROAD, three data points imputed using the multiple
regressions method

279

The difference between the imputed
and measured data in percent of the
measured data

Second available data point

Third

Fourth

40.0

20.0

0.0

-20.0
10.5

10.6

11.2
11.6
Beginning mile point

11.7

Figure D.21 The difference between the imputed and measured data in percent of the measured
data versus the BMP along SRID 099 in Washington, three data points imputed using the
multiple regressions method

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

6.0
4.0
2.0
0.0
-2.0
-4.0
3

4

5
6
Beginning mile point

7

Figure D.22 The difference between the RSL values based on imputed and measured data versus
the BMP along LA 21 (CS 0.02902) in Louisiana, three data points imputed using the multiple
regressions method

280

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

5

14

6.0
4.0
2.0
0.0
-2.0
1

2

3
Cell number

Figure D.23 The difference between the RSL values based on imputed and measured data versus
the cell number at MnROAD, three data points imputed using the multiple regressions method

Difference between RSL based on
imputed and that based on measured
data (year)

Second available data point

Third

Fourth

3.0
2.0
1.0
0.0
-1.0
10.5

10.6

11.2
11.6
Beginning mile point

11.7

Figure D.24 The difference between the RSL values based on imputed and measured data versus
the BMP along SRID 099 in Washington, three data points imputed using the multiple
regressions method

281

Maximum, minimum, and average
percent difference between imputed
and measured data

40.0
20.0
0.0

-20.0
-40.0
0

1

2
3
4
Imputation methods
1 = linear interpolation, 2 = regression,
3 = moving regression, 4 = multiple regression

5

Maximum, minimum, and average
percent difference between imputed
and measured data

Figure D.25 Maximum, minimum, and average percent difference between imputed and
measured data at BMPs 3, 4, 5, 6, and 7 along LA 21 (CS 0.02902) in Louisiana, using four
imputation methods
40.0
20.0
0.0
-20.0
-40.0
0

1

2
3
4
Imputation methods
1 = linear interpolation, 2 = regression,
3 = moving regression, 4 = multiple regression

5

Figure D.26 Maximum, minimum, and average percent difference between imputed and
measured data at cells 1, 2, 3, 5, and 14 at MnROAD, using four imputation methods

282

Maximum, minimum, and average
percent difference between imputed
and measured data

40.0
20.0
0.0

-20.0
-40.0
0

1

2
3
4
Imputation methods
1 = linear interpolation, 2 = regression,
3 = moving regression, 4 = multiple regression

5

Maximum, minimum, and average
RSL difference between imputed and
measured data (year)

Figure D.27 Maximum, minimum, and average percent difference between imputed and
measured data at BMPs 10.5, 10.6, 11.2, 11.6, and 11.7 along SRID 099 in Washington, using
four imputation methods
8.0
6.0
4.0
2.0
0.0
-2.0
-4.0
0

1

2
3
4
Imputation methods
1 = linear interpolation, 2 = regression,
3 = moving regression, 4 = multiple regression

5

Figure D.28 Maximum, minimum, and average difference between RSL values based on
imputed and measured data at BMPs 3, 4, 5, 6, and 7 along LA 21 (CS 0.02902) in Louisiana,
using four imputation methods

283

Maximum, minimum, and average
RSL difference between imputed and
measured data (year)

5.0
4.0
3.0
2.0
1.0
0.0
-1.0
0

1

2
3
4
Imputation methods
1 = linear interpolation, 2 = regression,
3 = moving regression, 4 = multiple regression

5

Maximum, minimum, and average
RSL difference between imputed and
measured data (year)

Figure D.29 Maximum, minimum, and average difference between RSL values based on
imputed and measured data at cells 1, 2, 3, 5, and 14 at MnROAD, using four imputation
methods
3.0
2.0
1.0
0.0

-1.0
-2.0
0

1

2
3
4
Imputation methods
1 = linear interpolation, 2 = regression,
3 = moving regression, 4 = multiple regression

5

Figure D.30 Maximum, minimum, and average difference between RSL values based on
imputed and measured data at BMPs 10.5, 10.6, 11.2, 11.6, and 11.7 along SRID 099 in
Washington, using four imputation methods

284

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285

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