Pavement Marking Specifications Compliance and Modeling of Retroreflectivity
Performance
by
Luana Clara de Sena Monteiro Ozelim
A thesis submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirements for the Degree of
Master of Science
Auburn, Alabama
May 6, 2012
Keywords: pavement markings, thermoplastic, retroreflectivity,
service life, modeling
Copyright 2012 by Luana Clara de Sena Monteiro Ozelim
Approved by
Rod E. Turochy, Chair, Associate Professor of Civil Engineering
Robert L. Vecellio, Associate Professor of Civil Engineering
Jeffrey J. LaMondia, Assistant Professor of Civil Engineering
ii
Abstract
This study provided an analysis of a database containing 7,840 observations of 40
highway pavement marking projects constructed in Alabama in 2007 to determine the extent to
which marking properties complied with ALDOT specifications. A statistical analysis was also
performed on these observations to determine mean, standard deviation, and coefficient of
variation by color and type of markings for marking properties. Results showed that
retroreflectivity had significant variation.
This research also developed models of retroreflectivity performance over time for
thermoplastic markings, which was executed for 15 projects that had measurements of
retroreflectivity for the same locations in 2007, 2008, 2009, and 2010. A linear model
considering age, initial retroreflectivity, and AADT as independent variables was the one which
best represented data, with R2 values of 0.398 for white markings and 0.479 for yellow markings.
iii
Acknowledgements
The preparation of this thesis during these years was possible because of the incredible
people I have in my life. I am deeply grateful to Dr Rod E. Turochy for giving me the
confidence to keep going with my research and the guidance to avoid getting lost when obstacles
appeared. I also thank him for the patience when helping me with my English, as I am Brazilian,
I know it was tough. Rod Turochy was a wonderful advisor and I just thank him and his wife,
Kathy Gregory, for being the most supportive people here in the United States.
I am very grateful to all staff of the Department of Civil Engineering of Auburn
University for the help and kindness during hard times. Dr Robert L. Vecellio and Dr Jeffrey J.
LaMondia, members of my committee, thank you for the advices and availability to always help
and clarify any doubts I had related to the research.
Gabriel Maciel Leite, an inspiration for me and for everybody that knows him, thank you
for being such this strong person that helped me since a long time ago and changed my life.
Derong Mai, my friend, I am so grateful for all your help when I needed, all the conversations,
and all the times you made me laugh.
Despite the geographical distance, my parents were a constant source of support.
Unfortunately, their English is not very good, so I have to thank them in Portuguese. Juvenal e
Lenilza, devo tudo de bom que acontece na minha vida a voc?s. Obrigada por sempre confiarem
em mim e me deixarem viver meus sonhos. M?e, sei que n?o foi f?cil ficar tanto tempo nos
Estados Unidos sem falar ingl?s, sempre ouvindo meus desabafos, sempre paciente com meu
iv
mau humor e estresse em v?rios momentos, eu nunca teria conseguido sem voc?. I also would
like to tell my brother, Luan, that he is the best person I know, thank you for just being you. I
know I can do anything because my family is the best, none of this could have happened without
them, so this thesis is dedicated to them.
v
Table of Contents
Abstract ........................................................................................................................................... ii
Acknowledgements ........................................................................................................................ iii
List of Tables ................................................................................................................................. ix
List of Figures ................................................................................................................................ xi
Chapter One .................................................................................................................................... 1
Introduction ..................................................................................................................................... 1
1.1. Background .......................................................................................................................... 2
1.2. Objectives ............................................................................................................................ 3
1.3. Scope .................................................................................................................................... 4
1.4. Outline.................................................................................................................................. 5
Chapter Two.................................................................................................................................... 6
Literature Review............................................................................................................................ 6
2.1. Characterization of Pavement Markings .............................................................................. 7
2.2. Retroreflectivity Threshold .................................................................................................. 9
2.3. Pavement Marking Retroreflectivity Modeling ................................................................. 14
vi
2.4. Pavement Marking Materials Specifications and Requirements ....................................... 21
2.5. Economic Evaluation of Thermoplastic Materials ............................................................ 23
2.6. Service Life of Thermoplastic Pavement Markings .......................................................... 29
2.7. Summary of findings.......................................................................................................... 31
Chapter Three................................................................................................................................ 34
Methodology ................................................................................................................................. 34
3.1. ALDOT specifications study ............................................................................................. 34
3.2. Data Mining and Analysis ................................................................................................. 35
3.3. Retroreflectivity Modeling................................................................................................. 40
3.3.1. Preparation of Data for Modeling ............................................................................... 44
3.3.2. Model Fitting .............................................................................................................. 46
3.4. Benefit/Cost Calculation .................................................................................................... 49
3.5. Modeling of Retroreflectivity Over Time .......................................................................... 49
3.6. Summary of Chapter Three ................................................................................................ 52
Chapter Four ................................................................................................................................. 53
Results ........................................................................................................................................... 53
4.1. ALDOT Data Mining and Analysis ................................................................................... 53
4.2. Retroreflectivity Modeling................................................................................................. 55
4.2.1. Retroreflectivity Curve ............................................................................................... 55
4.2.2. Model Fitting Analysis ............................................................................................... 56
vii
4.3. Benefit/Cost Calculation .................................................................................................... 59
4.4. Modeling of Retroreflectivity Over Time .......................................................................... 61
4.4.1. Approach One: Initial Retroreflectivity and Age of Marking as Independent
Variables????????????????????????????????63
4.4.2. Approach Two: Initial Retroreflectivity, Age of Marking, and Traffic Volume as
Independent Variables........................................................................................................... 69
4.4.3. Service Life ................................................................................................................. 71
4.5. Summary of Chapter Four ................................................................................................. 74
Chapter Five .................................................................................................................................. 76
Conclusions and Recommendations ............................................................................................. 76
5.1. Conclusions ........................................................................................................................ 76
5.2. Recommendations .............................................................................................................. 78
5.3. Recommendations for Subsequent Studies ........................................................................ 79
References ..................................................................................................................................... 81
Appendix A ................................................................................................................................... 85
Project STPSA-0185(500): Pictures ............................................................................................. 85
Appendix B ................................................................................................................................... 89
List of Mileposts by Project .......................................................................................................... 89
Appendix C ................................................................................................................................... 93
Retroreflectivity Modeling for Yellow Markings: Initial Retroreflectivity and Age as
Independent Variables .................................................................................................................. 93
Appendix D ................................................................................................................................... 98
viii
Retroreflectivity Modeling for Yellow Markings: Initial Retroreflectivity, Age, and Traffic
Volume as Independent Variables ................................................................................................ 98
ix
List of Tables
Table 1 ? Threshold dry retroreflectivity values suggested by FHWA to define end of pavement
marking service life....................................................................................................................... 11
Table 2 ? Minimum Maintained Retroreflectivity Levels for Longitudinal Pavement Markings 12
Table 3 ? Recommended minimum retroreflectivity values (mcd/m2/lux) .................................. 14
Table 4 ? Class of Traffic Stripe ................................................................................................... 21
Table 5 ? Initial Daytime Chromaticity for yellow materials ....................................................... 23
Table 6 ? Initial Daytime Chromaticity for yellow materials ....................................................... 23
Table 7 ? Summary of models to predict retroreflectivity ............................................................ 32
Table 8 ? Summary of Predicted Service Life .............................................................................. 33
Table 9 ? List of the 40 Pavement Marking Projects in the 2007 ALDOT Database .................. 35
Table 10 ? Meaning of ALDOT Database Entries ....................................................................... 37
Table 11 ? Minimum Required Values for Pavement Markings .................................................. 38
Table 12 ? Acceptable Values for Pavement Markings................................................................ 38
Table 13 ? Initial Daytime Chromaticity Coordinates (Corner Points) ........................................ 39
Table 14 ? Projects Included in the Retroreflectivity Modeling ................................................... 41
Table 15 ? Total Number of Retroreflectivity Curves .................................................................. 44
Table 16 ? ALDOT Historical Traffic Data ................................................................................. 46
Table 17 ? Material Property Compliance with Specifications .................................................... 54
Table 18 ? Color Check Comparison............................................................................................ 54
x
Table 19 ? Statistical Calculations ................................................................................................ 55
Table 20 ? Retroreflectivity Values of Project NHF-STPSAF-0053(525), for MP36 ................. 56
Table 21 ? Models in the Literature that Best Represented Actual Data ...................................... 58
Table 22 ? Example of Benefit/Cost and Service Life calculations ............................................. 59
Table 23 ? Developed Models considering initial retroreflectivity and age as independent
variables ........................................................................................................................................ 62
Table 24 ? Developed Models considering initial retroreflectivity, age, and AADT as
independent variables.................................................................................................................... 62
Table 25 ? Predicted Service Life: Initial Retroreflectivity and Age as Independent Variables .. 72
Table 26 ? Predicted Service Life: Initial Retroreflectivity, Age, and AADT as Independent
Variables ....................................................................................................................................... 73
xi
List of Figures
Figure 1 ? Glass Bead Retroreflection ............................................................................................ 9
Figure 2 ? Relative crash probability versus low retroreflectivity on freeways: white edge lines 13
Figure 3 ? Relative crash probability versus low retroreflectivity on freeways: yellow edge
lines ............................................................................................................................................... 13
Figure 4 ? Pattern representative of newly placed pavement markings ....................................... 16
Figure 5 ? Pattern for established sites ? markings older than about 300 days ............................ 17
Figure 6 ? Measuring user benefit: Kansas and Virginia ............................................................. 27
Figure 7 ? Alternative measurement of benefit ............................................................................ 28
Figure 8 ? Information from 2007 Database ................................................................................. 36
Figure 9 ? Initial Daytime Chromaticity: White ........................................................................... 39
Figure 10 ? Initial Daytime Chromaticity: Yellow ....................................................................... 40
Figure 11 ? Location of the 15 Projects with Retroreflectivity Data from 2007 to 2010 ............. 42
Figure 12 ? Section of Project STPSA-0185(500), on SR-185 .................................................... 43
Figure 13 ? Example of Correspondence from Stations to Mileposts .......................................... 44
Figure 14 ? Four Methods of Riemann Summation ..................................................................... 47
Figure 15 ? Comparison Between Areas Under Curves ............................................................... 48
Figure 16 ? Plot of Retroreflectivity Values of Project NHF-STPSAF-0053(525), for MP36 .... 56
Figure 17 ? Comparison between Models for Project STPSA-0185(500), MP10, Solid White .. 57
Figure 18 ? Thamizharasan et al. Linear Extrapolation of Actual Data ....................................... 60
xii
Figure 19 ? Sitzabee et al. Extrapolation of Actual Data ............................................................. 60
Figure 20 ? Linear Regression estimates for White Markings: Initial Retroreflectivity and Age as
Independent Variables .................................................................................................................. 63
Figure 21 ? White Markings Linear Regression for Different Initial Retroreflectivity Values:
Initial Retroreflectivity and Age as Independent Variables .......................................................... 64
Figure 22 ? Power Regression estimates for White Markings: Initial Retroreflectivity and Age as
Independent Variables .................................................................................................................. 65
Figure 23 ? White Markings Power Regression for Different Initial Retroreflectivity Values:
Initial Retroreflectivity and Age as Independent Variables .......................................................... 66
Figure 24 ? Quadratic Regression estimates for White Markings: Initial Retroreflectivity and
Age as Independent Variables ...................................................................................................... 67
Figure 25 ? White Markings Quadratic Regression for Different Initial Retroreflectivity Values:
Initial Retroreflectivity and Age as Independent Variables .......................................................... 67
Figure 26 ? Exponential Regression estimates for White Markings: Initial Retroreflectivity and
Age as Independent Variables ...................................................................................................... 68
Figure 27 ? White Markings Exponential Regression for Different Initial Retroreflectivity
Values: Initial Retroreflectivity and Age as Independent Variables ............................................ 69
Figure 28 ? Linear Regression estimates for White Markings: Initial Retroreflectivity, Age, and
AADT as Independent Variables .................................................................................................. 70
Figure 29 ? White Markings Linear Regression for Different Initial Retroreflectivity and AADT
Values: Initial Retroreflectivity, Age, and AADT as Independent Variables .............................. 71
1
Chapter One
Introduction
Highway systems are comprised of a number of elements, each with own role. Pavement
markings are elements which can convey regulations, guidance, warnings, and may also be used
as supplements to other traffic control devices. As pavement markings guide road users,
providing them information to understand what happens in the roadway, they can improve safety
by reducing the risk of accidents.
There are many different materials and colors used for pavement markings (e.g. primarily
white and yellow in the U.S.). Many factors can influence the performance of pavement
markings over time, and consequently, their useful life. Higher traffic volumes, for example, may
cause more rapid marking degradation, a centerline marking might have greater wear than an
edge line, and higher percent of trucks may cause greater deterioration. Also, geographic location
and climate can influence pavement marking durability.
Pavement markings need to be visible, during the day as well as at night, to support the
driver?s understanding of the roadway, supplementing other traffic control devices or used alone
to convey regulations, guidance, or warnings. A sufficient level of visibility, or serviceability,
can be determined through measurement of a number of properties. Minimum thickness
requirements support visibility of the marking and also avoid premature maintenance.
Chromaticity quantifies the color of the marking, and it needs to meet color specifications to
distinguish a yellow marking from a white marking very clearly. For each chromaticity, there is a
2
unique optimal color having its maximum luminance, which represents the amount of light
emitted from a particular area. Retroreflectivity measures the incident light from a vehicle?s
headlights reflected back toward the general area of the light source, particularly the eye of the
driver of the vehicle; this property is critical to nighttime visibility.
The rate of degradation of pavement marking retroreflectivity can be influenced by many
factors, such as type of material, geographic location and climate, traffic volume, and percent of
heavy vehicles. Determination of service life is essential to maintenance of markings, and it is
closely related to retroreflectivity. This topic is becoming increasingly important, which can be
attested to by the significant development of research on establishing minimum retroreflectivity
levels, including a proposed amendment to the Manual on Uniform Traffic Control Devices
(MUTCD) that would create a national standard (FHWA, 2010).
1.1. Background
Over the past decade, much advancement has been made with respect to quality and
durability of pavement marking materials. When quantifying the performance of pavement
markings, properties such as retroreflectivity, thickness, luminance, and chromaticity are
typically measured. Agencies responsible for construction and maintenance of highways
typically develop criteria for pavement markings to determine whether a new installation is
acceptable.
The Standard Specifications for Highway Construction, produced by the Alabama
Department of Transportation (ALDOT), is the document which provides the requirements for
all projects performed in the State of Alabama (ALDOT, 2008). The edition applicable to the
data analyzed in this study was published in 2006 and, since then, several changes on traffic
3
stripe, markings, and legends specifications have been made and included in a series of five
Special Provisions during 2007. The most recent publication is the draft of the 2012 edition of
the Standard Specifications for Highway Construction, but only the 2007 Special Provisions
apply to projects studied in this research.
There has not been a detailed study related to these changes in ALDOT specifications and
the quality of pavement marking projects in Alabama have not recently been evaluated. As a
result, there are some unanswered questions, such as the effects of ALDOT specification
changes, the cost-effectiveness of materials used by the ALDOT for pavement markings, and
durability of retroreflectivity.
A database containing observations of pavement marking properties on 40 projects in
Alabama in 2007 was obtained from ALDOT. Additionally, data from 2008 to 2010 for 15 of
these projects were available for analysis. The 2007 database includes properties such as
thickness, retroreflectivity, luminance, and chromaticity; the 2008, 2009, and 2010 data has only
retroreflectivity measurements. This thesis utilized this information to answer the important
questions mentioned above related to pavement markings in Alabama.
1.2. Objectives
To guide the analysis of data applied to this study, and also understand how pavement
markings in Alabama have performed, the main objectives of this research project are:
1. Document recent changes in ALDOT specifications (2007 Special Provisions);
2. Mine the database to:
a. Determine the extent to which observations from the 40 projects from 2007
meet specifications;
4
b. Execute a statistical analysis of the observations from the 40 projects from
2007 (mean, standard deviation, and coefficient of variation by color and type,
for each property measured);
c. Perform a benefit/cost analysis of pavement markings used in Alabama;
d. Model change in retroreflectivity over time, utilizing data from 2007 to 2010;
e. Develop a framework for future research, stating limitations of this study and
how the results of this research can be extended in long-term studies.
1.3. Scope
A general analysis of 7,840 observations from all 40 projects in the 2007 database was
performed. Properties of the markings of the projects in Alabama were compared to
specifications to examine the percentage of observations that met ALDOT requirements. A
statistical analysis, including mean, variance, standard deviation, and coefficient of variation is
also provided for properties such as chromaticity, thickness, luminance, and retroreflectivity.
This study also examined the feasibility of establishing a methodology to determine benefits
based on retroreflectivity. Cost data were obtained from the ALDOT Tabulation of Bids
database. Retroreflectivity modeling is also presented. Mathematical models were developed
associating available variables, within the limitations of the database. This thesis can also serve
as a starting point for more detailed studies in the future. Finally, the data included in these
analyses were collected by ALDOT, and these data represent only a small portion of all ALDOT-
sponsored projects that were constructed in 2007.
5
1.4. Outline
Chapter Two includes a detailed literature review which consists of a summary of
pavement markings characterization, including materials, colors, and measurable properties
related to them, such as thickness, retroreflectivity, luminance, and chromaticity. This chapter
also includes an overview of pavement marking retroreflectivity models in the literature. In this
chapter, a summary of pavement marking materials specifications and requirements in Alabama
is presented, according to the 2006 Edition of the ALDOT Standard Specifications for Highway
Construction and subsequent Special Provisions. Methods regarding economic evaluation,
including benefit/cost estimation examples, and details about pavement markings service life and
related retroreflectivity thresholds conclude the literature review.
Chapter Three contains the methods used to achieve the objectives of this research
project. It provides an overview of changes in ALDOT specifications during 2007, as well as the
approach to performing data mining and analysis of the 2007 database. Chapter Three also
provides a framework for the retroreflectivity modeling performed in this thesis. This process
includes the preparation of data for modeling and application of existing models in the literature
to the current dataset. The feasibility of a benefit/cost analysis, given the available data, is also
provided in this chapter. Finally, the development of several new models of retroreflectivity over
time is explained in Chapter Three.
Chapter Four includes the results related to the application of the methodology explained
in Chapter Three. Chapter Five presents the conclusions of this research and gives
recommendations for subsequent studies, considering limitations of the existing dataset and
approaches to overcome them.
6
Chapter Two
Literature Review
Pavement markings have an essential role in the highway system (Fu and Wilmot, 2008).
In some cases, markings are used to supplement other traffic control devices such as signs and
signals. In other instances, markings are used alone to effectively convey regulations, guidance,
or warnings in ways not obtainable by the use of other devices (FHWA, 2009). The risk of
accidents in roadways is reduced due to pavement markings, as they provide the driver?s
understanding of the roadway and his or her ability to stay on course (Montebello et al., 2000).
Characteristics of pavement markings can vary among the different materials and colors
available, these variables include luminance, retroreflectivity, and cost for each type of pavement
marking. An important issue with pavement markings is durability; the development of
mathematical models that can predict the service life of pavement markings is a common
approach to quantifying durability. These models typically refer to retroreflectivity as the main
variable of analysis and typical independent variables are initial retroreflectivity, age of marking,
and traffic. A highway agency typically develops requirements that have to be met. In Alabama,
acceptable values for pavement marking parameters are presented in ALDOT?s ?Standard
Specifications for Highway Construction? (ALDOT, 2008). Economic evaluation is also an
important analysis for the project.
This chapter describes general characteristics of pavement markings, indicating the most
commonly used types. It also provides an overview of existing models to predict life service of
7
pavement markings. Finally, it presents a summary of different methods of economic evaluation
analyses.
2.1. Characterization of Pavement Markings
There are a wide variety of characteristics, costs, and benefits among the different
pavement marking materials which can make it a challenging task deciding which factors should
be considered when selecting the type of pavement marking material for a particular road. There
are several manufacturers of pavement marking materials competing for business and they
distribute information on their products and on the competition?s products, making comparisons
based on this information difficult to understand and somewhat unreliable. (Montebello et al.,
2000).
There are numerous types of materials used for pavement markings in the field today,
including paint, epoxy, tape, and thermoplastic (Thomas et al., 2001). Each material has its own
set of unique characteristics related to durability, retroreflectivity, installation cost, and life-cycle
cost. Marking types are also wide-ranging and they include pavement and curb markings,
delineators, colored pavements, channelizing devices, and islands (FHWA, 2009). Most used
materials for pavement and curb markings placement are paints or thermoplastics (FHWA,
2009).
The materials used for markings should provide the specified color throughout their
useful life. The Manual on Uniform Traffic Control Devices (MUTCD) determines that markings
shall be yellow, white, red, blue, or purple. Black, in conjunction with one of the aforementioned
colors, is also a usable color (FHWA, 2009). Pavement markings include longitudinal lines,
transverse lines, words, and symbols. Longitudinal markings include centerlines, lane lines, and
8
edge lines on paved streets and highways (Fu and Wilmot, 2008). The general functions of
longitudinal lines are: a double line indicates maximum or special restrictions, a solid line
discourages or prohibits crossing (depending on the specific application), a broken line indicates
a permissive condition, and a dotted line provides guidance or warning of a downstream change
in lane function (FHWA, 2009).
White and yellow are the two most commonly used colors for pavement markings (Fu
and Wilmot, 2008). White markings, when used for longitudinal lines, delineate the separation of
traffic flows in the same direction or the right-hand edge of the roadway. Yellow markings, when
used for longitudinal lines, delineate the separation of traffic traveling in opposite directions, the
left-hand edge of the roadways of divided highways and one-way streets or ramps, or the
separation of two-way left-turn lanes and reversible lanes from other lanes (FHWA, 2009).
Marking systems should offer the best possible performance at the lowest possible cost.
Regarding performance, the purpose of the markings is to facilitate safe and efficient traffic flow
on highways (Cuelho et al., 2003). Configurations and visibility requirements of pavement
markings are generally well-defined by publications such as the Manual on Uniform Traffic
Control Devices (MUTCD) (Cuelho et al., 2003). Each standard marking shall be used only to
transmit the meaning prescribed for that marking in the MUTCD (FHWA, 2009). All necessary
markings should be in place before any new highway, private road open to public travel, paved
detour, or temporary route is opened to public travel (FHWA, 2009).
Service life is one of the first factors to be considered when choosing a pavement
marking material. Many factors can influence the service life of a pavement marking material
including weather conditions, winter maintenance activities, installation conditions and quality,
retroreflective optics used, binder type, binder thickness, binder color, traffic volume, and the
9
minimum selected retroreflectivity level. Among these, the major factors that are known to have
significant impacts on marking service life are traffic volume and minimum required pavement
marking retroreflectivity level (Songchitruksa et al., 2011).
2.2. Retroreflectivity Threshold
The determination of when a pavement marking material is no longer serviceable is
rather complex. Given a quantified terminal condition of a pavement marking material, it is not a
simple task to forecast the remaining service life. The performance of a pavement marking
material has been judged based primarily on its retroreflectivity. Retroreflectivity has been used
extensively in past studies as an important factor in analyzing the performance and cost-
effectiveness of a pavement marking material (Zhang et al., 2006). Retroreflectivity can be
defined as the portion of incident light from a vehicle?s headlights reflected back toward the eye
of the driver of the vehicle. Retroreflectivity is provided in pavement marking materials by glass
or ceramic beads that are partially embedded in the surface of the material (Thomas et al., 2001).
Figure 1 shows how retroreflection occurs.
Figure 1 ? Glass Bead Retroreflection
SOURCE: Thomas et al., 2001
10
Pavement markings are typically retroreflective. This retroreflective property of the
pavement markings is essential for nighttime visibility. Retroreflectivity is typically measured in
units of millicandelas per square meter per lux (mcd/m2/lux) using retroreflectometers. The
candela is the International System (SI) unit for luminous intensity, in a given direction, of a
source that emits monochromatic radiation of frequency 540?1012 hertz and that has a radiant
intensity in that direction of 1?683 watt per steradian. A common candle emits light with roughly
1 candela luminous intensity. The SI unit for illumination is defined as lux, and it represents the
illumination produced by a luminous flux of 1 lumen distributed uniformly over an area of 1
square meter, or the illumination produced at a surface all points of which are at a distance of
one meter from a uniform point source of one candela (NIST, 1979). According to the MUTCD,
markings that have to be visible at night shall be retroreflective except for the cases when
ambient illumination assures that the markings are adequately visible (FHWA, 2009).
In 2006, The National Cooperative Highway Research Program sponsored a study
focused on non-intersection, non-daylight crashes in California during 1992-1994 and 1997-2002
and related them to the retroreflectivity of the longitudinal pavement markings on the road at the
time of the crashes. Over 118,000 crashes were considered in the study, which covered over
5,000 miles of state maintained freeways and highways in California. A main finding of the
NCHRP study is that the amount of retroreflectivity is not important to driver safety as long as
the marking is present and visible to drivers (Bahar et al., 2006). Therefore, there is a need to
specify a minimum retroreflectivity value to determine if a marking is ?visible?.
Many researchers adopt FHWA candidate criteria for minimum pavement marking
retroreflectivity in their studies (FHWA, 2000). These recommended guidelines are impacted by
three factors: speed, roadway type, and the presence/absence of raised retroreflective pavement
11
markers (RRPM) or lighting (Migletz and Graham, 2002). For freeways, minimum guideline
retroreflectivity values of 150 mcd/m2/lux and 100 mcd/m2/lux are recommended for white and
yellow pavement markings, respectively, when there is no RRPM or lighting; while 70
mcd/m2/lux is used for both white and yellow pavement markings when there is RRPM or
lighting (FHWA, 2000). Table 1 shows these values.
Table 1 ? Threshold dry retroreflectivity values suggested by FHWA to define end of pavement marking
service life
Material
Roadway type/speed classification
Non-freeway
? 40 mph
Non-freeway
? 45 mph
Freeway
? 55 mph
White 85 100 150
White with lighting or RRPM 30 35 70
Yellow 55 65 100
Yellow with lighting or RRPM 30 35 70
SOURCE: FHWA, 2000
When installed, the retroreflectivity of yellow markings is typically about 35% lower
than that of white markings. As white and yellow markings are usually replaced at the same time,
there is a lower minimum value for yellow markings, as shown in Table 1 (Fu and Wilmot,
2008). In 2010, the Federal Highway Administration (FHWA) had drafted a revision to the 2009
Edition of the Manual on Uniform Traffic Control Devices (MUTCD) to specify minimum
retroreflectivity values for the pavement marking standard (FHWA, 2010). The FHWA is
currently reviewing the docket comments received and the proposed revisions regarding
maintaining minimum retroreflectivity of longitudinal pavement markings are tentatively
designated as Revision 1 to the 2009 edition of the MUTCD. The proposed revision establishes
that public agencies or officials having jurisdiction shall use a method designed to maintain
12
retroreflectivity of white and yellow longitudinal pavement markings, at or above the minimum
levels in Table 2. (FHWA, 2010).
Table 2 ? Minimum Maintained Retroreflectivity Levels for Longitudinal Pavement Markings
Roadway Type Posted Speed (mph) ? 30 35 - 50 ? 55
Two-lane roads with centerline markings
only n/a 100 250
All other roads n/a 50 100
SOURCE: Based on FHWA, 2010
Parker and Meja (2003) studied the relationship between retroreflectivity levels and user
perception, depending on user?s age. In addition to retroreflectivity, subjective ratings from a
survey conducted with the participation of the New Jersey driving public along a 32-mi circuit
were measured. Multiple regression techniques were used to correlate the average scores
reported by the study participants for each specific roadway section with the corresponding
measured retroreflectivity. The threshold value of acceptable versus unacceptable
retroreflectivity, for both yellow and white markings, was between 80 and 130 mcd/m2/lux for
New Jersey drivers younger than 55 and between 120 and 165 mcd/m2/lux for drivers over 55.
Smadi et al.?s (2008) analysis of safety effectiveness related to marking retroreflectivity
showed that low retroreflectivity, less than 200 mcd/m2/lux, is correlated to a higher crash
probability. Values higher than 200 mcd/m2/lux did not show significant increase in crash
probability (Smadi et al., 2008). Figure 2 and Figure 3 show the behavior of crash probability for
retroreflectivity lower than 200 mcd/m2/lux for freeways.
13
Figure 2 ? Relative crash probability versus low retroreflectivity on freeways: white edge lines
SOURCE: Smadi et al., 2008
Figure 3 ? Relative crash probability versus low retroreflectivity on freeways: yellow edge lines
SOURCE: Smadi et al., 2008
14
In 2008, Debaillon et al. (2008) used a computer model called the Target Visibility
Predictor (TarVIP) to study pavement marking retroreflectivity needs. Key factors affecting
pavement marking visibility included pavement marking configuration, pavement surface type,
vehicle speed, vehicle type, and presence of raised retroreflective pavement markers. The
recommended values of minimum retroreflectivity can be observed in Table 3.
Table 3 ? Recommended minimum retroreflectivity values (mcd/m2/lux)
Roadway Marking Configuration Without RRPMs With RRPMs ? 50 mph 55 - 65 mph ? 70 mph
Fully marked roadways (with centerline, lane
lines, and edge lines, as needed) 40 60 90 40
Roadways with centerlines only 90 250 575 50
SOURCE: Debaillon et al., 2008
2.3. Pavement Marking Retroreflectivity Modeling
In the mid-1990s Michigan State University (MSU) evaluated the performance of several
pavement marking materials for the Michigan DOT (Lee et al., 1999). Lee et al. (1999)
developed the following linear regression model for both white and yellow thermoplastic
markings. In order to establish if a model is good to represent the behavior of actual data,
goodness-of-fit measures can be considered. One of these measures is the coefficient of
determination, R2, which represents the fraction of total variation in the dependent variable that
is explained by the independent variables, and its value ranges from 0 to 1, with 1 indicating that
the regression line perfectly fits actual data. The R? value for Lee et al (1999) model is 0.14:
g1851=?0.3622g1850+254.82 (Eq. 2.1)
15
where
Y = retroreflectivity of pavement markings (mcd/m2/lux);
X = age of marking in days.
In 2002, Abboud and Bowman (2002 [2]) determined pavement marking retroreflectivity
using field retroreflectivity readings for 520 mi of longitudinal pavement markings in 9 Alabama
counties. The minimum retroreflectivity threshold was determined to be 150 mcd/m2/lux.
Logarithmic regression analysis was used to establish the following relationship between
pavement marking retroreflectivity and prolonged traffic exposure, for white thermoplastic
markings:
g1844g3013 =?70.806lng4666g1848g1831g4667+639.66 (Eq. 2.2)
where
RL=pavement marking retroreflectivity (mcd/m2/lux);
ln = natural logarithm;
VE = vehicle exposure.
Vehicle exposure is the total number of vehicles that have traversed a point on a highway
up to the time frame of interest and represents the prolonged effect of traffic over time,
combining the effects of marking age and traffic volume on the deterioration rate, and it is a
function of time and traffic volume per lane and was expressed by Abboud and Bowman as:
g1848g1831 =g1827g1830g1846g3013g3041 ?g1842g1839g1853g1859g1857?30.4?10g2879g2871 (Eq. 2.3)
where:
g1827g1830g1846g3013g3041 = average daily traffic per lane (thousands of vehicles/day/lane);
g1842g1839g1853g1859g1857 = age in months (using a month-to-day conversion factor of 30.4).
16
Abboud and Bowman (2002 [1]) developed another exponential regression model to
depict the relationship between pavement-marking retroreflectivity and vehicle exposure (VE).
The value of R? for this method, related to white thermoplastic markings is 0.58:
g1844g3013 =?70.806lng4666g1848g1831g4667+150.55 (Eq. 2.4)
Thamizharasan et al. (2003) identified patterns of retroreflectivity change over time in
South Carolina, as it can be observed in Figures 4 and 5. Figure 4 shows the first pattern, where
retroreflectivity increases for a short period of time, usually before 300 days after pavement
marking application, then gradually decreases thereafter, for newly placed markings. The initial
increase in retroreflectivity is because of more glass beads becoming exposed after some amount
of wear.
Figure 4 ? Pattern representative of newly placed pavement markings
SOURCE: Thamizharasan et al., 2003
The second pattern, which can be observed in Figure 5, is where retroreflectivity
decreases gradually with time. This is for the well-established markings that have passed the
initial increase period, defined by Thamizharasan et al. as 300 days.
17
Figure 5 ? Pattern for established sites ? markings older than about 300 days
SOURCE: Thamizharasan et al., 2003
Thamizharasan et al. (2003) developed two models to predict marking retroreflectivity,
including a non-linear model for the time the retroreflectivity increases when markings are newly
applied and a linear model for the time retroreflectivity decreases to a minimum value. The
models were stratified by marking color (white or yellow), surface type (AC or PCC), and
marking material (thermoplastic or epoxy). Traffic volume was not found to be significant in the
analysis.
The non-linear model, for white thermoplastic materials, has a R? value of 0.22:
g1830g1861g1858g1858g1857g1870g1857g1866g1855g1857uni0009g1861g1866uni0009g1844g1857g1872g1870g1867g1870g1857g1858g1864g1857g1855g1872g1861g1874g1861g1872g1877=?0.0005?g1830g1853g1877g1871g2870+0.18?g1830g1853g1877g1871+1.10 (Eq. 2.5)
where:
g1830g1853g1877g1871 = age of pavement marking (days).
For yellow thermoplastic materials, the R? value is 0.20:
g1830g1861g1858g1858g1857g1870g1857g1866g1855g1857uni0009g1861g1866uni0009g1844g1857g1872g1870g1867g1870g1857g1858g1864g1857g1855g1872g1861g1874g1861g1872g1877=?0.0001?g1830g1853g1877g1871g2870+0.04?g1830g1853g1877g1871+1.23 (Eq. 2.6)
The linear model, for white thermoplastic materials, has R? value of 0.47:
g1830g1861g1858g1858g1857g1870g1857g1866g1855g1857uni0009g1861g1866uni0009g1844g1857g1872g1870g1867g1870g1857g1858g1864g1857g1855g1872g1861g1874g1861g1872g1877=?0.06?g1830g1853g1877g1871?6.80 (Eq. 2.7)
18
For yellow thermoplastic materials, R? value is 0.21:
g1830g1861g1858g1858g1857g1870g1857g1866g1855g1857uni0009g1861g1866uni0009g1844g1857g1872g1870g1867g1870g1857g1858g1864g1857g1855g1872g1861g1874g1861g1872g1877=?0.03?g1830g1853g1877g1871?3.63 (Eq. 2.8)
The National Transportation Product Evaluation Program (NTPEP) has collected
retroreflectivity data from various sites located in different regions of California. The variables
contained within the NTPEP data set include age of marking, color, material type, traffic volume,
pavement surface, climate region, and snow removal (Bahar et al., 2006). The polynomial model
developed to predict the retroreflectivity was:
g1844 = 1g2010
g2868+g2010g2869?g1827g1859g1857+g2010g2870?g1827g1859g1857g2870
(Eq. 2.9)
where:
g1844 = retroreflectivity of pavement marking (mcd/m2/lux);
g2010g2868,g2010g2869,g2010g2870uni0009 = model parameters to be estimated;
g1827g1859g1857 = age of pavement marking (months).
For white thermoplastic markings in a hot humid climate and no usual snow removal, the
values found in the NTPEP study were g2010g2868 = 2.42 x 10-3, g2010g2869 = 1.32 x 10-4, and g2010g2870 = -1.18 x 10-6.
For yellow markings in the same conditions, g2010g2868 = 4.89 x 10-3, g2010g2869 = 1.85 x 10-4, and g2010g2870 = -8.00 x
10-8 (Bahar et al., 2006).
A general linear model was developed by Sitzabee et al. (2009) in North Carolina for
thermoplastics on asphalt based on the variables that were validated by the effects test (time,
initial retroreflective value, AADT, color, and lateral location). The thermoplastic model
produced an R? value of 0.60 which is greater than those found in previous studies reviewed in
the literature:
19
g1844g3013 =190+0.39?g1844g3013g3284g3289g3284g3295g3284g3276g3287 ?2.09?g1872g1861g1865g1857?0.0011?g1827g1827g1830g1846+20.7?g1850g2869?20.7
?g1850g2870+19?g1850g2871?19?g1850g2872
(Eq. 2.10)
where:
RL = retroreflectivity in mcd/m2/lux;
RL initial = initial retroreflectivity in mcd/m2/lux;
time = time since installation in months;
AADT = annual average daily traffic in vehicles per day;
X1=1 if edge line, 0 otherwise;
X2=1 if middle line, 0 otherwise;
X3=1 if white line, 0 otherwise;
X4=1 if yellow line, 0 otherwise.
In 2009, Clarke and Yan (2009) performed a retroreflectivity investigation in 85 sites
with 90-mil thermoplastic longitudinal markings located in 14 counties across the state of
Tennessee. Three models were developed by color, a linear, a logarithmic, and a quadratic. The
models for white 90-mil thermoplastic had R2 values of 0.015 (linear), 0.008 (logarithmic), and
0.017 (quadratic) and are expressed by Equations 2.11, 2.12, and 2.13, respectively:
g1851 =298.004?0.053g1872 (Eq. 2.11)
g1851 =331.366?9.510lnuni0009g4666g1872g4667 (Eq. 2.12)
g1851 =287.019+0.022g1872?0.000092g1872g2870 (Eq. 2.13)
where
Y = retroreflectivity (mcd/m2/lux);
t = age of marking (days).
20
Yellow 90-mil thermoplastic models, which had R2 values of 0.003 (linear), 0.007
(logarithmic), and 0.017 (quadratic) are represented by Equations 2.14, 2.15, and 2.16,
respectively.
g1851 =150.233+0.016g1872 (Eq. 2.14)
g1851 =120.845+6.181lnuni0009g4666g1872g4667 (Eq. 2.15)
g1851 =133.718+0.124g1872?0.000g1872g2870 (Eq. 2.16)
Traffic volume, typically expressed as AADT (Annual Average Daily Traffic), is a
continuous parameter that measures the volume of traffic on the roadway in vehicles per day.
Traffic volumes vary from day to day and over the course of a year, and are another source of
variation that contributes to the complexity of the analysis (Songchitruksa et al., 2011).
Thamizharasan et al. (2003) argued that AADT was not significant and was accounted for as a
function of time. However, some reports indicate that AADT has a significant impact on
pavement marking degradation apart from time (Sitzabee et al., 2009).
Different sources are considered to analyze retroreflectivity behavior over time. Karwa
and Donnell (2011) used Artificial Neural Networks (ANN) to model the degradation pattern of
pavement marking retroreflectivity (PMR) in North Carolina as a function of several input
variables, including the initial PMR, age of the markings, and traffic flow characteristics. It was
found that the degradation of thermoplastic pavement markings occurs generally at a nonlinear
rate, and the rate of decay appears to differ among different pavement marking types. It was also
found that there may be a different degradation process according to the geographic location of
the markings as well as by the color of the marking. The initial PMR also appears to be an
important service life predictor. The variability in traffic volume, however, does not appear to
21
have a strong association with retroreflectivity degradation for most of the pavement marking
types (Karwa and Donnell, 2011).
2.4. Pavement Marking Materials Specifications and Requirements
On contracts for the Alabama Department of Transportation (ALDOT), requirements for
all projects are based on the Alabama Standard Specifications for Highway Construction
(ALDOT, 2008). The 2007 Special Provisions, an interim update to the 2006 Edition of
ALDOT?s Standard Specifications for Highway Construction, will be the reference for this thesis
as the projects on which data were collected are governed by the 2006 Edition and its subsequent
Special Provisions. These specifications define classes of traffic stripe. The required type of
material is designated by "Class" in accordance with Table 4 (ALDOT, 2007).
Table 4 ? Class of Traffic Stripe
Class of Traffic Stripe
Class Material
1 Paint
1H High Build Paint
2 Standard Thermoplastic Material
2T Thin Film Spray Applied Thermoplastic Material
3 Tape
W Warranted Traffic Marking Material
SOURCE: ALDOT, 2007
Thermoplastics are generally composed of four ingredients: binder, glass beads, titanium
dioxide and calcium carbonate. The binder is used to hold the mixture together as a rigid mass,
the glass beads are used to provide reflectivity, the titanium dioxide is used for reflectivity
enhancement, and calcium carbonate or sand is used as an inert filler material. Typical
thermoplastic markings are 15 to 33 percent binder, 14 to 33 percent glass beads, 8 to 12 percent
titanium dioxide and 48 to 50 percent filler (Cuelho et al., 2003).
22
Thermoplastic is a blend of solid ingredients that becomes liquid when heated and returns
to a solid state on cooling. Thermoplastics are classified into two types: hydrocarbon-based
plastics derived from petroleum, and alkyd, which is a naturally occurring resin (Migletz and
Graham, 2002). Alkyd-based binders are more widely used because they are resistant to
chemical decomposition from motor oil and other hydrocarbon contaminants. Thermoplastics
can be applied to the roadway surface by spraying or extrusion. Extruded thermoplastics are
thicker than sprayed thermoplastics (Fu and Wilmot, 2008).
According to Lindly and Marci, (2006), thermoplastic markings are all-weather pavement
markings. These markings should be visible at night during a rainfall of up to 0.25 inch per
hour. Thermoplastic has been used successfully in warmer climates for a number of years.
Class 2 thermoplastic is the marking type for which data will be analyzed in this research.
Class 2 thermoplastic may be applied to asphalt and concrete surfaces, and according to ALDOT
specifications, they have to be placed to produce a minimum uniform thickness of 0.100 inch for
all stripes. Thickness less than 95% of this required value may be deemed unacceptable. The
retroreflectivity is required to be a minimum of 450 mcd/m2/lux for white stripe and 350
mcd/m2/lux for yellow stripe. The Contractor may be compelled to replace stripe that is 90% or
less of this retroreflectivity requirement (ALDOT, 2007).
Class 2T thermoplastic markings are also analyzed in this study. Class 2T thermoplastic
may be applied to asphalt and concrete surfaces, and ALDOT specifications require that they
need to be placed to produce a minimum uniform thickness of 0.040 inch. Thickness less than
95% of this required value is not acceptable. The retroreflectivity has to be a minimum of 300
mcd/m2/lux for white stripe and 250 mcd/m2/lux for yellow stripe. The Contractor is required to
replace stripe that is 90% or less of this retroreflectivity requirement (ALDOT, 2007).
23
ALDOT specifications require initial daytime chromaticity for yellow materials to fall
within the box created by the coordinates presented in Table 5 (ALDOT, 2007).
Table 5 ? Initial Daytime Chromaticity for yellow materials
Initial Daytime Chromaticity Coordinates (Corner Points)
1 2 3 4
X 0.530 0.510 0.455 0.472
Y 0.456 0.485 0.444 0.400
SOURCE: ALDOT, 2007
The initial daytime chromaticity for white materials must fall within the box created by
the coordinates showed on Table 6 (ALDOT, 2007).
Table 6 ? Initial Daytime Chromaticity for yellow materials
Initial Daytime Chromaticity Coordinates (Corner Points)
1 2 3 4
X 0.355 0.305 0.285 0.335
Y 0.355 0.305 0.325 0.375
SOURCE: ALDOT, 2007
According to ALDOT specifications, luminance factor requirements for white markings
are daylight luminance factor at 45 degrees / 0 degrees - 50% minimum, and daylight luminance
factor at 45 degrees / 0 degrees ? 35% minimum for yellow markings.
2.5. Economic Evaluation of Thermoplastic Materials
Another critical factor to consider when choosing the best material for pavement
markings is the associated cost. But it is not only the initial cost that should be analyzed, as a
material with a higher initial cost could also have a longer lifetime, possibly resulting in a more
cost-effective material (Thomas et al., 2001).
The total cost of pavement markings includes not only the cost of the material, but also
the cost of the crew and the application equipment, as well as manufacturer guarantees over a
24
specified time, in which case manufacturers replace deteriorating materials free of charge if their
product does not achieve certain guidelines (Thomas et al., 2001). Basic costs of the materials
and the equipment, and time required for their installation, fundamentally determine marking
system costs, but secondary issues also can have a noticeable impact. The volume of markings to
be installed and whether or not markings are installed by private firms or public agencies are
some secondary issues that can influence the cost of pavement markings. Usually, the greater
volume of markings to be installed, the lower the unit cost of their installation. The reasons for
the differential in costs between private and public agency installation are uncertain, although
they may be related, in part, to volume of work (Cuelho et al., 2003).
Even if there are many factors to be considered when choosing the type of pavement
marking material to be used, the decision is often dictated by the initial cost. There are limited
guidelines leading to a more cost-effective selection and this approach to pavement marking can
result in lack of durability, poor retroreflectivity, increased long-term costs and increased
exposure to traffic for staff (Montebello et al., 2000).
Service life is an important parameter in selecting a marking system and it is mainly
determined from the level of retroreflectivity provided by the pavement marking. Other
conditions that may end the service life of a marking include detachment from the pavement,
extensive loss of pigment, and obliteration by pavement maintenance activities. Some of the
major factors that affect the performance and service life of a particular type of pavement
marking include type of road surface, volume of traffic, orientation with respect to traffic, and
schedule of pavement maintenance activities (Cuelho et al., 2003).
Thermoplastic materials have been used in the United States since the 1950s, and they are
one of the most widely used pavement marking materials (Jiang, 2008). Thermoplastic markings
25
provide excellent performance when applied properly, being the most durable of the commonly
used pavement marking systems. The life of thermoplastic markings varies widely because of its
dependence on installation procedures, volume of traffic, atmospheric conditions when placed,
and snowplow activity. The range of life expectancy is typically from four to seven years
(KDOT, 2002). This relatively long service life can sometimes exceed the interval between
pavement maintenance activities (Cuelho et al., 2003).
There are some issues to be considered when applying thermoplastic to pavement
markings, in addition to service life. One of the advantages of using thermoplastic is that the
material can be re-applied over older thermoplastic markings, thereby refurbishing the older
marking as well as saving on the costs of removing old pavement markings. However,
thermoplastic color and appearance are disadvantages. Thermoplastic is grayish, making it less
visible by day and it has a tendency to crack. (Jiang, 2008).
Thermoplastics are expensive in comparison to conventional paints, with installed costs
ranging between $0.19 and $0.26 per linear foot based on a four-inch wide longitudinal strip
(KDOT, 2002). Thermoplastics, on the other hand, are the most durable of the commonly used
pavement marking systems, which can result in a more cost-effective use of thermoplastics in the
long-term (KDOT, 2002). In Alabama, the averages of contract bid prices are $0.26 per linear
foot for Class 2T thermoplastic materials and $0.65 per linear foot for Class 2 thermoplastic
materials (ALDOT, 2010[1]).
The objective of a pavement marking economic evaluation is to identify the most
economical pavement marking materials. Some methods have been employed. For example,
Kansas DOT (KDOT, 2002) developed a sophisticated methodology to determine the most
economical type of pavement marking to be used under different conditions. Materials are
26
selected based on the remaining pavement service life, traffic volume level, and a Brightness
Benefit Factor (BBF). In the Kansas DOT document, there is one table for each remaining
service life, between 1 and 7 years; columns of these tables represent AADT levels (<5,000,
5,000-50,000, and >50,000 veh/day) and rows represent BBF for each type of material; the
material with the highest BBF represents the best combination of durability, retroreflectivity, and
cost for the considered remaining service life and ADT. The BBF is a benefit/cost ratio
representing the combined effects of a material?s retroreflectivity, durability, and installed cost.
The BBF is defined as:
g1828g1828g1832 =g1844g3028g1846g3046g1845 (Eq. 2.17)
where:
Ra = average useful retroreflectivity over the anticipated service life of the project in
mcd/m2/lux;
Ts = pavement marking service life in years;
S = average cost per unit length in dollars per meter.
In the calculation of BBF, additional retroreflectivity over the minimum required level is
considered a benefit to the user. As a result, the higher the retroreflectivity obtained during the
material lifetime, the higher the BBF (KDOT, 2002).
Cottrell and Hanson (2001) used cost-effectiveness analysis to select marking materials
for Virginia DOT (VDOT). They found that there is not much benefit in using a marking with a
retroreflectivity value greater than 600 mcd/m2/lux compared to one with a value of 300
mcd/m2/lux. As a result, their study did not use retroreflectivity as a benefit, only service life.
Figure 6 illustrates the two methods. The horizontal axis is time measured by month; the vertical
axis is retroreflectivity; Rmin is the minimum retroreflectivity threshold (Fu and Wilmot, 2008).
27
Figure 6 ? Measuring user benefit: Kansas and Virginia
SOURCE: Fu and Wilmot, 2008
Lindly and Wijesundera (2003) used life cycle cost analysis (LCCA) to compare different
marking materials for Alabama DOT. LCCA assumes the alternatives yield the same level of
service, provided the retroreflectivity of the pavement markings meets the minimum value
requirement. LCCA requires identification of pavement marking service life and total cost and
then calculates the net present worth (NPW) or the equivalent uniform annual cost (EUAC). The
material with the lowest NPW or EUAC is selected.
Loetterle et al.?s study of public perception of pavement marking retroreflectivity leads to
an intuitively appealing way to measure user benefit. Based on their data, user benefit can be
considered to increase approximately in a linear fashion when retroreflectivity is under 200
mcd/m2/lux, while above 200 mcd/m2/lux, there is little additional benefit. Thus, provided the
retroreflectivity is at least 200 mcd/m2/lux, full benefit of the pavement marking is received
(Loetterle et al., 2001).
28
On the other hand, below a certain minimum threshold value of retroreflectivity,
pavement markings are considered to be unacceptable and have no value to the driving public.
This minimum value indicates the end of service life of the pavement marking. Calling these two
values Rmax and Rmin, respectively, then Figure 7 demonstrates an alternative measurement of
benefit.
Figure 7 ? Alternative measurement of benefit
Fu and Wilmot (2008) shows that the suggested user benefit is measured by the area
between Rmin and Rmax. Benefit is measured in units of month*vehicle*mcd/m2/lux. The
benefit/cost ratio can be simply calculated by:
g1854g1857g1866g1857g1858g1861g1872
g1855g1867g1871g1872 =
g1854g1857g1866g1857g1858g1861g1872?g1827g1827g1830g1846
g1872g1867g1872g1853g1864uni0009g1855g1867g1871g1872
(Eq. 2.18)
29
2.6. Service Life of Thermoplastic Pavement Markings
Migletz and Graham (2002) established a retroreflectivity of 150 mcd/m2/lux as a
threshold to predict the service life of white thermoplastic pavement markings on freeways. The
obtained mean estimated service life was 22.6 months, in a range of 7.4 to 49.7 months. The
mean service life of yellow markings on freeways in the Migletz and Graham (2002) study was
24.7 months, in a range of 11.0 to 41.6 months. The minimum retroreflectivity threshold for
yellow thermoplastic was considered as 100 mcd/m2/lux. Minimum retroreflectivity thresholds
were based on the FHWA suggested values (FWHA, 2000).
Abboud and Bowman (2002 [1]) considered in their study the useful lifetime of white
edge lines. For low ADT (<2500 veh/day), the service life for white edge thermoplastic markings
was found to be 53 months; for intermediate ADT (2500 to 5000 veh/day), useful lifetime
dropped to 18 months; for high ADT (>5000 veh/day), the service life was 10.5 months.
According to the FHWA (2000), the threshold for minimum acceptable retroreflectivity was
considered equal to 150 mcd/m2/lux and the midpoint of each ADT range was used as
representative (Abboud and Bowman, 2002 [1]).
Thamizharasan et al. (2003) developed a model to predict retroreflectivity and established
the threshold of 100 mcd/m2/lux, for both yellow and white markings, as the minimum
acceptable retroreflectivity; this threshold was chosen based on an NCHRP study (Andrady,
1997). Average service life for white thermoplastic marking on asphalt pavement was found to
be 65 months, for retroreflectivity variation in a range from 30 to 690 mcd/m2/lux, with an
average of 203 mcd/m2/lux. For yellow thermoplastic marking on asphalt pavement, the average
useful lifetime was 103 months, for retroreflectivity variation in a range from 26 to 429
mcd/m2/lux, with an average of 135 mcd/m2/lux.
30
Sitzabee et al. (2009) used an AADT of 10,000 veh/day to estimate the service lives of
thermoplastic markings. For white edge lines, average service life was 102 months; for white
broken lines, average useful lifetime was 84 months; for yellow edge lines, average service life
was 85 months; and for yellow broken lines, average useful lifetime was 65 months. For white
markings, the minimum retroreflectivity value was 150 mcd/m2/lux; for yellow markings, the
considered threshold was 100 mcd/m2/lux, based on most common research recommendations.
Initial retroreflectivity was 375 mcd/m2/lux for white markings and 250 mcd/m2/lux for yellow
markings.
Clarke and Yan (2009) performed a study which investigated changes in retroreflectivity
over time for 90-mil thermoplastic markings of 85 sites in 14 counties of Tennessee. The average
service life of the 90-mil thermoplastic white markings is 1,100 days (36 months) while that of
the yellow markings is 900 days (30 months).
Karwa and Donnell (2011) predicted service life of pavement markings using Artificial
Neural Networks. Service life was estimated for white and yellow line types, considering
centerlines and edgelines separately. Two different threshold values for minimum
retroreflectivity were considered: 150 and 200 mcd/m2/lux. Also, three different ADT levels
were considered, along with two different percent truck and two different initial PMR levels.
White edgeline markings generally had longer predicted service lives than all other pavement
marking types. The shortest mean predicted service life was most often computed for the yellow
centerline markings. There was also considerable variability in the predicted service life across
the engineering divisions, which shows the importance of geographic location when developing
models to predict service life. In addition, increasing the ADT from 5,000 to 25,000 reduced the
mean predicted service life by 7 months or less. The impact of different vehicle types was also
31
analyzed, and it was found that roadways with higher truck traffic volumes decrease pavement
markings service life due to abrasion between the tires and the markings (Karwa and Donnel,
2011).
2.7. Summary of findings
Pavement markings have an essential role in the highway system. It is a complex
decision, balancing many competing objectives, to decide which factors should be considered
when selecting the type of pavement marking material for a particular road. This is essentially an
agency?s policy decision, which can be supported by research. There is a wide variety of
characteristics, costs, and benefits of the different pavement marking materials.
There are numerous types of materials used for pavement markings in the field today,
including paint, epoxy, tape, and thermoplastic. Thermoplastic is the most widely used.
AADT was sometimes not significant for service life analysis. However, most reports
indicate that AADT has a significant impact on pavement marking degradation apart from time.
The performance of a pavement marking material has been judged based primarily on its
retroreflectivity. There are many models to predict marking retroreflectivity. The best prediction
found in the literature is a general linear model that was developed by Sitzabee et al. (2009), with
R? equal to 0.60 for thermoplastics. Table 7 shows a summary of all models cited in Section 2.3
of this thesis.
32
Table 7 ? Summary of models to predict retroreflectivity
Study Location Type of Marking Independent Variables R2
Lee et al. (1999) Michigan White and Yellow Thermoplastic Age of marking 0.14
Abboud and Bowman
(2002 [1])
Alabama
White Thermoplastic ADT per lane 0.58
Age of marking
Abboud and Bowman
(2002 [2]) White Thermoplastic
ADT per lane N/A
Age of marking
Thamizharazan et al.
(2003) Non-Linear
South Carolina
White Thermoplastic
in Asphalt
Age of marking
0.22 Initial
Retroreflectivity
Yellow
Thermoplastic in
Asphalt
Age of marking
0.2 Initial
Retroreflectivity
Thamizharazan et al.
(2003) Linear
White Thermoplastic
in Asphalt
Age of marking
0.47 Initial
Retroreflectivity
Yellow
Thermoplastic in
Asphalt
Age of marking
0.21 Initial
Retroreflectivity
Bahar et al. (2006) California
White Thermoplastic,
Hot Humid, No snow
removal
Age of marking N/A
Yellow
Thermoplastic, Hot
Humid, No snow
removal
Age of marking N/A
Sitzabee et al. (2009) North Carolina White and Yellow Thermoplastic
Initial
Retroreflectivity
0.6
Age of marking
AADT
Marking location
(edge, middle)
Marking color
(white, yellow)
Clarke and Yan (2009)
Linear
Tennessee
White 90-mil
Thermoplastic Age of Marking 0.015
Yellow 90-mil
Thermoplastic Age of marking 0.008
Clarke and Yan (2009)
Logarithmic
White 90-mil
Thermoplastic Age of Marking 0.017
Yellow 90-mil
Thermoplastic Age of marking 0.003
Clarke and Yan (2009)
Quadratic
White 90-mil
Thermoplastic Age of Marking 0.007
Yellow 90-mil
Thermoplastic Age of marking 0.017
33
Economic evaluation is also important when deciding which material will be used for
pavement markings. Basic costs of the materials and the equipment and service life are the most
characteristics analyzed to perform a cost-effective evaluation. The objective of a pavement
marking economic evaluation is to identify the most economical pavement marking materials.
Some methods have been employed.
Prediction of service life, usually based on retroreflectivity levels, varies from one model
to another. A summary of predicted service life for pavement markings analyzed in Section 2.6
can be observed in Table 8. Adopted retroreflectivity thresholds are also in Table 8.
Table 8 ? Summary of Predicted Service Life
Study Marking
Retroreflectivity
(mcd/m2/lux) Service Life (months)
Threshold Average Initial Minimum Maximum Average
Migletz and
Graham
(2002)
White Thermoplastic 150 - 7.4 49.7 22.6
Yellow Thermoplastic 100 - 11 41.6 24.7
Abboud and
Bowman
(2002)
White Edge
Thermoplastic 150 - 10.5 53 -
Thamizharasan
et al. (2003)
White Thermoplastic
on Asphalt 100 203 - - 65
Yellow Thermoplastic
on Asphalt 100 135 - - 103
Sitzabee et al.
(2009)
White Edge
Thermoplastic 150 375 - - 102
White Middle
Thermoplastic 150 375 - - 84
Yellow Edge
Thermoplastic 100 250 - - 85
Yellow Middle
Thermoplastic 100 250 - - 65
Clarke and
Yan (2009)
White 90-mil
Thermoplastic - 296.1 - - 92
Yellow 90-mil
Thermoplastic - 154.5 - - 75
Karwa and
Donnell
(2011)
Yellow Edgelines 150, 200 300, 400
(values differ according to ADT and
percent trucks)
Yellow Centerlines 150, 200 300, 400
White Edgelines 150, 200 300, 400
White Skip Lines 150, 200 300, 400
34
Chapter Three
Methodology
Chapter Three provides details of the methods applied to this thesis with the purpose of
achieving the objectives stated in Chapter One. These methods include the data mining and
analysis of a database of pavement markings applied in 2007 highway projects for ALDOT. This
process determined the extent to which observations from this database meet the ALDOT
Standard Specifications for Highway Construction for thickness, retroreflectivity, luminance,
and color of pavement markings. A statistical analysis was also executed to evaluate trends in
mean, standard deviation, and coefficient of variation for each class and color of markings.
Retroreflectivity modeling based on models found in the literature was developed in this research
project. A methodology for development of new models related to preparation of data and model
fitting, as well as considerations regarding benefit/cost analysis are also discussed in this chapter.
3.1. ALDOT specifications study
The database analyzed in this thesis was developed by ALDOT in 2007 and includes
measurements of pavement markings observed at 7,840 locations from 40 projects in Alabama.
In this year, five different General Application Special Provisions for Traffic Stripe, which
constitute updates to ALDOT?s Standard Specifications for Highway Construction, were
approved. A documentation of the recent changes in these special provisions was prepared.
35
3.2. Data Mining and Analysis
The database studied in this thesis contains multiple pavement marking measurements
from 40 projects in Alabama. The list including the number of these projects and their locations
can be observed in Table 9.
Table 9 ? List of the 40 Pavement Marking Projects in the 2007 ALDOT Database
Project Number County
99-307-203-100-701 Covington County
99-307-346-010-701 Henry County
STPNU-3128(200) Geneva County
STPNU-3140(200) Geneva County
99-307-164-167-701 Geneva County
STPNU-2014(200) Covington County
EB-0042(507) Mobile County
EB-0074(513) Cullman County
99-302-391-101-701 Lauderdale County
99-307-162-088-703 Coffee County
STPNU-4816(201) Marshall County
99-304-154-009-701 Cleburne County
STPAA-0052(506) Geneva County
99-305-632-069-703 Tuscaloosa County
STPSA-0021(515) & 99-306-434-021-701 Lowndes County
STPNU-CN07(203) (1Y) OLD McGEHEE Montgomery County
STPNU-CN07(203) (1W) OLD McGEHEE Montgomery County
STPNU-CN07(203) (2Y) MARLER Montgomery County
STPNU-CNO7(203) (2W) MARLER Montgomery County
99-308-663-089-706 & STPSA-0089(500) Wilcox County
EB-0016(505) Baldwin County
STPSA-0185(500) & 99-306-074-185-701 Butler County
STPAA-0079(506) Blount County
STPNU-3423(201) Henry County
99-302-473-013-704 Marion County
36
Table 9 (Continuation) ? List of the 40 Pavement Marking Projects in the 2007 ALDOT Database
Project Number County
EB-0004(509) Jefferson County
STPSA-0001(529) & 99-301-285-001-705 Etowah County
99-303-595-003-709 Shelby County
NHF-STPSAF-0053(525) & 99-307-234-053-
701 Dale County
NHF-0056(500) & BRF-0102(527) Montgomery County
STPNU-1713(201) Colbert County
99-302-473-171-706 Marion County
STPNU-2221(201) Cullman County
99-305-632-069-702 Tuscaloosa County
EBF-0012-(522) Houston County
EBF-0012-(522)B Houston County
EB-0035(506) DeKalb County
99-303-582-004-708 St. Clair County
STPSA-0079(505) & 99-301-484-079-708 Marshall County
STPSA-0079(505) & 99-301-484-079-708(2) Marshall County
All projects in the 2007 database contain measurements of Class 2 (Standard
Thermoplastic) or Class 2T (Thin Film Spray Applied Thermoplastic), and colors are white or
yellow. After identifying changes in 2007 General Application Special Provisions, a data mining
plan was developed. The original database obtained from ALDOT was a Microsoft Access file
that was then imported into Microsoft Excel. All data were assembled into one table. A screen
capture of Microsoft Excel, in Figure 8, shows an example of the available information for all 40
projects. Table 10 presents the meaning of each entry represented on Figure 8.
Figure 8 ? Information from 2007 Database
37
Table 10 ? Meaning of ALDOT Database Entries
Entry Meaning
PROJECT_NO Number used to identify the project
CONTRACTOR Contractor of project
COUNTY County where project is located
BEAD_MAN Bead Manufacturer
THERMO_MAN Thermoplastic Manufacturer
PROJECT_MAN Project Manager
INSPECTOR Inspector of the Project
APP_METHOD Method used on the application of marking
CLASS Class of marking
LOT_ID Identification of marking in ALDOT records
PLACED_DATE Date when marking was placed
TEST_DATE Date when marking properties were measured
RETRO_ID Identification of the equipment used to measure retroreflectivity
COLOR_ID Identification of the equipment used to measure color
STRIPE_TYPE Type of marking (solid or broken)
STRIPE_COLOR Color of marking (white or yellow)
DIRECTION Direction of traffic where marking was measured (e.g., "West" means "Westbound")
Station Location of the marking
Thickness Initial Thickness of the marking
Retro Initial Retroreflectivity of the marking
Luminance Initial Luminance of the marking
Color x Coordinates of chromaticity measures
Color y
Color P/F Determination as to whether color passes or fails to meet specifications
Analyses were performed using data available from the 2007 ALDOT database. The
evaluation of measurements of retroreflectivity, thickness, luminance, and chromaticity in regard
to specifications was the first executed process, followed by a statistical analysis. Pavement
marking measurements were compared with values given in the Standard Specifications for
Highway Construction Special Provisions (ALDOT, 2007) to determine whether the values in
the database complied with ALDOT requirements. As it was observed in Section 3.1, there were
38
no changes in quantitative requirements from one special provision to another. Therefore, all
Special Provisions presented the same required values shown on Table 11.
Table 11 ? Minimum Required Values for Pavement Markings
Class Color Thickness (in) Retroreflectivity (mcd/m2/lux) Luminance (%)
2 White 0.10 450 50
2 Yellow 0.10 350 35
2T White 0.04 300 50
2T Yellow 0.04 250 35
Although the values shown in Table 11 are the minimum required, the special provisions
inform that a thickness greater than 95% of the minimum value is acceptable and a
retroreflectivity greater than 90% of the minimum value meets requirements (ALDOT, 2007).
Therefore, the values used to verify if the measured thickness, retroreflectivity, and luminance in
Alabama were acceptable are shown in Table 12.
Table 12 ? Acceptable Values for Pavement Markings
Class Color Thickness (in) Retroreflectivity (mcd/m2/lux) Luminance (%)
2 White 0.095 405 50
2 Yellow 0.095 315 35
2T White 0.038 270 50
2T Yellow 0.038 225 35
The analysis of color was also performed according to the 2007 General Application
Special Provisions (ALDOT, 2007). The initial daytime chromaticity for white and yellow
materials must fall within the box created by the coordinates shown in Table 13 for the
chromaticity to be in compliance with specifications.
39
Table 13 ? Initial Daytime Chromaticity Coordinates (Corner Points)
White Yellow
x y x y
0.335 0.375 0.472 0.400
0.355 0.355 0.530 0.456
0.305 0.305 0.510 0.485
0.285 0.325 0.455 0.444
SOURCE: ALDOT, 2007
The box created by the plot of the coordinates from Table 13, for white materials, can be
observed in Figure 9 and the plot of the coordinates from Table 13, for yellow materials, is
shown in Figure 10. If measured chromaticity values were located within constrained space in
Figures 9 and 10, then color observations complied with specifications.
Figure 9 ? Initial Daytime Chromaticity: White
0.280
0.290
0.300
0.310
0.320
0.330
0.340
0.350
0.360
0.370
0.380
0.250 0.270 0.290 0.310 0.330 0.350 0.370
Color -White
40
Figure 10 ? Initial Daytime Chromaticity: Yellow
After analyzing all field measurements from the 40 projects in Alabama, some
conclusions could be made. The percentage of projects that were according to specifications
requirements can be observed in Chapter Four: Results. Finally, statistical measures were
calculated, for each marking color and type. Mean, standard deviation and coefficient of
variation were computed to demonstrate the variation of the measured observations of the 40
projects in Alabama. This analysis can provide the information on the central tendency for each
marking property and the dispersion from the average. The detailed statistical analysis for each
class and color of markings can be seen in Chapter Four: Results.
3.3. Retroreflectivity Modeling
For all 40 projects in the initial ALDOT database, from 2007, only 15 have
retroreflectivity data from 2008, 2009 and 2010. Table 14 and Figure 11 describe the location of
0.350
0.370
0.390
0.410
0.430
0.450
0.470
0.490
0.510
0.440 0.460 0.480 0.500 0.520 0.540
Color -Yellow
41
these 15 projects. For these 15 projects, cost information was obtained from the Tabulation of
Bids, from ALDOT (ALDOT, 2010 [1]).
Table 14 ? Projects Included in the Retroreflectivity Modeling
Project ID County Division Location Map Key
EB-0016(505) Baldwin County 9 SR-16 (US-90) from Robertsdale to Florida State line 9A
STPSA-
0185(500)
Butler
County 6
SR-185 from SR-263 in Greenville to the
Lowndes county line 6A
EB-0074(513) Cullman County 1 SR-74 (US-278) from east of CR-420 to I-65 in Cullman 1A
NHF-
STPSAF-
0053(525)
Dale
County 7
SR-53 (US-231) from near CR-63 in
Pinckard to near CR-18 7A
EB-0035(506) DeKalb County 1 SR-35 from SR-7 (US-11) to MP 25.40 in Fort Payne 1B
STPSA-
0001(529)
Etowah
County 1
SR-1 (US-431) from west of I-59 in
Attalla to 0.2 miles south of CR-137 1C
99-307-164-
167-701
Geneva
County 7
SR-167 from the Florida state line to near
the south city limit of Hartford 7B
99-307-346-
010-701
Henry
County 7
SR-10 from SR-1 (US-431) to SR-95 in
Abbeville 7C
99-302-391-
101-701
Lauderdale
County 2
SR-101 from the north end of Wheeler
Dam to SR-2 (US-72) in Elgin 2A
STPSA-
0021(515)
Lowndes
County 6
SR-21 from the Wilcox county line to
south of CR-45 near Mount Willing 6B
99-302-473-
171-706
Marion
County 2
SR-171 from the Fayette county line in
Winfield to SR-118 2B
STPSA-
0079(505)
Marshall
County 1
SR-79 from SR-1 (US-431) through
Columbus City to the Jackson county line 1D
99-303-595-
003-709
Shelby
County 3
SR-3 (US-31) from Seventh Avenue in
Calera to I-65 3A
99-305-632-
069-702
Tuscaloosa
County 5
SR-69 from the north end of the Lake
Tuscaloosa bridge to south of Windham
Springs
5A
STPSA-
0089(500)
Wilcox
County 8
SR-89 from SR-21 west of Snow Hill to
the Dallas county line 8A
42
Figure 11 ? Location of the 15 Projects with Retroreflectivity Data from 2007 to 2010
SOURCE: Based on University of Alabama, 2011
43
All projects are located on State Routes, U.S. Routes, or Interstates, with 2 lanes (one in
each direction) or four lanes (separated, two lanes on one side, two lanes on the other side).
Figure 12 shows an example of a two-lane state route, a section of project STPSA-0185(500), in
Butler County, on SR-185. More pictures showing details of these 4-year old pavement markings
of project STPSA-0185(500) can be observed in Appendix A.
Figure 12 ? Section of Project STPSA-0185(500), on SR-185
Retroreflectivity for 2007 data was measured at specific points, within stations.
Retroreflectivity for 2008, 2009 and 2010 was measured in different locations, within mileposts.
To build the retroreflectivity curves, it was necessary to correlate locations from the 2007
44
database and the 2008 to 2010 data. From ALDOT project records, the ?Begin Project? location,
in station, and the corresponding milepost were identified. Figure 13 shows an example for
project NHF-STPSAF-0053(525). The project begins at Milepost 32.1, which is the same
location as Station 251+67.
Figure 13 ? Example of Correspondence from Stations to Mileposts
For each milepost, there was a range of corresponding stations. The average
retroreflectivity for this range of stations was calculated and set as the milepost retroreflectivity
value for 2007. One retroreflectivity curve was built for each milepost, according to color and
type of marking. Table 15 shows the total number of mileposts, across all projects, for each color
and type; therefore, the number of retroreflectivity curves available for analysis. The complete
list of mileposts by projects can be observed in Appendix B.
Table 15 ? Total Number of Retroreflectivity Curves
TOTAL
CURVES
Solid White Broken White Solid Yellow Broken Yellow
76 17 67 32
3.3.1. Preparation of Data for Modeling
The end of a pavement marking service life can be represented in a retroreflectivity curve
as the time when the curve reaches a minimum retroreflectivity threshold. The adopted minimum
45
values are 150 mcd/m2/lux for white markings and 100 mcd/m2/lux for yellow markings, as these
were the most common values found in the literature.
The retroreflectivity curves that were built for each milepost, based on 4 years of data, do
not reach these minimum retroreflectivity values; therefore, it is necessary to extrapolate curve
points. Many existing models in the literature were applied to the available data to determine
which one would be the best option to represent actual data. Among these models, those
developed by Abboud and Bowman, and Sitzabee et al., required traffic information as input
data. The Average Annual Daily Traffic (AADT) for the 15 project locations was obtained from
the ALDOT website (ALDOT, 2010 [2]).
As there was not an exact correspondence between locations in the ALDOT traffic
database and the location of the projects? measurements, some assumptions were made when
determining AADT for each milepost. Three locations from the ALDOT traffic database, similar
to locations of projects, were chosen, and the average AADT for these three locations was
considered as the AADT for each milepost of the considered project.
To illustrate this process, Project 99-302-391-101-701, on SR-101, is shown as an
example. It has retroreflectivity data at milepost 25.7, milepost 26.2, milepost 27.0, and milepost
28.0. The ALDOT traffic database contains traffic data at milepost 24.99, milepost 26.78, and
milepost 28.24, as historical data, as shown in Table 16. The average of these three AADT
historical data was calculated. From that, a linear regression analysis was applied in order to
obtain an equation to estimate AADT as a function of time to relate AADT values to the times
when retroreflectivity measurements were taken. All existing mileposts for this project (MP 25.7,
MP 26.2, MP 27.0, and MP 28.0) will have the same AADT equation to calculate vehicles as a
function of time.
46
Table 16 ? ALDOT Historical Traffic Data
Traffic Counters 2010 Traffic Counters 2010 Traffic Counters 2010
Counter ID AL-39-522 Counter ID AL-39-521 Counter ID AL-39-520
Station 522 Station 521 Station 520
County 39 County 39 County 39
City N/A City N/A City N/A
Route 101 Route 101 Route 101
Milepoint 24.99 Milepoint 26.78 Milepoint 28.24
AADT 2010 5990 AADT 2010 7390 AADT 2010 5640
AADT 2009 6580 AADT 2009 7370 AADT 2009 5360
AADT 2008 6380 AADT 2008 7140 AADT 2008 5150
AADT 2007 7050 AADT 2007 7480 AADT 2007 5400
AADT 2006 6980 AADT 2006 7300 AADT 2006 5270
AADT 2005 6890 AADT 2005 7590 AADT 2005 5540
AADT 2004 6930 AADT 2004 7760 AADT 2004 5300
AADT 2003 6540 AADT 2003 7460 AADT 2003 5100
AADT 2002 6370 AADT 2002 7040 AADT 2002 4860
K 11 K 11 K 11
D 55 D 75 D 55
TDHV 8 TDHV 7 TDHV 7
TADT 11 TADT 9 TADT 9
Heavy 50 Heavy 50 Heavy 50
Functional
Class 6
Functional
Class 6
Functional
Class 7
SOURCE: ALDOT, 2010 [2]
This calculated AADT was used to estimate models in the literature. For Abboud and
Bowman model, AADT per lane was considered; for Sitzabee et al. model, AADT for all lanes
was used to calculate retroreflectivity.
3.3.2. Model Fitting
The determination of the best-fitting model from the literature when applied to ALDOT
data was based on three performance measures: Area Under Curve Ratio, Average Model Error,
and Average Percent Error.
47
The behavior of a curve can be represented by the area under it. The definite
integral gives the area between the graph of the input and the x-axis. The technical definition of
the definite integral is the limit of a sum of areas of rectangles, called a Riemann sum. There are
four methods of Riemann summation: left sum, right sum, middle sum, and trapezoidal rule. The
left Riemann sum approximates the function by its value at the left-end point; the right Riemann
sum approximates the value at the right endpoint; the middle Riemann sum approximates the
function at the midpoint of each interval; and the trapezoidal rule considers that the values of the
function on an interval are approximated by the average of the values at the left and right
endpoints (Thomas and Finney, 1996). Figure 14 shows how these four summation methods can
be visualized.
Figure 14 ? Four Methods of Riemann Summation
SOURCE: Adapted from Thomas and Finney, 1996
48
The trapezoidal rule is applied to calculate the area under the curve resulted from actual
data and the area under each curve representing a model in literature. Figure 15 illustrates the
comparison between two curves considering this area.
Figure 15 ? Comparison Between Areas Under Curves
To have a numerical parameter of comparison between all models and a method to
identify the ?best-fitting? model, a ratio is calculated for each model, for each milepost, as shown
in Equation 3.1.
g1844g1853g1872g1861g1867= g1827g1870g1857g1853uni0009g4666g1839g1867g1856g1857g1864g4667g1827g1870g1857g1853uni0009g4666g1827g1855g1872g1873g1853g1864uni0009g1830g1853g1872g1853g4667 (Eq. 3.1)
The closer this ratio is to 1, the better fitting is the model.
Another way to compare models is to calculate the average model error. This relationship
is simply the difference between the model and actual data and it is given by Equation 3.2.
g1827g1874g1857g1870g1853g1859g1857uni0009g1839g1867g1856g1857g1864uni0009g1831g1870g1870g1867g1870=g1839g1867g1856g1857g1864?g1827g1855g1872g1873g1853g1864uni0009g1830g1853g1872g1853 (Eq. 3.2)
49
The last method used to evaluate the suitability of models found in the literature is
average percent error. It is calculated by Equation 3.3.
g1827g1874g1857g1870g1853g1859g1857uni0009g1842g1857g1870g1855g1857g1866g1872uni0009g1831g1870g1870g1867g1870=g1839g1867g1856g1857g1864?g1827g1855g1872g1873g1853g1864uni0009g1830g1853g1872g1853g1827g1855g1872g1873g1853g1864uni0009g1830g1853g1872g1853 ?100 (Eq. 3.3)
3.4. Benefit/Cost Calculation
Retroreflectivity curves developed for each milepost of the 15 projects in Alabama were
extrapolated based on the best-fitting models from the literature, established according to the
methodology described in Section 3.3.2. As shown in Chapter Two, there is a wide range of
methods used to determine benefit/cost relationship of each available marking material. The
method developed by Fu and Wilmot, considering the area between Rmin and Rmax as the benefit
of the marking, was the most relevant to this study.
According to what was analyzed in Chapter Two, it is possible to set Rmax = 200
mcd/m2/lux, Rmin = 150 mcd/m2/lux for white markings, and Rmin = 100 mcd/m2/lux for yellow
markings. Cost data were available from ALDOT Tabulation of Bids (ALDOT, 2010[1]). AADT
was obtained from ALDOT Traffic Data (ALDOT, 2010 [2]). The benefit/cost ratio can be
calculated by Equation 3.4.
g1854g1857g1866g1857g1858g1861g1872
g1855g1867g1871g1872 =
g1854g1857g1866g1857g1858g1861g1872?g1827g1827g1830g1846
g1872g1867g1872g1853g1864uni0009g1855g1867g1871g1872
(Eq. 3.4)
3.5. Modeling of Retroreflectivity Over Time
Using the data from the 15 projects with several years of observations, new models will
be developed to represent the behavior of retroreflectivity over time in Alabama. First, locations
are grouped by color and type: solid white, broken white, solid yellow, and broken yellow. The
50
Standard Specifications for Highway Construction Special Provisions (ALDOT, 2007), which
were in effect at the time the projects included in this study were constructed, state that initial
retroreflectivity shall be a minimum of 450 mcd/m2/lux for white markings and 350 mcd/m2/lux
for yellow markings. Therefore, locations with initial retroreflectivity less than the required
values are not considered in the modeling.
In the literature, separate models for solid and broken markings are not presented.
Therefore, two groups of data will be considered in this study: white and yellow; within each
color, measurements from solid and broken lines will be combined. It can also be inferred from
the literature that most models consider only age as the independent variable, some consider the
initial retroreflectivity, and a few consider traffic volume.
Regressions that consider only one independent variable are simple regressions; if 2 or
more independent variables are included, they are defined as multiple regressions. For all
developed models in this thesis, 2 or more independent variables are used; therefore, they are
multiple regressions. When analyzing available data from ALDOT databases, two independent
variables can be considered for the models: Initial Retroreflectivity and Age. AADT can be
another independent variable as this data was obtained by the linear regression analysis based on
ALDOT traffic data demonstrated in Section 3.3.1. Some research considers that AADT does not
influence retroreflectivity degradation significantly; other studies affirm it is an important
variable when estimating retroreflectivity over time. Therefore, this study will consider two
approaches when predicting retroreflectivity models: the first one considers initial
retroreflectivity and age of markings as independent variables, the second approach also
considers AADT as an independent variable.
51
For the retroreflectivity modeling based on initial retroreflectivity and age of markings,
four models will be evaluated according to the tendencies of data: linear, power, quadratic, and
exponential. Models will be estimated using the software IBM Statistical Package for the Social
Sciences (SPSS). The linear model general expression for two independent variables is
represented by Equation 3.5.
g1877=g1865g2869g1876g2869+g1865g2870g1876g2870+g1854 (Eq. 3.5)
where:
g1877 = Dependent Variable;
g1876g2869,g1876g2870 = Independent Variables;
g1865g2869,g1865g2870= Coefficients;
g1854 = Constant.
The power model can be represented by Equation 3.6.
g1877=g1854?g1865g2869g3051g3117 ?g1865g2870g3051g3118 (Eq. 3.6)
The general expression for a quadratic model is observed in Equation 3.7.
g1877=g1865g2869g1876+g1865g2870g1876g2870 +g1854 (Eq. 3.7)
The exponential model can be represented by Equation 3.8.
g1877=g1876g2869g1857g2879g3029g3051g3118 (Eq. 3.8)
Considering initial retroreflectivity, age of markings, and traffic volume as independent
variables to model retroreflectivity, a linear model will be developed based on the tendencies of
data and existing model forms in the literature with these three variables. The model will also be
estimated using the software IBM Statistical Package for the Social Sciences (SPSS) and its
general expression is observed in Equation 3.9.
g1877=g1865g2869g1876g2869+g1865g2870g1876g2870 +g1865g2871g1876g2871+g1854 (Eq. 3.9)
52
Comparisons between all models, details related to each one and conclusions about the
results obtained with all four regressions can be analyzed in Chapter Four: Results.
3.6. Summary of Chapter Three
This chapter presented the methods used to analyze the 2007 database, which included
the determination whether observations met specifications and a statistical analysis to evaluate
trends in mean, standard deviation, and coefficient of variation. Also provided herein are details
related to the methodology applied to retroreflectivity modeling based on models found in the
literature and preparation of data for development of new models. Model forms under
consideration include linear, power, quadratic, and exponential when considering initial
retroreflectivity and age of markings as independent variables to predict retroreflectivity; a linear
model will be developed when AADT is also considered. The results obtained with the use of
methods from this chapter will be presented in Chapter Four: Results.
53
Chapter Four
Results
This chapter presents the results for the procedures adopted in this thesis, described in
Chapter Three. Chapter Four provides a summary illustrating the proportion of all 7840
observations among the 40 projects in Alabama that met ALDOT specifications, considering the
properties of retroreflectivity, thickness, luminance, and chromaticity. Statistical calculations of
mean, standard deviation, and coefficient of variation are also presented in this chapter.
The retroreflectivity modeling process provided several results. The development of
retroreflectivity curves for each milepost of the 15 projects with data from 2007 to 2010 is
described in this Chapter, as well as application and determination of best-fitting models from
the literature. Considerations for the benefit/cost analysis are presented in this chapter. Finally,
different proposed models of retroreflectivity over time are suggested to represent projects in
Alabama.
4.1. ALDOT Data Mining and Analysis
After analyzing all measures from the 2007 database of 40 projects in Alabama, some
conclusions can be made pertaining to compliance with specifications and statistical attributes.
The first two columns of Table 17 indicate how many observations met specifications and how
many did not; how many of the observation points did not have a property measured is also
represented in the table. The final two columns show the percentage of observations which
54
passed specifications and the percentage of total observations which was measured for the
considered property of thickness, retroreflectivity, luminance, or chromaticity.
Table 17 ? Material Property Compliance with Specifications
Property Pass Do not pass Measured Not measured Total % Passing % Measured
Thickness 6025 1551 7576 264 7840 79.53 96.63
Retroreflectivity 5344 2356 7700 140 7840 69.40 98.21
Luminance 5831 1865 7696 144 7840 75.77 98.16
Color 7227 459 7686 154 7840 94.03 98.04
In addition, the 2007 ALDOT database provided data on whether chromaticity values met
specifications. In this analysis a color check was also performed, and results of the present
analysis and ALDOT analysis were compared. As can be observed in Table 18, some
conclusions of the color measurements being in accordance with the Special Provisions were
different, which means the ALDOT analysis found some color measurements passed the criteria
and this data analysis did not, or vice-versa. In spite of these differences, 98.70% of the total
compared showed equal conclusions.
Table 18 ? Color Check Comparison
Different Equal Total % Compared %Equal
99 7536 7635 97.39 98.70
To describe the variation of the measured values from the 40 projects in Alabama in
2007, a statistical analysis was performed. Table 19 shows these measures for each analyzed
group, by class and color of the material.
55
Table 19 ? Statistical Calculations
Property Class Mean Standard Deviation
Coefficient
of Variation
(%)
Number of
Observations
(n)
Thickness (in)
Class 2 - white 0.117 0.034 29.06 3971
Class 2 - yellow 0.115 0.035 30.43 3031
Class 2T - white 0.078 0.043 55.13 306
Class 2T - yellow 0.065 0.033 50.77 268
Retroreflectivity
(mcd/m2/lux)
Class 2 - white 496 141.383 28.50 4000
Class 2 - yellow 330 72.020 21.82 3126
Class 2T - white 326 113.324 34.76 306
Class 2T - yellow 202 87.783 43.46 268
Luminance (%)
Class 2 - white 55 10.189 18.53 3996
Class 2 - yellow 37 5.241 14.16 3126
Class 2T - white 65 5.437 8.36 306
Class 2T - yellow 40 2.910 7.28 268
Table 19 shows that the most consistent property was luminance, with the lowest
coefficients of variation. Thickness appears to be the less consistent one, as coefficient of
variation can be as high as 55.13%. Retroreflectivity also has very dispersed observations, with a
high coefficient of variation of 43.44% among the four color/class categories, and also very
different means when contrasting all classes and types.
4.2. Retroreflectivity Modeling
4.2.1. Retroreflectivity Curve
Table 20 and Figure 16 show an example of the data and plot developed for all mileposts
of the 15 projects that had data for four years. The total observations allowed for development of
76 curves for solid white markings, 17 for broken white, 67 for solid yellow and 32 for broken
yellow markings.
56
Table 20 ? Retroreflectivity Values of Project NHF-STPSAF-0053(525), for MP36
Curve 3: MP 36 Solid Yellow
Date Tested (months) Retroreflectivity (mcd/m2/lux)
0.00 249.90
8.40 291.00
22.77 224.00
34.67 220.50
Figure 16 ? Plot of Retroreflectivity Values of Project NHF-STPSAF-0053(525), for MP36
4.2.2. Model Fitting Analysis
The end of pavement marking service life can be determined when retroreflectivity
reaches minimum values. The plots developed in Section 4.2.1 had retroreflectivity data for three
years after markings? application, which did not represent the end of service lives.
Retroreflectivity data had to be extrapolated until it could reach minimum threshold values, and
to accomplish that, several models existing in the literature were tested to determine which one
best represented actual data. For solid white and broken white pavement markings, 10 models
were compared to actual data, Lee et al., Abboud and Bowman [1], Thamizharasan et al. linear,
Sitzabee et al, Abboud and Bowman [2], Thamizharasan et al. non-linear, Bahar et al., Clarke
57
and Yan linear, Clarke and Yan logarithmic, and Clarke and Yan quadratic. For solid yellow and
broken yellow markings, the same models were tested, except for Abboud and Bowman models,
which were developed specifically for white markings.
An example of application of the models found in the literature to the observed data,
using data from Project STPSA-0185(500), Milepost 10, Solid White, can be observed in Figure
17.
Figure 17 ? Comparison between Models for Project STPSA-0185(500), MP10, Solid White
-200.00
0.00
200.00
400.00
600.00
800.00
1000.00
0.00 10.00 20.00 30.00 40.00
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Date Tested (months)
Project STPSA-0185(500) MP10 Solid White
Actual Data
Lee et al.
Abboud and Bowman [1]
Thamizharasan et al. Linear
Sitzabee et al.
Abboud and Bowman [2]
Thamizharasan et al. Non-
Linear
Bahar et al.
Clarke and Yan Linear
Clarke and Yan Logarithmic
Clarke and Yan Quadratic
58
The comparison between models, using the methods area under curve ratio, average
model error, and average percent error, as described in Section 3.3.2, was performed. The three
best-performing models for each color and type can be observed in Table 21. Number of
locations indicate the number of curves for each marking color and type (the number of existing
mileposts with data).
Table 21 ? Models in the Literature that Best Represented Actual Data
Marking
Color
and Type
Number
of
Locations
Best-Performing Models
Area Under Curve Ratio Average Model Error Average Percent Error (%)
Solid
White 76
Thamizharasan
Linear 1.02
Thamizharasan
Linear 10.54 Sitzabee -7.48
Sitzabee 0.86 Sitzabee -55.84 Thamizharasan Linear 8.20
Thamizharasan
Non-Linear 0.85
Thamizharasan
Non-Linear -89.76
Thamizharasan
Non-Linear -20.27
Solid
Yellow 67
Sitzabee 0.91 Thamizharasan Non-Linear 24.79 Sitzabee -1.33
Thamizharasan
Linear 1.14
Thamizharasan
Linear 29.84
Clarke
Quadratic -19.37
Thamizharasan
Non-Linear 1.14 Sitzabee -30.44
Thamizharasan
Non-Linear 22.49
Broken
White 17
Sitzabee 0.97 Thamizharasan Non-Linear -13.68 Thamizharasan Non-Linear 0.78
Thamizharasan
Non-Linear 1.09 Sitzabee -19.76 Sitzabee 4.91
Clarke
Logarithmic 0.83
Thamizharasan
Linear 76.96
Clarke
Logarithmic -11.45
Broken
Yellow 32
Thamizharasan
Non-Linear 1.06
Thamizharasan
Non-Linear 7.92
Thamizharasan
Non-Linear 8.61
Thamizharasan
Linear 1.06
Thamizharasan
Linear 13.63 Sitzabee -9.58
Sitzabee 0.86 Sitzabee -40.49 Thamizharasan Linear 11.55
59
4.3. Benefit/Cost Calculation
The determination of a benefit/cost ratio for each observation from the 15 projects with
retroreflectivity data from 2007 to 2010 is described in this section. This analysis can identify
which projects were best executed, by color and type, and make them models for future
pavement marking construction in Alabama. The most adequate benefit/cost method to be
applied in this study was the Fu and Wilmot method, and for that retroreflectivity extrapolation
was required. From Table 21, it can be seen that Thamizharasan et al. Linear and Sitzabee et al.
models were found to be the most appropriate to represent actual data. Therefore, an
extrapolation of actual data, beyond the 4 years for which data are available, was performed,
based on these two models. However, the service life, determined by when retroreflectivity
reaches the minimum threshold value of 150 mcd/m2/lux for white markings and 100 mcd/m2/lux
for yellow markings, is much higher than observed values for markings found in the literature.
This fact can be illustrated by Figure 18, which shows estimated service life equal to 250
months; Figure 19, where estimated service life is 150 months; and Table 22, from where it can
be observed that all service life values are greater than the maximum found in the literature (102
months for white markings).
Table 22 ? Example of Benefit/Cost and Service Life calculations
SOLID WHITE
Project MP
Benefit/Cost Thamizharasan
et al. Model
(month*vehicle*mcd/m2/lux)
Benefit/Cost Sitzabeeet al.
Model
(month*vehicle*mcd/m2/lux)
Service Life
Thamizharasan
et al. Model
(months)
Service
Life
Sitzabee
et al.
Model
(months)
99-307-
164-167-
701
1 12379 7156 256 152
2 10587 6555 221 140
3 10946 6670 228 142
4 9883 6311 207 135
5 11381 6823 236 145
6 9742 6273 204 135
60
Figure 18 ? Thamizharasan et al. Linear Extrapolation of Actual Data
Figure 19 ? Sitzabee et al. Extrapolation of Actual Data
61
Table 22 also shows that the Benefit/Cost values do not provide a useful idea of benefit
related to cost; the meaning of the unit ?month*vehicle*mcd/m2/lux? is not tangible. In the
literature, this method was valuable when comparing different materials, such as markings of
Class 1 compared to markings of Class 2, and compared to markings of Class 2T, and
determining the most cost-effective material among them. As the observations of the 15 projects
in Alabama use only one type of material, thermoplastic Class 2, this benefit/cost analysis
approach is not suitable in the case of the available data.
4.4. Modeling of Retroreflectivity Over Time
The models found in the literature, when applied to the Alabama data and extrapolated to
acceptable minimum retroreflectivity values, do not result in reasonable service life projections.
Therefore, new models were developed to try to represent better the behavior of retroreflectivity
over time. First, locations were grouped by color and type: Solid White (76 locations), Broken
White (17 locations), Solid Yellow (67 locations), and Broken Yellow (32 locations).
For model development, observations from all 15 projects were grouped only by color,
one model for yellow and another for white markings; additionally, those below minimum initial
retroreflectivity thresholds required by ALDOT were not considered. This approach to data
organization for model development is consistent with those found in the literature. After
applying this procedure, there are 63 observations for white markings and 42 for yellow
markings.
In the literature, it is possible to observe that most models consider initial retroreflectivity
and age of marking as the independent variables to estimate retroreflectivity; some models also
consider traffic volume as an independent variable. For this reason, two different approaches
62
were adopted in this study; first, four models were developed, by color, for data in Alabama:
linear, power, quadratic, and exponential, as mentioned in Section 3.5. Table 23 shows all
developed models for this approach and the corresponding R2 for white markings in 63 locations
and yellow markings in 42 locations. The dependent variable is retroreflectivity (g1844), measured in
mcd/m2/lux; the two independent variables are initial retroreflectivity (g1844g2868g4667, measured in
mcd/m2/lux, and age of marking (g1872), measured in months.
Table 23 ? Developed Models considering initial retroreflectivity and age as independent variables
Color Model Equation R2
White
Linear R = 0.3242Ro - 4.745t + 384.4 0.325
Power R = 366.8 * 1.001Ro *0.9900t 0.335
Quadratic R = Ro - 2.865t - 0.05300t2 + 1.231 0.181
Exponential R = Ro * e-0.009747t 0.261
Yellow
Linear R = 0.1222R0 - 4.778t + 338.3 0.465
Power R = 276.8 * 1.001Ro *0.9839t 0.480
Quadratic R = Ro - 1.926t - 0.05119t2 - 23.67 0.320
Exponential R = Ro * e-0.01682t 0.440
The second approach to the retroreflectivity estimate considered initial retroreflectivity,
age of marking, and AADT as independent variables. Only linear models were developed, by
color, which was consistent with the existing models in the literature. Table 24 shows the models
for this approach and the corresponding R2 for white markings in 63 locations and yellow
markings in 42 locations.
Table 24 ? Developed Models considering initial retroreflectivity, age, and AADT as independent variables
Color Model Equation R2
White Linear R = 0.2296Ro - 4.967t - 0.004665AADT + 470.7 0.398
Yellow Linear R = 0.03928Ro - 4.932t - 0.002030AADT + 381.4 0.479
63
4.4.1. Approach One: Initial Retroreflectivity and Age of Marking as Independent Variables
The linear model developed in this section was applied to estimate retroreflectivity over
time for age and initial retroreflectivity values of actual data. The comparison for white
markings between actual data points and linear model data points can be observed in Figure 20.
It can be inferred from the figure that the range of data points representing the linear regression
is not very similar to the range representing actual observations. The R2 value for this
relationship, as shown in Table 23, was 0.325. The data set could not be divided into more
ranges because the number of locations in each would not be significant.
Figure 20 ? Linear Regression estimates for White Markings: Initial Retroreflectivity and Age as
Independent Variables
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Linear Regression)
Linear Estimates
Actual Data
64
In order to ascertain how different initial retroreflectivity values influence where the
model intercepts the Y axis, and also to compare the range of points in the model to the range
formed by actual data points, different initial retroreflectivity values were tested from age zero
until 40 months. For this analysis, with white markings, initial retroreflectivity values were set
equal to 450 mcd/m2/lux, 550 mcd/m2/lux, 650 mcd/m2/lux, and 750 mcd/m2/lux. It can be
noticed in Figure 21 that the regression lines occupy the middle region of the area formed by
actual data points. The initial points as obtained from the model are not actual initial
retroreflectivity values. This happens because the general linear model has a constant and a
coefficient multiplying initial retroreflectivity causing that when age is equal to zero,
retroreflectivity is not equal to initial retroreflectivity.
Figure 21 ? White Markings Linear Regression for Different Initial Retroreflectivity Values: Initial
Retroreflectivity and Age as Independent Variables
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Linear Regression)
Actual Data
Ro=450mcd/m2/lux
Ro=550mcd/m2/lux
Ro=650mcd/m2/lux
Ro=750mcd/m2/lux
65
In trying to develop non-linear relationships between data and determine which models
better represent retroreflectivity behavior over time in Alabama, a power regression model was
developed. The comparison for white markings between actual data points and power model data
points can be observed in Figure 22. In this case, as with the linear model, the range of data
resulting from the power regression is narrower than the range of actual observations. The R2 for
this relationship, as shown in Table 23, was 0.335. Figure 23 shows that the power regression
curves for initial retroreflectivity values of 450, 550, 650, and 750 mcd/m2/lux also occupy the
middle region of the area formed by actual data points; a similar pattern as was seen in Figure 23
for the linear model is apparent.
Figure 22 ? Power Regression estimates for White Markings: Initial Retroreflectivity and Age as Independent
Variables
0
100
200
300
400
500
600
700
800
900
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Power Regression)
Power Estimates
Actual Data
66
Figure 23 ? White Markings Power Regression for Different Initial Retroreflectivity Values: Initial
Retroreflectivity and Age as Independent Variables
A quadratic model was also developed in this section and applied to calculate
retroreflectivity over time for age and initial retroreflectivity values of actual data. The
comparison for white markings between actual data points and quadratic model data points can
be observed in Figure 24. It is possible to observe that the range of data points from the quadratic
regression is very similar to the range of actual observations, more so than was seen with the
linear and power functions. The R2 value for this relationship, as shown in Table 23, was 0.181.
It can be observed in Figure 25 that points projected by the quadratic regression curves are in
almost the entire region formed by the actual data points. There is high accuracy on where
regression lines start, their initial points are very close to the observed initial retroreflectivity
values. This happens because the constant in the quadratic model is not very high (1.231) and
there is not a coefficient multiplying initial retroreflectivity.
0
100
200
300
400
500
600
700
800
900
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Power Regression)
Actual Data
Ro=450mcd/m2/lux
Ro=550mcd/m2/lux
Ro=650mcd/m2/lux
Ro=750mcd/m2/lux
67
Figure 24 ? Quadratic Regression estimates for White Markings: Initial Retroreflectivity and Age as
Independent Variables
Figure 25 ? White Markings Quadratic Regression for Different Initial Retroreflectivity Values: Initial
Retroreflectivity and Age as Independent Variables
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Quadratic Regression)
Quadratic Estimates
Actual Data
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Quadratic Regression)
Actual Data
Ro=450mcd/m2/lux
Ro=550mcd/m2/lux
Ro=650mcd/m2/lux
Ro=750mcd/m2/lux
68
This study included an exponential model as well. The comparison for white markings
between actual data points and exponential model data points can be observed in Figure 26.
Figure shows that the range of data points estimated by the exponential regression is very similar
to actual observations. The R2 value for this relationship, as shown in Table 23, was 0.261.
Figure 26 ? Exponential Regression estimates for White Markings: Initial Retroreflectivity and Age as
Independent Variables
Figure 27 shows that the exponential regression curves occupy almost all the area formed
by actual data points. Unlike the other model forms developed, the initial points of the
exponential model are exactly initial retroreflectivity values. This happens because when age is
equal to zero, the exponential function of age has a value of one.
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Exponential Regression)
Exponential Estimates
Actual Data
69
Figure 27 ? White Markings Exponential Regression for Different Initial Retroreflectivity Values: Initial
Retroreflectivity and Age as Independent Variables
The same process was conducted for yellow markings. Adopted initial retroreflectivity
values, to verify the behavior of the developed models in the area occupied by actual
observations, were equal to 350 mcd/m2/lux, 400 mcd/m2/lux, 450 mcd/m2/lux, and 500
mcd/m2/lux. Conclusions were the same as the observed for white markings. Detailed charts are
presented in Appendix C.
4.4.2. Approach Two: Initial Retroreflectivity, Age of Marking, and Traffic Volume as
Independent Variables
With three independent variables, only a linear model was developed by color, as it is
usually seen in the literature. Figure 28 shows the data estimated by the linear regression
compared to actual data. Figure 29 illustrates estimated data for initial retroreflectivity values
0.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
0.00 10.00 20.00 30.00 40.00 50.00
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings Exponential Regression
Actual Data
Ro=450mcd/m2/lux
Ro=550mcd/m2/lux
Ro=650mcd/m2/lux
Ro=750mcd/m2/lux
70
equal to 450, 600, and 750 mcd/m2/lux and AADT equal to 350, 7000, and 18000 veh/day. These
values were observed to be the minimum, average, and maximum values of actual initial
retroreflectivity for white markings and traffic volume data, respectively, for the 15 study sites.
Both figures show that the initial points of the model are not actual initial retroreflectivity values,
because the linear model has a constant and a coefficient multiplying initial retroreflectivity and
AADT causing that when age and AADT are equal to zero, retroreflectivity is not equal to initial
retroreflectivity. However, this linear regression estimated values for retroreflectivity closer to
actual values than the linear model that did not consider AADT as an independent variable; this
can be verified by comparing Figures 28 and 29 to Figures 20 and 21, and also Table 24 to Table
23, which shows a higher R2 value (0.398) for the regression considering AADT. The same
procedure was applied to yellow markings for initial retroreflectivity values equal to 350, 425,
and 500 mcd/m2/lux, and the conclusions were similar; details can be seen in Appendix D.
Figure 28 ? Linear Regression estimates for White Markings: Initial Retroreflectivity, Age, and AADT as
Independent Variables
0.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Linear Regression)
Linear Estimates
Actual Data
71
Figure 29 ? White Markings Linear Regression for Different Initial Retroreflectivity and AADT Values:
Initial Retroreflectivity, Age, and AADT as Independent Variables
4.4.3. Service Life
Another important issue to be considered is service life. Considering as thresholds for
minimum retroreflectivity 150 mcd/m2/lux for white markings and 100 mcd/m2/lux for yellow
markings, the predicted service life using each developed model in this section was calculated.
Table 25 shows estimated service life for different values of initial retroreflectivity, considering
initial retroreflectivity and age of marking as independent variables (approach one). It can be
observed in Table 26 estimated service life also considering traffic volume as an independent
variable (approach two).
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
White Markings (Linear Regression)
Actual Data
Ro = 450 mcd/m2/lux and AADT =
350 veh/day
Ro = 450 mcd/m2/lux and AADT =
7000 veh/day
Ro = 450 mcd/m2/lux and AADT =
18000 veh/day
Ro = 600 mcd/m2/lux and AADT =
350 veh/day
Ro = 600 mcd/m2/lux and AADT =
7000 veh/day
Ro = 600 mcd/m2/lux and AADT =
18000 veh/day
Ro = 750 mcd/m2/lux and AADT =
350 veh/day
Ro = 750 mcd/m2/lux and AADT =
7000 veh/day
72
Table 25 ? Predicted Service Life: Initial Retroreflectivity and Age as Independent Variables
Model Color
Predicted
Service Life
(months)
Considered
Initial
Retroreflectivity
(mcd/m2/lux)
Minimum
Retroreflectivity
Threshold
(mcd/m2/lux)
White
Linear 81
450
150
Power 134
Quadratic 54
Exponential 110
Linear 87
550 Power 144 Quadratic 65
Exponential 130
Linear 94
650 Power 154 Quadratic 74
Exponential 147
Linear 101
750 Power 164 Quadratic 83
Exponential 161
Yellow
Linear 59
350
100
Power 85
Quadratic 51
Exponential 74
Linear 61
400 Power 88 Quadratic 58
Exponential 82
Linear 62
450 Power 92 Quadratic 64
Exponential 89
Linear 63
500 Power 95 Quadratic 70
Exponential 95
73
Table 26 ? Predicted Service Life: Initial Retroreflectivity, Age, and AADT as Independent Variables
Color Model
Predicted
Service
Life
(months)
Considered
AADT (veh/day)
Considered
Initial
Retroreflectivity
(mcd/m2/lux)
Minimum
Retroreflectivity
Threshold
(mcd/m2/lux)
White Linear
86 350
450
150
79 7000
68 18000
93 350
600 86 7000
75 18000
99 350
750 93 7000
82 18000
Yellow Linear
60 350
350
100
57 7000
53 18000
61 350
425 58 7000
54 18000
61 350
500 59 7000
54 18000
It could be observed in the literature that the service life for white thermoplastic markings
was in a range between 22.6 and 102 months. It is important to notice that the maximum service
life was a function of an initial retroreflectivity equal to 375 mcd/m2/lux. Table 25 shows that the
maximum service life for white markings is 166 months, but it considers an initial
retroreflectivity of 750 mcd/m2/lux, higher than the values found in the literature.
For yellow thermoplastic markings, service life in the literature was in a range between
24.7 and 103 months. The maximum service life considered an initial retroreflectivity equal to
135 mcd/m2/lux. Table 25 shows that the maximum service life for yellow markings is 96
months, but it considers an initial retroreflectivity of 500 mcd/m2/lux, higher than the values
74
found in the literature. Therefore, values shown on Table 25 are considered consistent with what
was found in the literature. Some high estimation for service life may be due to the high initial
retroreflectivity values from actual observations.
It can be observed in Table 26 the estimated service life values for different initial
retroreflectivity and AADT values, considering three independent variables (approach two).
Similar conclusions from service life estimated by approach one were found.
4.5. Summary of Chapter Four
Chapter Four presented the results regarding the application of methodology described in
Chapter Three. The analysis to verify if measures of markings met specifications showed that the
most consistent property was chromaticity, with 94.04% of total measurements passing
minimum required values. Thickness and luminance measurements presented 79.53% and
75.77%, respectively, of total observations meeting specifications. The property which presented
fewer measurements passing minimum required values was retroreflectivity, with 69.40%
observations meeting specifications.
The statistical analysis of observations in the 40 projects of the 2007 database showed
that the most consistent property was luminance, with the lowest coefficients of variation.
Thickness was found to be the less consistent one, because some standard deviations are almost
half of, or more than the mean value, and coefficient of variation could be as high as 55.13%.
Retroreflectivity also had very dispersed observations, with a high coefficient of variation of
43.44% among the four color/class categories, and also very different means when contrasting all
classes and types.
75
Modeling of retroreflectivity over time was performed and all observations of the 15
projects that had data for four years allowed the development of 76 curves for solid white
markings, 17 for broken white, 67 for solid yellow and 32 for broken yellow markings. Four
models were developed, by color, based on the observations of these 15 projects. Considering
initial retroreflectivity and age of marking as independent variables, for white markings the R2
values were 0.325 for linear, 0.335 for power, 0.181 for quadratic, and 0.261 for exponential
models; for yellow markings, the R2 values were 0.465 for linear, 0.480 for power, 0.320 for
quadratic, and 0.440 for exponential models. Considering also AADT as an independent
variable, the R2 values were 0.398 for white and 0.479 for yellow models, both linear.
The benefit/cost method analyzed in this Chapter did not provide good results, especially
because the service life, determined by when retroreflectivity reaches the minimum threshold
value of 150 mcd/m2/lux for white markings and 100 mcd/m2/lux for yellow markings, was
much higher than the observed values for markings in literature and, therefore, not reliable.
76
Chapter Five
Conclusions and Recommendations
5.1. Conclusions
The documentation of 2007 ALDOT Special Provisions changes showed that no
significant modifications related to specifications were observed; text modifications constituted
the changes among different Special Provisions. An examination of the 2007 database containing
7,840 observations for 40 projects in Alabama to determine whether thickness, retroreflectivity,
luminance, and color complied with ALDOT specifications found that 79.53% of the
observations complied with thickness specifications, 69.40% were according to retroreflectivity
standards, 75.77% conformed to luminance specifications, and 94.03% were according to color
standards.
A statistical analysis was performed for all observations among the 40 projects, based on
mean, standard deviation, and coefficient of variation, by color and type (class) of markings for
thickness, retroreflectivity, and luminance. Results showed that luminance measures were
consistent, with highest coefficient of variation of 18.33%. Thickness values were not very
consistent within each color/type group, with a coefficient of variation as high as 55.13%, but
means between groups were similar, varying from 0.065 to 0.117 in. Retroreflectivity, however,
presented huge variations within groups, with standard deviation as great as 141.383 mcd/m2/lux,
and between groups, with mean varying from 202 to 496 mcd/m2/lux.
77
Retroreflectivity modeling was also executed in this thesis. Joining retroreflectivity data
from the 2007 database and subsequent ALDOT data on retroreflectivity from 2008 to 2010, it
was possible to create models of retroreflectivity over time. Only 15 projects had measurements
of retroreflectivity for the same locations from 2007, 2008, 2009, and 2010 databases, which
represented 76 observations for solid white markings, 17 for broken white, 67 for solid yellow,
and 32 for broken yellow markings. Since only four years of data exist, the created curves had to
be extrapolated to reach minimum retroreflectivity values (until the end of service life). In order
to accomplish this, the most relevant models in the literature were applied to the data to evaluate
model fit. The Thamizharasan et al. and Sitzabee et al. were the models that best represented
actual data from ALDOT projects. To determine best-fitting models, comparisons of area under
curve ratio, average model error and average percent error between model curve and actual curve
were performed.
When extrapolating actual data based on the best-fitting models in the literature, it was
found that service life was about twice the common values for thermoplastic materials found in
the literature, and sometimes higher than typical pavement service life, being as high as 250
months (almost 21 years). Cost data was obtained from and organized based on the Tabulation of
Bids, from ALDOT. However, without retroreflectivity curves that yielded realistic service lives,
it was not possible to calculate benefits based on this model. In addition, benefit/cost
relationships given by this method did not provide meaningful and applicable results for the
observations of the 15 projects in Alabama, since there was only one type of material,
thermoplastic Class 2, and this benefit/cost analysis is most appropriate when comparing
different materials.
78
New models needed to be developed to represent actual points from projects in Alabama
more realistically. The modeling of retroreflectivity over time considered retroreflectivity as the
dependent variable; age and initial retroreflectivity were considered as the independent variables
for the first modeling approach and traffic volume was also considered for a second modeling
approach. Models developed when considering age and initial retroreflectivity as independent
variables were linear, power, quadratic, and exponential, for each color. For white markings,
there were 63 different locations and for yellow markings, 42. White markings had R2 values
equal to: 0.325 (linear), 0.335 (power), 0.181 (quadratic), and 0.261 (exponential); yellow
markings had R2 values equal to: 0.465 (linear), 0.480 (power), 0.320 (quadratic), and 0.440
(exponential). For the consideration of AADT as an additional independent variable, linear
models were developed for the same locations by color and R2 values were 0.398 for white
markings and 0.479 for yellow markings. In the literature, R2 values from models for white
markings vary from 0.007 to 0.600 and from 0.003 to 0.600 to yellow markings; the R2 values of
the models developed in this study are higher than most models in the literature.
5.2. Recommendations
The linear model considering age of marking, initial retroreflectivity, and traffic volume
as independent variables had the highest R2 value among all predicted models for white
markings. For yellow markings, the power model considering age of marking and initial
retroreflectivity as independent variables and the linear model considering traffic volume as an
additional independent variable, yielded R2 values equal to 0.480. The linear model considering
the three independent variables to estimate retroreflectivity over time was found to be the most
adequate when representing Alabama data because of the simplicity in its equation, the capacity
79
to well-represent retroreflectivity for a time equal to zero, and the highest R2 values among
predicted models.
5.3. Recommendations for Subsequent Studies
Limitations to the present study can be noticed throughout this thesis. From all 40
projects applied in 2007 in Alabama, only 15 had retroreflectivity data, which were used to
develop models. In addition, historical retroreflectivity measurements were made only from 2007
to 2010. This means that models can be improved if data are provided for new locations and
measurements continue for the existing sites. New sites can also be added to increase sample size
and provide more accurate results.
The wide range of initial retroreflectivity values for different observations of the 15
projects was something that also deserves further investigation. A detailed analysis of the
equipment used to measure each observation and development of adjustment factors between
measures from one retroreflectometer to another can be ways to explain potential source of
variability.
Another point to be considered is which variables influence retroreflectivity behavior. In
this thesis, age of marking, initial retroreflectivity, and traffic volume were the considered
independent variables. However, additional variables might be analyzed to improve models. It
was observed in the literature that white edgeline markings generally had longer predicted
service lives than all other pavement marking types and the shortest mean predicted service life
was most often computed for the yellow centerline markings, showing that position of marking
on pavement may be considered when predicting retroreflectivity. In addition, it was observed in
the literature that there was considerable variability in the predicted service life across different
80
engineering divisions, which shows the importance of geographic location when developing
models to predict service life. The impact of different vehicle types was also mentioned in the
literature, and it was found that roadways with higher truck traffic volumes decrease pavement
markings service life due to abrasion between the tires and the markings; therefore, vehicle type
might also be an independent variable to predict retroreflectivity. A benefit/cost analysis is
useful, especially if information of other types of markings is available; comparison between
different materials to determine the most appropriate to Alabama conditions can be interesting.
Pay adjustment factors procedure in the 2008 ALDOT Standard Specifications for
Highway Construction does not provide consistent justification on how the percentage that the
stripe will be paid for was established. The stripe is accepted without a price adjustment for
retroreflectivity 85% or greater than the minimum required value; for retroreflectivity less than
85% and greater than 50% the target value, the stripe is paid for at a percentage equal to the
percentage determined from the measurements; for retroreflectivity less than 50%, the stripe
needs to be removed. This procedure could be refined; therefore, the development of pay
adjustment factors may also be another suggestion for future studies. This analysis can be based
on the data that did not meet minimum requirements as well as those that did in the 2007
ALDOT database, in addition to a study considering benefit/cost models.
81
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85
Appendix A
Project STPSA-0185(500): Pictures
86
87
88
89
Appendix B
List of Mileposts by Project
90
Project MP
99-302-391-101-701
Solid White Broken White Solid Yellow Broken Yellow
25.7 - 25.7
26.2 - 26.2
27 - 27
28 - 28
99-302-437-171-706 53 53 53
99-303-595-003-709 244 - 244 244 245 - 245 245
99-305-632-069-702
157.1 - - 157.1
158 - 158 -
159 - 159 159
160 - 160 -
161 - 161 161
162.1 - 162.1 -
163.1 - 163.1 -
164 - 164 -
165 - 165 -
166 - 166 -
167 - 167 -
99-307-164-167-701
1 - - 1
2 - 2 -
3 - - 3
4 - - 4
5 - - 5
6 - 6 -
99-307-346-010-701 216 216 216 - 217 - 217 217
91
EB-0016(505)
60 - 60 -
61 - 61 61
62 - 62 -
63 - 63 63
64 - 64 -
65 - 65 65
66 - 66 66
67 - 67 67
68 - - 68
69 - 69 69
70 - 70 70
71 - 71 -
72 - 72 -
73 - 73 -
74 - 74 -
75 - - 75
76 - - 76
EB-0035(506)
- 23 23 23
- 24 24 24
- 25 25 -
EB-0074(513) 76 76 76 - 77 77 77 77
NHF-STPSAF-
0053(525)
32 32 32 -
33 33 33 -
34 34 34 -
35 35 35 -
36 36 36 -
STPSA-0001(529)
267 267 267 -
268 268 268 -
269 269 269 -
270 270 270 -
271 271 271 -
92
STPSA-0021(515)
98 - 98 -
99 - 99 99
100 - 100 -
101 - - 101
102 - 102 102
103 - 103 -
104 - 104 -
105 - 105 -
106 - - -
107 - 107 -
108 - 108 108
STPSA-0079(505)
- - 72 -
- - 73 -
- - - 74
- - - 75
- - 76 -
- - 77 -
- - - 78
- - 79 -
- - 80 -
- - - 81
STPSA-0089(500)
1 - 1 -
2 - 2 -
3 - - 3
STPSA-0185(500)
8 - - -
9 - - -
10 - - -
11 - - -
12 - - -
13 - - -
14 - - -
93
Appendix C
Retroreflectivity Modeling for Yellow Markings: Initial Retroreflectivity and Age as
Independent Variables
94
0
100
200
300
400
500
600
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings (Linear Regression)
Linear Estimates
Actual Data
0
100
200
300
400
500
600
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings (Power Regression)
Power Estimates
Actual Data
95
0
100
200
300
400
500
600
0.00 10.00 20.00 30.00 40.00 50.00
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings (Quadratic Regression)
Quadratic Estimates
Actual Data
0
100
200
300
400
500
600
0.00 10.00 20.00 30.00 40.00 50.00
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings (Exponential Regression)
Exponential Estimates
Actual Data
96
0.00
100.00
200.00
300.00
400.00
500.00
600.00
0.00 10.00 20.00 30.00 40.00 50.00
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings Linear Regression
Actual Data
Ro=350mcd/m2/lux
Ro=400mcd/m2/lux
Ro=450mcd/m2/lux
Ro=500mcd/m2/lux
0.00
100.00
200.00
300.00
400.00
500.00
600.00
0.00 10.00 20.00 30.00 40.00 50.00
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings Power Regression
Actual Data
Ro=350mcd/m2/lux
Ro=400mcd/m2/lux
Ro=450mcd/m2/lux
Ro=500mcd/m2/lux
97
0.00
100.00
200.00
300.00
400.00
500.00
600.00
0.00 10.00 20.00 30.00 40.00 50.00
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings Quadratic Regression
Actual Data
Ro=350mcd/m2/lux
Ro=400mcd/m2/lux
Ro=450mcd/m2/lux
Ro=500mcd/m2/lux
0.00
100.00
200.00
300.00
400.00
500.00
600.00
0.00 10.00 20.00 30.00 40.00 50.00
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings Exponential Regression
Actual Data
Ro=350mcd/m2/lux
Ro=400mcd/m2/lux
Ro=450mcd/m2/lux
Ro=500mcd/m2/lux
98
Appendix D
Retroreflectivity Modeling for Yellow Markings: Initial Retroreflectivity, Age, and Traffic
Volume as Independent Variables
99
0.00
100.00
200.00
300.00
400.00
500.00
600.00
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings (Linear Regression)
Linear Estimates
Actual Data
0
100
200
300
400
500
600
0 10 20 30 40 50
Re
tro
ref
lec
tiv
ity
(m
cd
/m
2/
lux
)
Age (months)
Yellow Markings (Linear Regression)
Actual Data
Ro = 450 mcd/m2/lux and AADT =
350 veh/day
Ro = 450 mcd/m2/lux and AADT =
7000 veh/day
Ro = 450 mcd/m2/lux and AADT =
18000 veh/day
Ro = 600 mcd/m2/lux and AADT =
350 veh/day
Ro = 600 mcd/m2/lux and AADT =
7000 veh/day
Ro = 600 mcd/m2/lux and AADT =
18000 veh/day
Ro = 750 mcd/m2/lux and AADT =
350 veh/day