Degradation Modeling of Polyurea Pavement Markings

Introduction

State Departments of Transportation (DOTs) across the nation are engaged in a perpetual cycle of removal and replacement of pavement markings. Pavement markings, specifically the retroreflectivity (R_L) of the markings, are important in keeping the safety of public road system at acceptable performance levels (Sasidharan, Vishesh, & Donnell, 2009). In 1993, the U.S. Congress directed the U.S. Secretary of Transportation to revise the Manual of Uniform Traffic Control Devices (MUTCD) to include minimum standards for pavement marking retroreflectivity (U.S. Congress, 1993). In April 2010, these minimum standards were proposed for adoption (Federal Highway Administration, 2010). To meet and keep these minimum standards, a proper management plan must be in place by which this cycle of removal and replacement is made most effective; both cost-wise and safety-wise. The backbone of many such management plans are performance models, which are used to predict the current state and life cycle of pavement markings.

Degradation models are the basis of performance modeling and critical to predicting the life cycles of various types of pavement marking retroreflectivity levels (Rasdorf, Hummer, Harris, & Sitzabee, 2009). Knowing when a particular marking material is likely to fall below the proposed minimum accepted retroreflectivity standard will allow DOTs to create a plan to replace that material at the proper time. Without degradation models, it is simply a subjective approach as to when a given marking needs to be replaced. The purpose of this article is to present the results of Ordinary Least Square degradation modeling of polyurea pavement markings. The resulting model provides additional tools for asset managers and pavement marking managers to use in their development of pavement marking management plans and allocation of limited resources as well as manpower. Keep in mind anyone who is managing pavement markings with an interest in keeping the cost down and extending the life of the material is an asset manager and can benefit from implementing performance-based modeling into their marking strategies. According to the Federal Highway Administration, an asset manager is anyone who uses a strategic approach to manage a physical infrastructure asset using cost-effective solutions based on sound engineering and business practices (Cambridge Systematics Inc., 2002). In this case, an asset manager is anyone who would implement a performance-based model to manage pavement marking infrastructure systems.

Objective and Scope

Degradation models currently exist for a variety of pavement marking materials to include waterborne paint, epoxy, and thermoplastic pavement markings, which make up the majority of pavement markings nationwide; however, these degradation models vary based on marking type, geographic location, and marking manufacturer, to name a few (Sarasua, Clark, & Davis, 2003; Sitzabee, Hummer, & Rasdorf, 2009). Polyurea is a common pavement marking material; yet it does not currently have acceptable degradation models that can accurately predict its life cycle. As a result, this research focuses on the use of polyurea data collected throughout North Carolina.

Polyurea is the fourth most common material used in North Carolina, after waterborne paint, thermoplastics, and epoxy (Sitzabee et al., 2009). This research considers data collected in North Carolina over a period of 5 years on one of the largest state-maintained road systems. Specifically, this research formulates a service life degradation model for polyurea by considering the following variables:

Background

The underlying reason for constructing degradation models is to have better understanding of material performance when developing asset management plans and allocating limited resources as well as manpower. Each year, DOTs spend millions of dollars in pavement marking expenditures and due to proposed national standards, expenditures are with an expected increase of 64 million US dollars, as a result of the proposed national standards (Hawkins, Lupes, Schertz, Satterfield, & Carlson, 2010). Not only is the cost of marking materials included in that price, but thousands of man-hours must also be paid in the execution of management plans; and this material cost does not include the intangible cost of worker safety. DOTs also consider the potential for worker injury or equipment destruction when considering the full cost of pavement marking application and maintenance. With a better understanding of the life cycle of a given marking material, both monetary and intangible costs can be minimized while maximizing retroreflectivity performance and effectively utilizing limited resources.

Previous Research

Over 83% of pavement markings in use today on the nation’s roadways are comprised of paints and thermoplastics (Migletz & Graham, 2002). DOTs typically apply paint to secondary roads with a low traffic volume while thermoplastics are used mainly on primary roads. However, polyurea is also used along with several other types of markings, such as preformed plastics, epoxy, and polyester for high volume roads. Polyurea is significantly more expensive than thermoplastic or paint and cures faster; therefore it is typically used in specific applications such as concrete bridge decks (NCDOT, 2006).

Research on pavement marking retroreflectivity has been ongoing since the mid-1980s. Early studies by Lee et al. (1999) demonstrate that markings degrade in a linear fashion, but the resulting models possessed a poor fit (Sitzabee et al., 2009). While the majority of literature reviewed was based on linear regression modeling, other methods were used as well such as logarithmic and Linear Mixed Effects Modeling (LMEM; Abboud & Bowman, 2002; Hummer, Rasdorf, & Zhang, 2011). The simplicity of linear regression is what makes it a proven modeling technique; however, linear regression may not always produce the most predictive model.

Table 1 highlights studies that date back to 1999 and represent a significant sample of a large body of knowledge on modeling pavement marking retroreflectivity degradation. Each of these studies, representing key research for the last decade, evaluates retroreflectivity degradation and identifies key variables, which impact and significantly describe R_L performance over time. These studies provide the foundation for the methodology used in this study of polyurea pavement markings.

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Table 1.

Summary of Literature.

Year	Authors	Model type	R 2	Marking material
1999	Lee et al.	Linear	.14	Thermoplastic
2001	Migletz et al.	Linear	N/A	Durable
2002	Abboud and Bowman	Logarithmic	.32
2003	Sarasua et al.	Complex curve with a Linear region	N/A	Thermoplastics
2004	Kopf	Linear	N/A	Paint, Thermo
2007	Fitch	Logarithmic	.53-.86	Polyurea
2009	Sitzabee et al.	Linear	.60	Thermoplastic
2011	Hummer et al.	Mixed effects	.68	Paint

Migletz, Graham, Harwood, and Bauer (2001) compiled a pavement marking synthesis, which summarized a great deal of the literature on pavement markings. However, very little performance modeling had been accomplished by then. Current literature has focused more on performance modeling and shows several factors influence pavement marking retroreflectivity values and degradation rates. Factors such as age, material type, color, surface type, snow plowing, and annual average daily traffic (AADT) have all been considered in modeling pavement marking performance.

Marking age is the predominate factor in pavement marking degradation with most studies showing retroreflectivity linearly associated with age (Lee et al., 1999; Sarasua, 2003; Bahar, Masiliah, Erwin, & Tan, 2004; Kopf, 2004). Other studies proposed using nonlinear modeling such as an exponential or logarithmic transformation to estimate retroreflectivity according to age of pavement marking after installation (Andrady, 1997; Perrin, Martin, & Hansen, 2001). For instance, Karwa and Donnell (2011) proposed a nonlinear model to estimate retroreflectivity according to initial retroreflectivity, the age of the markings, traffic flow, pavement marking type, and route location information. Hummer et al. (2011) showed the usefulness of a Linear Mixed Effects Model for retroreflectivity. Craig, Sitzabee, Rasdorf, and Hummer (2007) showed that white and yellow markings achieve different levels of retroreflectivity with white generally measuring higher than yellow markings. Additionally, Craig et al. (2007) proved that line location laterally across the road segment was a key variable that significantly impacts degradation. Traffic volume has been a controversial factor with some studies showing that AADT is a factor while others show it is not. For example, Sitzabee et al. (2009) showed that traffic volumes (AADT) affect markings while Abboud and Bowman (2002) suggested that vehicle exposure (time × AADT) replaces time or traffic volume alone. With retroreflectivity depending on glass beads (Zhang & Wu, 2006), it would seem that more studies would have evaluated the impact of beads on degradation.

Need for Performance Models

With the nationwide cost of pavement markings exceeding two billion dollars annually (Hawkins et al., 2010), it has become necessary to build performance models for each pavement-marking material. An asset manager, who, in this case, is anyone who manages pavement markings, can use performance models to create more effective asset management programs, which could easily reduce annual budgets. Furthermore, with federal minimum standards for retroreflectivity pending (FHWA, 2009), it is even more critical that DOTs have better asset management tools to assist in managing pavement-marking programs. Knowing when a particular pavement marking is going to fail is critical to optimizing DOT pavement-marking budgets. Without performance models, decisions on when to replace a given marking is based on best guess and rules of thumb, which are not scientific and do not maximize service lives of pavement markings. This research specifically benefits anyone who plans, programs, schedules, or executes pavement-marking operations. These can include all levels of transportation asset managers such as district engineers; federal, state, and local maintenance crews; and public administrators.

Data Collection

The retroreflectivity data for this study were collected over a 5-year period for approximately 30,000 miles of roads (multilane highways to two-lane roads) at initial installation and then again at 6, 12, 24, 36, 48, and 60 months after installation via a modified Laserlux mobile retroreflectometer (model LLR5) mounted on a Chevrolet Suburban. The initial R_L values were measured within 30 days of installation, but the researchers did not possess data that indicate the installation dates of the pavement markings. Mobile retroreflectometers are especially effective for collecting large volumes of data because they can be used at highway speeds. This allows the technician to remain safely inside the vehicle and collect a large amount of data in a short period of time. For a data collection effort of this magnitude, a handheld retroreflectometer simply would be too time-consuming to be practical.

The LLR5 uses the standard 30-m geometry as required by ASTM E 1710-97 and averages the R_L readings at every 10th of a mile increments (ASTM, 2005). As a result of the equipment averaging the reading every 10th of a mile, the researchers were not able to conduct repeated measures from year to year to determine a temporal correlation. The units were recorded in mcd/m²/lux by an onboard computer to eliminate user error when entering data. The resulting data set contained 1,142 entries.

Vehicle-mounted retroreflectometers are safe and accurate, but they are not without error. To minimize this error, a rigorous calibration process was adhered to for the duration of the data collection. Prior to every trip, the unit was calibrated against a known test bed of pavement markings at the NCDOT maintenance facility. This test bed R_L value was established with a handheld LTL2000 retroreflectometer. Each time the LLR5 was calibrated against the test bed, adjustments were made to account for suspension changes, tire pressure, and ambient light. Additionally, the LTL2000 was taken into the field on each trip and used to verify the calibration of the mobile unit each time any conditions changed in the field such as amount of daylight or weather conditions.

The data used in this study were collected by an independent contractor and originally intended for quality assurance purposes. Since regression analysis wasn’t the primary focus of the data collection, there were some limitations to the analysis of these data. However, after extensive data mining, the resulting reduced data set was found to be of high quality for use in linear modeling. The data mining process largely consisted of separating polyurea data from a larger data set that included all types of markings in North Carolina. Additionally, the researchers removed extraneous information from the database such as the names of the technicians collecting the data, street names, and phone number, to name a few. The most significant removal of information was the deletion of retroreflectivity values equal to zero mcd/m²/lux. These values represent a data collection error, which was confirmed with the data collectors. Even though the resulting data set was significantly smaller than the original, the information contained therein could immediately be used for modeling purposes. Many possible variables were contained in the data set, but only variables meeting the customary 0.05 significance level were included in a least-squares analysis.

Method

This study used the method of Ordinary Least Squares (OLS) or linear least squares to estimate the unknown parameters in the model. The method of OLS aims to predict a response variable, y, from a set of explanatory variables, x. OLS accomplishes this by minimizing the Sum of Squared Errors (SSE), which is the sum of the squared residuals (the difference between the ys and the predicted values, Ŷs). OLS investigates for a mathematical association and not necessarily a cause and effect relationship. The overall model that OLS develops is statistically accessed via an F-test that tests for any statistical significance between y and any of the x predictors. The level of significance for this test is 0.05, the customary Type I error for hypothesis tests. For the OLS model to have statistical inferential validity, the model residuals must be normally distributed, display homoscedasticity, and be serially uncorrelated. These assumptions are checked and tested for with respect to the OLS model presented in this article.

Specifically this section presents the development of the OLS regression model for predicting the retroreflectivity level (R_L) value of polyurea. Initially, attempts were made to have R_L as the dependent variable; however, the customary OLS assumptions of normality and homoscedasticity of model residuals did not hold for such a model. Figure 1 illustrates this heteroscedasticity (nonconstant variance) of model residuals. These residuals resulted from a preliminary OLS model of regressing R_L onto AADT (average number of vehicles per day on a given roadway), bead type (standard bead or highly reflective elements), time (in months from 6 months to 60 months), initial retroreflectivity level (IRL), and lateral line location (center or edge).

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Figure 1.

Scatterplot of model residuals (R_L Residual) by (R_L Predicted).

To partially remedy this heteroscedasticity issue the dependent variable was changed to the ratio of R_L to IRL. Second, individual regression models were developed for each range of AADT before incorporating all the models into one macro OLS model. It was discovered that besides R_L causing issues with heteroscedasticity of model residuals, the average amount of vehicles traveling on a road also contributed to this nonconstancy of variance. The type of variables and the magnitude effect of those variables greatly change depending on the AADT range. This latter finding is discussed in more detail in the conclusion section.

Analysis and Results

The modeling database consisted of 1,142 points of which only one point was excluded. This point was removed because of an inordinate decline in retroreflectivity from an IRL of 999 to a R_L of 408 in 6 months. This calculated decline of approximately 60% in a relatively short span of time indicated a problem with marking application and not with polyurea itself. From this modeling database of 1,141 points, the dependent variable of R_L to IRL was calculated. AADT was also broken into 10 traffic volume categories (average number of vehicles passing on that roadway a day) based on the similarities of independent variables that proved predictive for that range. By allowing the OLS model to incorporate certain ranges of AADT, the model would look to only those data points within that particular range to model the ratio of R_L to IRL for that AADT range.

For all AADT ranges, the independent variables presented proved very statistically significant. With the exception of one independent variable (and its p value was .0003), all the explanatory variables had a p value < .0001. (Note: even the intercepts proved to be significant with the smallest p value being .002.) To verify the modeling building process, all-subsets stepwise regression analysis was conducted post hoc and no other simple statistical trends were discovered to override what is presented. All analysis to include linear regressions was performed using the JMP^® statistical software.

Before listing the explanatory variables for each AADT range, it is noted that the decay rate of the polyurea proved to be highly predictive for nearly all of the ranges (this variable is called ‘Time Adj Decay’ in Table 2 with an associated p value of .0001 or lower). The decay rate of R_L does not follow a linear trend; in fact it appears more of an exponential decay and changes depending on bead type. Figure 2 highlights these decay rates. Equation (1) shows the mathematical equation for the decay rate for standard beads, while Equation (2) shows the mathematical equation for the highly reflective beads. Both equations are only applicable for up to 60 months, to coincide with the time range of the database. Both equations are nonlinear in nature and Microsoft’s Solver^® was used to estimate the decay parameters using the method of maximum likelihood.

R L Standard Bead = 486 . 3 − 139 . 9 * t i m e 0 . 2

R L Highly Reflective Bead = 836 . 5 − 191 . 2 * t i m e 0 . 25

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Table 2.

Predictive Explanatory Variables for Each Range of AADT.

AADT band (Vehicles per day)	Variable name	Parameter estimate	p value
<2,000	Intercept	−176.21	0.0020
<2,000	Initial RL	0.68	<0.0001
<2,000	Time adj decay	0.83	<0.0001
2,000-5,000	Intercept	162.64	<0.0001
2,000-5,000	Center line	−123.22	<0.0001
2,000-5,000	Time adj decay	0.60	<0.0001
5,800-7,800	Intercept	−718.74	<0.0001
5,800-7,800	Initial RL	0.63	<0.0001
5,800-7,800	Time adj decay	1.66	<0.0001
5,800-7,800	Standard bead	298.85	<0.0001
8,200-9,800	Intercept	986.06	<0.0001
8,200-9,800	Time (months)	−2.05	<0.0001
8,200-9,800	AADT	−0.078	0.0003
10,000-11,000	Intercept	−979.89	<0.0001
10,000-11,000	Time adj decay	2.49	<0.0001
10,000-11,000	Standard bead	408.03	<0.0001
10,000-11,000	Initial RL	0.36	<0.0001
14,000-29,000	Intercept	−664.18	<0.0001
14,000-29,000	Time adj decay	1.78	<0.0001
14,000-29,000	Standard bead	352.49	<0.0001
14,000-29,000	Initial RL	0.24	<0.0001
30,000-38,000	Intercept	−1602.78	<0.0001
30,000-38,000	Initial RL	0.62	<0.0001
30,000-38,000	Time adj decay	1.56	<0.0001
30,000-38,000	AADT	0.027	<0.0001
30,000-38,000	Standard bead	283.15	<0.0001
30,000-38,000	Snow plowed	67.94	<0.0001
45,000-79,000	Intercept	−311.99	<0.0001
45,000-79,000	Initial RL	0.54	<0.0001
45,000-79,000	Time adj decay	0.93	<0.0001
45,000-79,000	Standard bead	178.94	<0.0001
83,500-89,500	Intercept	−991.75	<0.0001
83,500-89,500	Time adj decay	1.94	<0.0001
83,500-89,500	Initial RL	0.65	<0.0001
100.5K-116K	Intercept	−714.49	<0.0001
100.5K-116K	Time adj decay	1.49	<0.0001
100.5K-116K	Standard bead	409.47	<0.0001
100.5K-116K	Initial RL	0.58	<0.0001

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Figure 2.

Retroreflectivity level (R_L) decay rates for polyurea.

Table 2 next presents the predictive explanatory variables for each range of AADT in the model database. The variables listed in Table 2 are defined as follows: Initial R_L(mcd/m²/lux) is the initial retroreflectivity level at time of application, while Time Adj Decay is the decay function described in either Equations (1) or (2) depending on which bead (standard bead or highly reflective) is being used for R_L prediction. Center Line, Standard Bead, and Snow Plowed represent dummy variables (dichotomous variables) wherein these explanatory variables assume a “1” if the prediction is for either middle of the road, standard bead, or snow plowed application, and zero otherwise. AADT represents the annual average daily traffic for that particular AADT range (see Table 2 for the applicable range).

With respect to interpreting the estimated OLS parameter estimates for each AADT band, none of them are directly interpretable except for IRL. This is because the decay function presented in Equations (1) or (2) depends on bead type used for that roadway. That is, one cannot hold the explanatory variable Standard Bead constant while varying the decay function of time (the variable Time Adj Decay in Table 2) and vice versa because both of these variables are related via the nonlinear functions in Equations (1) and (2). In addition, the intercept estimate also is changing, which in turn makes any explanatory variable that adjusts the baseline, that is, Snowplowed, not interpretable. Since IRL is never involved with changing the baseline or involved with Equations (1) or (2) and is a continuous measure, it is the only explanatory variable whose parameter estimate is directly interpretable. Those parameter estimates are all positive, which is in the direction one would expect.

The main utility of the parameter estimates in Table 2 comes from knowing which values to use, within the applicable AADT range, and then applying them to the macro OLS model to get an estimated R_L. For the most part, the parameter estimates in Table 2 modify the decay functions as shown in Equations (1) and (2) by altering the rate of degradation or the horizontal asymptote. But more importantly than that, the parameter estimates show the great variability between them as one looks at the AADT ranges. In other words, the fact the same explanatory variables are not appearing in each AADT as well as having the same magnitude sign illustrates aflux in variability caused by AADT. For had AADT not played a significant role in model building, one would expect the parameter estimates to be reasonably close to one another from one AADT block to another. As an example of this variability, the intercept estimates range from −1602.28 to 986.6, and the parameter estimates for the decay functions (the Time Adj. Decay variable in Table 2) varies from 0.6 to 2.49, which for a nonlinear function represents a wide range.

In terms of model application, one would first find the applicable AADT range within Table 2 and use the associated parameter estimates from within that interval to arrive at the initial predictive response of R_LAADT. After which, one would then apply Equation (3)

R LADDT * 0 . 87 + Initial R L * 0 . 09

to arrive at the OLS estimate of R_L. Equation (3) represents the overall macro OLS model and has an R² value of .64. This model passes the residual assumptions of normality via the Shapiro-Wilk test and homoscedasticity via the Breusch-Pagan test. Both pass at the customary 0.05 level of significance. A possible negative aspect of using this model is that one would need to know the Initial R_L. Given there are usual minimum R_L standards required for a contractor or worker to adhere to when initially applying the polyurea, this minimum could be used as the IRL.

With respect to an application of the OLS model, suppose one wished to predict the R_L of a road painted with polyurea (standard bead) 2 years into the future that has an AADT of 50,000 and an initial IRL of 400. One would then arrive at the following RL_AADT estimate using Table 2: 289.54 = −311.99 + 0.54 * 400 + 0.93 * 222.14 + 178.94, where 222.14 is obtained from the decay function shown in Equation (1) for standard bead and time equal to 24 months. Plugging 289.54 into Equation (3) along with an Initial R_L of 400, one arrives at the R_L estimate of 287.9.

This example illustrates two key points from the analysis: One, a fallback estimate of R_L via the decay functions shown in Figure 1 is given for roadways whose AADT does not appear within the intervals modeled (can be somewhat considered the unconditional R_L estimate); using the decay functions themselves results in an R² value of .45 for predicting R_L. Second, AADT plays a major role in determining R_L in the sense that for different ranges some explanatory variables appear predictive while others do not. And even for the key drivers of Initial R_L, bead type, and decay rate over time, their effects change from range to range (as mentioned earlier). The analysis suggests that AADT may or may not be deemed predictive for other studies depending on the AADT range being considered for a study on a micro scale. For larger or macro studies, AADT appears to be a major driver in determining R_L. Consistent with the literature, this study shows that AADT is significant and pavement managers need to consider the effects of AADT on pavement markings, but is often hidden in the function of time because of the selective application of material by pavement marking managers.

Lastly, both the Mean Absolute Percentage Error (MAPE) and the Median Absolute Percentage Error (MdAPE) were used to descriptively determine the accuracy of the OLS model developed and shown in Equation (3). All 1,141 data points were used to determine these descriptive measures. Overall, the MAPE and MdAPE scores consisted of 17% and 12%, respectively. Considering no other polyurea regression models were found in the literature, these numbers now serve as a baseline for others to compare.

Conclusion

With no real model for polyurea presented in the reviewed literature, the results of this study are significant and can be considered the baseline for future research for this material. Furthermore, this study proved unique by highlighting that the physical characteristics of polyurea and its decay rate are different from paint and thermoplastic and that the material can be successfully modeled as an exponential function. Recall that the majority of the previous studies presented in this article show that paint and thermoplastic pavement markings degrade in a linear fashion.

A significant finding of this study is the impact of AADT on pavement marking degradation. We clarify why AADT proves significant in some studies and not significant in others. The proposed models reflect what the literature has been stating and show the inconsistency in AADT, which does affect degradation. However, the lack of consistency in the literature is more likely a result of management application policies and not the actual impact of traffic volume. For example, some studies show AADT as predictive and others have not. If a study only looked at a narrow band of AADT it is very possible AADT didn’t show up as being predictive, since the key variables within that range didn’t change much. However, as the AADT range was further expanded to perhaps “encroach” on another band that we identified then some key variables would suddenly appear while others dropped out. This shifting in and out of predictor variables reflects AADT being a conditional variable and hence key driver in determining R_L. Future studies need to consider the selective application of materials when determining the impact of AADT on performance.

Finally, this study shows the tremendous variability with polyurea, especially with the highly reflective beads, which seems to come from the initial installation of material. High variability is consistent with the literature and one of the frustrations performance modelers have been dealing with for over a decade. This finding would suggest a need for the industry to develop more stringent controls on installation specifications, which would ultimately result in better degradation rates and consistent performance of pavement marking materials such as polyurea. Overall, these performance-based degradation models serve to predict the remaining service life of a given polyurea pavement marking to allow pavement marking managers to better allocate limited manpower and resources while providing a standard level of service for retroreflectivity.

Future Research

The significant finding produced by this study is the impact of bead type on degradation. While highly reflective elements produce pavement markings with much higher initial R_L values, the decay rate is substantially greater than standard bead degradation. However, based on the models, at the 60-month mark pavement markings containing highly reflective elements produce almost twice the retroreflectance than those containing standard beads.

It is recommended that future research collect data specific to highly reflective elements. Advancements in understanding the performance characteristics of highly reflective elements have the potential to significantly impact the effectiveness of pavement marking performance models. Future studies should collect data pertaining to pavement markings with highly reflective elements, recording at a minimum the same variables used in this study. It is recommended that the collection effort continue for at least 8 years to improve on the current model presented in this article.