Construction and Building Materials 162 (2018) 192–201
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Effect of overlay thickness, overlay material, and pre-overlay treatment on evolution of asphalt concrete overlay roughness in LTPP SPS-5 experiment: A multilevel model approach Ye Yu a, Lu Sun a,b,⇑ a b
School of Transportation, Southeast University, Nanjing, Jiangsu 210096, China School of Engineering and Applied Science, Princeton University, Princeton, NJ 08544, USA
h i g h l i g h t s A multilevel model was developed to model evolution of asphalt overlay roughness. Clustered longitudinal structure of overlay roughness was fully captured. Interactive effects between factors on roughness were systemically investigated. Overlay material and overlay thickness affect roughness after overlay. Overlay thickness have a significant effect on roughness evolution.
a r t i c l e
i n f o
Article history: Received 26 February 2017 Received in revised form 13 October 2017 Accepted 5 December 2017
Keywords: Long-term pavement performance (LTPP) Multilevel model Overlay Roughness Clustered longitudinal data
a b s t r a c t The objective of this study is to investigate the effect of overlay thickness, overlay material and preoverlay treatment on roughness evolution of asphalt overlay in the Long-term Pavement Performance (LTPP) SPS-5 experiment. Roughness data collected from SPS-5 experimental sites has a clustered longitudinal structure. A multilevel model is established to simultaneously account for measurement correlation within the same test section and roughness evolution correlation within the same experimental site. It was discovery that while as-built roughness depends on overlay material and overlay thickness, roughness growth rate only depends on overlay thickness. Ó 2017 Published by Elsevier Ltd.
1. Introduction The Long-Term Pavement Performance (LTPP) program is a study of the behaviour of pavement test sections located on inservice roadways constructed using highway agency specifications and contractors, and subjected to real-life traffic loading throughout the United States and Canada [1]. As the largest pavement performance research experiment ever undertaken, LTPP is designed to monitor and collect data from over 2500 in-service pavement test sections over a 20-year period [2]. A key aspect of the LTPP project is to investigate the specific effects on long-term pavement performance of various design features, traffic and environment,
⇑ Corresponding author at: School of Engineering and Applied Science, Sherred Hall 225, Princeton University, Princeton, NJ 08544, USA. E-mail addresses:
[email protected] (Y. Yu),
[email protected] (L. Sun). https://doi.org/10.1016/j.conbuildmat.2017.12.039 0950-0618/Ó 2017 Published by Elsevier Ltd.
materials, construction quality, and maintenance practices based on systematic, exhaustive, and in-depth analysis of sufficient data. The Specific Pavement Studies Experiment 5 (SPS-5) in the LTPP program was designed to study the effects of overlay thickness, overlay material, and pre-overlay treatment on the performance of asphalt overlay [3,4]. There are 18 experimental sites throughout the United States and Canada. At each site, there are eight 150 m test sections built side-by-side and monitored for long-term pavement performance development. All the eight type of treatments are commonly used by highway agencies in practical [2]. The primary objective of this study is to investigate the effect of overlay thickness, overlay material and pre-overlay treatment on roughness evolution based on the IRI data collected in the LTPP SPS-5 experiment. As shown in Fig. 1, the IRI data used in this study, which was collected from 18 experimental sites, has a clustered longitudinal structure. Repeated measures of pavement
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differences in roughness evolution resulted from in-situ conditions such as pavement structure, climate and traffic loads. It can be used to compare the expected roughness evolution of overlay over time on the basis of various attributes such as overlay thickness, overlay material, and pre-overlay treatment. 2. Literature review
Fig. 1. Clustered longitudinal structure of pavement performance data for site 1205 in the LTPP SPS-5 project.
performance are collected on each test section over time while multiple test sections are nested within each experimental site. As a consequence, multiple measurements of IRI over time for the same test section are likely to be correlated. In addition, IRI evolution of several test sections nested within the same experimental site may tend to be similar because these test sections are subject to the same in-situ conditions (hereinafter referred to as site effect) such as pavement structure, climate and traffic loads. The above-mentioned clustered longitudinal structure must be well accounted in the analysis process in order to capture the effect of overlay thickness, overlay material and pre-overlay treatment on roughness evolution accurately. Table 1 presents the factors for performance development of the SPS-5 test sections. In this study a multilevel model is established to account for such a clustered longitudinal data structure. Multilevel models, also known as hierarchical linear models, nested data models, mixed models, random coefficient models, random-effects models, random parameter models, individual growth models, or split-plot designs, are statistical models of parameters that vary at more than one level. [5,6]. The multilevel model for IRI evolution developed in this study includes sub-models at three levels: (1) a level-1 sub-model that describes how IRI of pavement sections change over time; (2) a level-2 sub-model that describes how these changes vary across pavement sections within the same experimental sites; and (3) a level-3 sub-model that describes how these changes vary across experimental sites [5]. It can embody three type of research questions regarding to roughness evolution: level-1 questions about within-section roughness evolution over time, level-2 questions about between-section within-site differences in roughness evolution resulted from different overlay thickness, overlay material and pre-overlay treatment, and level-3 questions about between-site
Table 1 Factors for performance development of the SPS-5 test sections. Level
Factors on each level
Site (Level 3)
In-situ conditions such as pavement structure, climate, and traffic loads Section-level design factors (i.e., overlay thickness, overlay material, and pre-overlay treatment Time elapsed after overlay
Section (Level 2) Measurement (Level 1)
Thus far, several studies have been conducted using the LTPP SPS-5 data. Hong and Chen [7] investigated effects of overlay thickness, material and pre-overlay treatment on transverse crack propagation of asphalt pavement overlay based on LTPP SPS-5 test sections in Texas. They employed sigmoid or S-shaped models to study the development of transverse cracking. Hong, Chen and Mikhail [8] conducted a similar but more comprehensive study in which transverse cracking length, rut depth, and ride quality of SPS-5 test sections were evaluated, respectively. In regard to roughness, it was found that there was no statistical difference between the recycled (RAP) and virgin (non-RAP) test sections according to paired-t test. Carvalho, Shirazi, Ayres and Selezneva [9] analyzed the impact of reclaimed asphalt pavement (RAP) on the performance of flexible pavement overlays based the LTPP SPS-5 project. Statistical methodology used in their study was repeated measures analysis of variance. They compared roughness, rutting, fatigue cracking, and deflection of the recycled (RAP) and virgin (non-RAP) test sections subjected to the same traffic and environment. For roughness, it was suggested that there was no significant difference between roughness of the RAP sections and that of non-RAP sections for the majority of sites. However, non-RAP sections tend to perform slightly better than the RAP sections when the overlay was thin. West, Michael, Turochy and Maghsoodloo [3] compared pavement performance of the SPS-5 test sections with and without RAP using paired t-test. International roughness index (IRI), rutting, fatigue cracking, longitudinal cracking, transverse cracking, block cracking, and ravelling were chosen as indicators for pavement performance. They also investigated the effect of location, age, overlay thickness, and pre-overlay milling on the performance of the overlays using analysis of variance (ANOVA). It was shown that thicker overlay performed better in terms of IRI. The effect of milling on roughness was found to be significant. However, no evidence of the effect of overlay material was detected. Dong and Huang [10] investigated the effectiveness and cost-effectiveness of typical asphalt pavement rehabilitations and identified major influence factors through multiple regression. Logarithmic transformation and square root transformation were utilized to normalize response variables in the multiple regression models. Their study was conducted using IRI data collected from the LTPP SPS-3, SPS-5 and GPS-6B test sections. Analyzed factors included specific rehabilitation methods, pre-overlay pavement condition, traffic volume, and overlay thickness. The results indicated that pavement with thicker overlay, milling, and low preoverlay roughness were smoother after rehabilitation. It should be noted that, apart from the data of the LTPP SPS-5 test sections, their study utilized the pavement performance data from the SPS-3 and GPS-6B test sections. Ahmed, Labi, Li and Shields [2] analyzed the effectiveness of pavement rehabilitation treatments based on LTPP SPS-5 test sections in west region. Effectiveness was measured in both short term (roughness reduction) and long term (estimated treatment service life and area bounded by the performance curve). Ordinary least square regression was employed in their research to develop treatment effectiveness models. It was found that overlay thickness and pre-overlay treatment have a profound effect on roughness performance. There were generally no difference between
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roughness performance of different overlay materials (virgin vs. recycled). Mannan and Tarefder [11] analyzed pavement performance of the LTPP SPS-5 test sections located in New Mexico for various factors such as age, overlay material, overlay thickness, and preoverlay treatment (milling prior overlay construction). Aspects of performance included in their research were International Roughness Index (IRI), rutting, fatigue cracking, longitudinal cracking, and transverse cracking. Analysis of variance (ANOVA) was performed to examine the impact of the influence factors on each performance aspect. In addition, paired t-test was conducted to compare pavement performance of different overlay materials (virgin vs. recycled). Concerning roughness, it was shown that overlay thickness had a strong effect on roughness evolution. In addition, the effect of pre-overlay treatment was also detected while the effect of overlay material was not significant. Wang [12] compared long-term performance of SPS-5 test sections of different overlay materials (virgin vs. recycled) on fatigue cracking, longitudinal cracking, transverse cracking, rutting, and roughness. Non-parametric survival analysis and pair-t tests were employed to examine possible performance differences. In respect of roughness, it was reported that recycled (RAP) test sections were rougher than virgin (non-RAP) test sections for thin overlays. However, for thick overlays with intensive pre-overlay treatment, recycled (RAP) test sections were significantly smoother than virgin (non-RAP) test sections while there was no significant difference between virgin and recycled test sections for thick overlays with minimum pre-overlay treatment. Table 2 summarises the findings of previous studies regarding to the effect of overlay thickness, overlay material and preoverlay treatment on roughness evolution of the SPS-5 test sections. In general, these previous studies were conducted based on different dataset using different statistical methods. Although the studies listed in Table 2 were all carried out using the SPS-5 data, they were actually conducted based on the SPS-5 data available at different times and some of them only utilized data from specific states or regions which were of particular interest. As a result, it is not very surprising that these studies obtained different results. There are two points to be made in respect of previous studies on roughness evolution of SPS-5 test sections. Firstly, the clustered longitudinal data structure, especially roughness evolution correlation across test sections within the same experimental site, was not well accounted in previous published studies. In this study, a multilevel model will be developed to analyse test sections within all sites simultaneously while accounting both measurement correlation within the same test section and roughness evolution correlation within the same experimental site. Secondly, there has been little quantitative and systematic analysis of interactive effects among overlay thickness, overlay material, pre-overlay treatment, and time elapsed after overlay, on roughness evolution of overlay. It should be noted that, time elapsed after overlay has been reported to be the most influential
factor on roughness evolution [3,11]. In this study, possible interactive effects among overlay thickness, overlay material, pre-overlay treatment, and elapsed time after overlay will be systemically explored.
3. Data The data used in this study are collected in SPS-5 project as part of the Long-term Pavement Performance (LTPP) program. The SPS5 experiment evaluates the effectiveness of typical asphalt overlays on existing asphalt pavements that are commonly used by highway agencies. It has 18 test sites located on the North American continent and each test site has eight separate sections at which different rehabilitation treatments were applied [2]. Each section is about 152.4 m long and 3.66 m wide and has been periodically monitored to collect various performance data [12]. This study focus on the development of pavement roughness. The average International Roughness Index (IRI) value at both wheel paths is utilized to characterize roughness condition of the entire test section. As shown in Table 3, the eight test sections for each experimental site were set up with different overlay thickness (51 mm vs. 127 mm), different type of asphalt used in overlay (virgin vs. recycled), and different extent of surface preparation before the rehabilitation (minimal vs. intensive preparation) [2,12]. Virgin materials are new materials which have not been used in previous construction while recycled materials contains 30% recycled asphalt pavement (RAP) [13]. Minimal pre-overlay treatment consists of patching of severely distressed areas and potholes, and placement of levelling course in ruts of more than 0.5 in. deep whereas intensive pre-overlay treatment includes milling, patching of distressed areas and potholes, and crack sealing [14]. The primary difference between the minimal and intensive level of pre-overlay treatment is milling of the surface which is performed to remove oxidized or stripped material and correct transverse distortion owing to rutting [15]. The milled depth is selected from 38.1 mm (1.5 in.) to 50.8 mm (2 in.) in order that the final surface is more than 12.7 mm (0.5 in.) above or below an interface between materials layers [14]. Table 3 Factors for eight test sections within each experimental site. Section Number
Overlay thickness
Overlay material
Pre-overlay treatment
02 03 04 05 06 07 08 09
50.8 mm (2 in.) 127 mm (5 in.) 127 mm (5 in.) 50.8 mm (2 in.) 50.8 mm (2 in.) 127 mm (5 in.) 127 mm (5 in.) 50.8 mm (2 in.)
Recycled Recycled Virgin Virgin Virgin Virgin Recycled Recycled
Minimal Minimal Minimal Minimal Intensive Intensive Intensive Intensive
Table 2 Findings of previous studies regarding to roughness performance in the LTPP SPS-5 experiment. Source
Statistical methodology
Overlay thickness (T)
Overlay material (M)
Pre-overlay treatment (P)
Hong et al. [8] Carvalho et al. [9]
Paired-t test Repeat measure ANOVA
West et al. [3] Ahmed et al. [2] Mannan and Tarefder [11] Wang [12]
ANOVA & paired-t test OLS regression ANOVA & paired-t test Survival analysis & paired-t test
p (M*T: ) p
Note:
p
Significant; Not significant; Not explored/reported.
p p p
p (M*T*P: )
p p
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Table 5 Variables of the MLM for roughness evolution.
4. Methodology To account for the clustered longitudinal data structure of the SPS-5 IRI data, a multilevel model (MLM) is developed in this study. The clustered longitudinal data structure can violate the independence assumption required by popular statistical techniques such as ordinary lest-squares (OLS) multiple regression and ANOVA [16]. Ignoring this data structure can result in underestimation of the standard errors and inflation of the Type I errors, making the results untrustworthy. Additionally, it may distort the estimated error variance, confidence intervals, P values, and effect sizes [17]. Multilevel models, which have recently emerged, are better suited to such a clustered longitudinal data structure. 4.1. Model specification In this study, a 3-level multilevel model is developed for roughness evolution. In the MLM framework, covariates for IRI are assigned on corresponding levels. Table 4 shows the formulas on each level. Table 5 summaries the variables on each level. The level-1 sub-model represents the shape of each pavement section’s IRI trajectory over time. Each section’s successive measurements can be represented by an individual growth curve and random error. Time elapsed after overlay (i.e., TIME) is the only explanatory variable defined at the lowest level of MLM. The level-2 sub-model formulates the relationship between random parameters in level-1 sub-model and time-invariant characteristics of specific pavement section. Here, the effect of overlay thickness, overlay material and pre-overlay treatment on the development of pavement roughness is of particular interest. A set of section-level time-invariant predictors (i.e., THICKNESS, MATERIAL, TREATMENT) are added to explain IRI evolution variation across test sections. The level-3 sub-model investigates difference in IRI evolution across experimental sites by examining variation of random parameters in level-2 sub-model. In-situ conditions such as pavement structure, climate, and traffic loads may have a substantial influence on roughness performance. Considering that the primary objective of this study is to investigate the effect of section-level predictors, this study rules out site effect as a whole and does not include any specific site-level predictor to trace the cause of the site effect. 4.2. Model estimation and model selection A number of techniques such as maximum likelihood, generalized estimating equations, and Markov chain Monte Carlo method have been developed to estimate regression coefficients and
Variable
Definition
IRItij
IRI value of pavement section i in experimental site j measured at the tth measurement Time elapsed at tth measurement after overlay of pavement section i in experimental site j Overlay thickness (i.e., 51 mm = 0, 127 mm = 1) of pavement section i in experimental site j Overlay material (i.e., virgin = 0, recycled = 1) of pavement section i in experimental site j Pre-overlay treatment (i.e., minimal = 0, intensive = 1) of pavement section i in experimental site j
TIMEtij THICKNESSij MATERIALij TREATMENT ij
variance components in multilevel models. This study uses full maximum likelihood (FML) method which is the most popular method in multilevel modelling. The FML method can produce a statistic called the deviance, which indicates how well the model fits the data. Models with a lower deviance fit better. A particular advantage of FML methods over other estimation methods is that a formal chi-square test can be performed to compare nested models statistically based on the likelihood values. Nested models means that a specific model can be derived from a more general model by removing parameters of that general model [6]. This test is also called likelihood ratio test (LRT). The LRT statistic equals 2 times the difference between the log-likelihood value for the nested model and that for the reference model.
LRT ¼ 2ðln Lnested Lreference Þ v2df
ð4Þ
The statistic follows a chi-square distribution, with degrees of freedom equal to the difference in the number of parameters estimated in the nested models [6]. 4.3. Advantages of MLM A great advantage of using MLM is that the clustered longitudinal structure of the SPS-5 pavement performance data can be well accounted. Long-term pavement performance program typically involves repeatedly collecting performance data at the same pavement sections over time. As the inherent data structure can be well accounted, the results of section-level predictor effect is more trustworthy. Another advantage is that multilevel models are highly flexible in handling unequally spaced measurements on different individuals over time and missing data, thereby making full use of all data available. Both unequally spaced measurements and missing data are very common phenomena in pavement performance data set. 5. Analysis of results
Table 4 Formulas of MLM on each level.
5.1. Research question considered in this study
Level 1 (measurement-level): IRItij ¼ p0ij þ p1ij TIMEtij þ etij
(1)
Level 2 (section-level): p0ij ¼ b00j þ b01j THICKNESSij þ b02j MATERIALij þ b03j TREATMENT ij þ U 0ij p1ij ¼ b10j þ b11j THICKNESSij þ b12j MATERIALij þ b13j TREATMENT ij þ U 1ij
(2a) (2b)
Level 3 (site-level): b00j ¼ c000 þ V 00j b01j ¼ c010 þ V 01j b02j ¼ c020 þ V 02j b03j ¼ c030 þ V 03j b10j ¼ c100 þ V 10j b11j ¼ c110 þ V 11j b12j ¼ c120 þ V 12j b13j ¼ c130 þ V 13j
(3a) (3b) (3c) (3d) (3e) (3f) (3g) (3h)
The following research questions are clarified in this research before the analysis of SPS-5 IRI data set. (a) How does IRI value change over time? In other words, what is the shape of IRI change trajectory? A variety of previous studies indicate that the change trajectory of IRI is a straight line. This assumption will be validated and evaluated in this study. (b) Is there significant variability across pavement sections in change trajectory of IRI? Does any of the three sectionlevel predictors have significant impact on the rate of IRI deterioration? What about the interactions among the three section-level factors and time elapsed after overlay?
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(c) Is there significant variability across experimental sites in the rate of IRI deterioration? This study take a step-up model-building strategy [18] in the analysis of the SPS-5 IRI data. Fig. 2 illustrates the modelbuilding strategy of this study. 5.2. Exploratory data analysis Figs. 3 and 4 show raw IRI values for each pavement section vs. TIME by experimental site and experimental number, respectively. As shown in Fig. 3, the observed IRI values for each pavement sections have substantial variation from experimental site to site while different pavement sections within the same experimental site have similar IRI change trajectory. Fig. 5 also illustrates that pavement sections with the same experimental number have great variation across experimental sites. This suggests that experimental site can have a great effect on roughness performance and should be accounted in the following analysis. In general, there is a clear trend of increasing for the observed IRI values, indicating that roughness performance is deteriorating with time. Fig. 5 presents raw IRI change trajectory for each pavement section vs. Time by overlay thickness, overlay material, and preoverlay treatment, respectively. No significant difference were found between the two groups in any of the three figures. However, it is not easy to draw any conclusion based on inspection of those figures visually. The effect of overlay thickness, overlay material and pre-overlay treatment will be investigated quantitatively in the framework of multilevel model in this study. 5.3. Step 1. Calculate intra-class correlation To confirm whether multilevel model is needed for the SPS-5 IRI data set, an unconditional means model was estimated to compute intra-class correlation coefficient (ICC). An unconditional means model for the SPS-5 IRI data set is a three-level model with a fixed intercept, and random effects associated with the intercept for sections (Level 2) and sites (Level 3). The unconditional means model is formulated as follows.
Level-1 : Y tij ¼ p0ij þ etij
ð5aÞ
Level-2 : p0ij ¼ b00j þ U 0ij
ð5bÞ
Level-3 : b00j ¼ c000 þ V 00j
ð5cÞ
Combined : Y tij ¼ c000 þ V 00j þ U 0ij þ etij
ð5dÞ
The IRI value for pavement section i of experimental site j at the tth measurement is modelled as a function of each pavement section’s mean IRI value plus a time-specific residual term that reflects the difference between each pavement section’s observed and predicted IRI value. In turn, each pavement section’s mean IRI value is modelled as a function of a mean IRI value for pavement sections within specific experimental site plus a term that reflects deviations in a pavement section’s mean IRI value around the site mean. Similarly, each experimental site’s mean IRI value is modelled as a function of a grand mean value for all pavement sections plus a term that reflects deviations in an experimental site’s mean IRI value around the grand mean. The unconditional means model was estimated using the IRI data described above and the results are presented in Table 6. For each level of clustering, an intra-class correlation coefficient (ICC) can be defined as follows.
ICC site ¼
r2site r2site þ r2sec tion þ r2
ICC sec tion ¼
r
2 site
r2sec tion þ r2sec tion þ r2
ð6aÞ
ð6bÞ
where r2site is the variance of random effects associated with experimental sites,r2sec tion is the variance of random effects associated with test sections nested within the same experimental sites, and r2 is the variance of residuals. The results showed that 63.5% (i.e., 0.0616/[0.0151 + 0.0203 + 0.0616]) of IRI variation occurred across experimental sites while 20.9% (i.e., 0.0203/[0.0151 + 0.0203 + 0.0616]) of IRI variation occurred across pavement sections nested within the same experimental sites. The total random variation is dominated by the variance of the random site effects. In other words, the IRI values of test sections within the same site are relatively homogeneous while IRI values across experimental sites tend to vary widely. Interestingly, site effect has a much greater effect on roughness
Fig. 2. Model building process for the analysis of the SPS-5 IRI data.
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Fig. 3. Raw IRI values for each section vs. TIME by site.
variation comparing to the three section-level factors (i.e. overlay thickness, overlay material, and pre-overlay treatment). This indicates the need for multilevel modelling to account for site effect.
5.6. Step 4. Add level-2 and level-3 random slopes associated with level-1 predictors
Adding fixed effects associated with TIME variable which is measured on Level 1 allows each pavement section’s IRI trajectory to be modelled with a straight line with a non-zero slope. TIME variable is defined as the time elapsed from overlay construction to performance measurement and is the only Level 1 covariate considered in this study. This model is hereinafter referred to as Model 1. Compared to the unconditional means model, fixed effects associated with level-1 predictors are added in Model 1. It is obvious that both the AIC and BIC values decreased from the unconditional model to Model 1, indicating that Model 1 preforms much better than the unconditional model.
Model 3 add random slopes associated with TIME variable on both Level 1 and Level 2 to Model 1. The most striking result to emerge from Model 3 is that the estimated fixed effects for TIME variable increased sharply from 0.0152 to 0.0225. Random effects must be carefully accounted and evaluated before interpreting the estimated parameters of fixed effects. Next three steps focus on testing whether to keep random intercepts, random slopes and their correlation on each level in Model 3, respectively. The measurement-level variance for intercept is estimated to be 0.0038, which is much smaller than that of unconditional means model (0.0151). As would be expected, the addition of fixed effects (TIME) and random effects (section-level random slope, site-level random slope and section-level correlation) greatly reduced the unexplained variance in IRI value.
5.5. Step 3. Test nonlinearity in IRI evolution trajectory
5.7. Step 5. Test level-2 and level-3 random slopes
To investigate the nonlinearity in IRI growth trajectory over time, an additional quadratic effect (TIME-squared) are added to Model 1. The results of this model (Model 2) are shown in Table 6. It is clear that the coefficient of TIME-squared term in Model 2 is not significant, indicating that linear trajectories are enough to model IRI evolution trajectories. As a result, the TIME-squared term are omitted in the following analysis.
To test whether level-2 and level-3 random slopes could be omitted from Model 3, Model 4A and 4B are fitted. Model 4A omitted only section-level random slopes while Model 4B omitted only site-level random slopes. Model 4A and 4B are compared with Model 3 using likelihood ratio test, respectively. Based on the results of Table 7, both level-2 and level-3 random slopes are retained in all subsequent models.
5.4. Step 2. Add fixed effects associated with level-1 predictors
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Fig. 4. Raw IRI values for each section vs. TIME by experiment.
5.8. Step 6. Test level-2 and level-3 random intercepts To test level-2 and level-3 random intercepts, Model 5A and 5B are developed. Model 5A omitted only section-level random intercepts while Model 5B omitted only site-level random intercepts. Model 5A and 5B are compared with Model 3 by performing likelihood ratio test, respectively. The results are presented in Table 7. Based on the results, random slopes on both levels are retained in all subsequent models.
At this stage of analysis, Model 6B is chosen as preferred model. As shown in Table 6, the coefficient of TIME variable is estimated to be 0.0225 while site-level variance for random slope is estimated to be 0.0004 and section-level variance for random slope is estimated to be 0.0005. Obviously, there are a lot of section-level and site-level random variation on the slope parameter. Similarly, the level-1 model also indicated significant variance for random intercepts, which is representations of model-based as-built IRI values, both across sites and sections. 5.10. Step 8. Add fixed effects associated with level-2 predictors
5.9. Step 7. Test correlation between random intercepts and slopes on each level In Model 3, random intercepts and slopes are specified to covary. To test whether correlation between random intercepts and slopes on each level could be omitted from Model 3, a nested model omitting the correlation on level-2 (Model 6A) and a nested model omitting the correlation on level-3 (Model 6B) are fitted. Model 6A and 6B are compared with Model 3 using likelihood ratio test, respectively. Based on the results of the likelihood tests, correlation between random intercepts and slopes on level-3 is omitted while correlation between random intercepts and slopes on level-2 is retained in all subsequent models. In other words, the random intercepts and slopes on level-2 are specified to co-vary while the random intercepts and slopes on level-3 are defined to be independent.
In this step, the fixed effects associated with the three sectionlevel predictors (THICKNESS, MATERIAL, and TREATMENT) are added to Model 6B and tested using the corresponding coefficients in the new model. After removing all the insignificant terms, Model 7 is obtained. 5.11. Step 9. Add fixed effects associated with interactions between level-1 and level-2 predictors In this step, the fixed effects associated with interactions between level-1 predictor (i.e. TIME) and level-2 predictors (i.e. THICKNESS, MATERIAL, and TREATMENT) are investigated. In total, there are 6 two-way interactions (TIME by THICKNESS, TIME by MATERIAL, TIME by TREATMENT, THICKNESS by MATERIAL, THICKNESS by TREATMENT, MATERIAL by TREATMENT), 4 three-
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Fig. 5. Raw IRI values for each section vs. Time elapsed after overlay by overlay thickness, overlay material, and pre-overlay treatment, respectively.
way interactions (TIME by THICKNESS and MATERIAL, TIME by THICKNESS and TREATMENT, TIME by MATERIAL and TREATMENT, THICKNESS by MATERIAL and TREATMENT), and 1 four-way interaction (TIME by THICKNESS, MATERIAL, and TREATMENT). These interaction terms are added to Model 7 and carefully investigated using the fitted results of the new model. After removing insignificant terms, Model 8 are obtained. What is interesting about the result of Model 8 is that the fixed effect of overlay thickness becomes not significant after adding fixed effect of TIME by overlay thickness interaction. However, all the main effects (i.e. TIME, THICKNESS, MATERIAL) that compose the significant interaction terms (i.e. TIME by THICKNESS, and THICKNESS by MATERIAL) should also be included to follow the principle of marginality [6,19]. Based on the results of likelihood ratio test between Model 7 and Model 8, which is shown in Table 7, it is concluded that Model 8 is the preferred model. 5.12. Model interpretation The results of Model 8 indicates that there are no evidence that pre-overlay treatment or any interaction including pre-overlay treatment has a significant influence on roughness evolution. According to Model 8, roughness evolution is affected by TIME, THICKNESS, MATERIAL, TIME by THICKNESS interaction, and THICKNESS by MATERIAL interaction. To interpret the fixed effects of Model 8 in detail, the regression equations are wrote out and listed in Table 8. There are several
points to be made with regard to Table 8. Firstly, overlay thickness has a great effect on IRI deterioration rate. For thin overlay (50.8 mm), the coefficient of TIME variable is estimated to be 0.0297 m/km/year, indicating that IRI score tends to increasing 0.0297 m/km per year. For thick overlay (127 mm), this value drop to 0.0152 m/km/year. This conforms that thicker overlay can mitigate the growth effect of TIME variable. Secondly, it is evident that overlay material only impacts the intercept of IRI change trajectory with the overlay thickness being constant. In other words, there are no significant difference between the deterioration rates of IRI when two test sections only differ in overlay material (virgin vs. recycled). Thirdly, it is interesting to note that using recycled material increases the intercept for thin overlay while decreases the intercept for thick overlay. For thin overlay, the intercept for IRI change trajectory improves from 0.8608 m/km to 0.9230 m/ km when recycled material are used instead of virgin materials. In contrast, the intercept drops from 0.8999 m/km to 0.8501 m/ km for thick overlay. The intercept of change trajectory can be interpreted as a representation of as-built IRI value. Using recycled materials can slightly improve roughness performance for thick overlay whereas slightly reduce roughness performance for thin overlay. Taken together, while as-built IRI is influenced by both overlay thickness and overlay material, IRI growth rate is only impacted by overlay thickness. Take for example test sections with thin overlay and virgin materials, the intercept for pavement section i within experimental ^ 0ij þ u ^ 0j . u ^ 0j is site-specific adjustsite j is estimated as 0:8608 þ u
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Table 6 Model summaries.
Fixed effects Intercept P-value TIME P-value TIME-squared P-value THICKNESS(T) P-value MATERIAL(M) P-value TIME*T P-value T*M P-value
Unconditional
Model 1
Model 2
Model 3
Model 4A
Model 4B
Model 5A
Model 5B
Model 6A
Model 6B
Model 7
Model 8
1.0071
0.9193 0.0000 0.0152 0.0000
0.9185 0.0000 0.0155 0.0000 0.0000 0.8540
0.8834 0.0000 0.0225 0.0012
0.8917 0.0000 0.0201 0.0006
0.8823 0.0000 0.0232 0.0000
0.8806 0.0000 0.0240 0.0008
0.8962 0.0000 0.0220 0.0019
0.8835 0.0000 0.0226 0.0011
0.8835 0.0000 0.0225 0.0011
0.9117 0.0000 0.0225 0.0011
0.8608 0.0000 0.0297 0.0001
0.0557 0.0358
0.0391 0.3109 0.0622 0.0933 0.0145 0.0012 0.1120 0.0324
0.0800 0.0004
0.0799 0.0004
0.0801 0.0004
0.0038
0.0231 0.0005 0.3100 0.0038
0.0234 0.0005 0.3800 0.0038
0.0222 0.0005 0.3500 0.0038
2082.5 2042.7 1049.3 2098.5
2088.1 2048.3 1052.1 2104.1
2090.1 2045.3 1054.1 2108.1
2099.2 2039.5 1061.6 2123.2
Random effects Level-3 intercept 0.0616 Level-3 slope Level-3 correlation Level-2 intercept 0.0203 Level-2 slope Level-2 correlation Residuals 0.0151 Model summary AIC BIC Log-likelihood Deviance
0.0681
0.0681
0.0101
0.0101
0.0813 0.0004 0.2800 0.0230 0.0005 0.3100 0.0038
1475.2 1450.3 742.6 1485.2
1473.2 1443.4 742.6 1485.2
2087.1 2042.3 1052.6 2105.1
0.0224
1102.7 1082.8 555.4 1110.7
0.0224
0.0807 0.0003 0.2900 0.0235
Model Model Model Model Model Model Model Model Model Model Model Model
0 vs. Model 1 1 vs. Model 2 1 vs. Model 3 4A vs. Model 3 4B vs. Model 3 5A vs. Model 3 5B vs. Model 3 6A vs. Model 3 6B vs. Model 3 6B vs. Model 7 6B vs. Model 8 7 vs. Model 8
Test Statistics 374.500 0.034 619.930 363.350 35.621 631.200 123.640 6.631 1.021 4.023 19.088 15.065
MIXTURE = 0 MIXTURE = 1
0.0004
0.0011
0.0072
0.0038
0.0091
0.1001 0.0007 0.5300 0.0038
1727.8 1692.9 870.9 1741.8
2055.5 2020.7 1034.8 2069.5
1459.9 1425.1 737 1473.9
1967.5 1932.6 990.7 1981.5
0.0814 0.0004 0.3000 0.0215 0.0005
Table 9 Comparison of results of multilevel model and OLS regression. Degrees of freedom 1 1 4 2 2 2 2 1 1 1 4 3
P-value 0.0000 0.8540 0.0000 0.0000 0.0000 0.0000 0.0000 0.0100 0.3122 0.0449 0.0008 0.0018
Table 8 Interpretation of Model 8.
Model 8
0.0836 0.0003 0.3000
0.0260 0.0010
Table 7 Summaries of likelihood ratio test results. Model compared (Nested vs. Reference)
0.0757
THICKNESS = 0
THICKNESS = 1
0.8608 + 0.0297*TIME 0.9230 + 0.0297*TIME
0.8999 + 0.0152*TIME 0.8501 + 0.0152*TIME
^ 0ij is ment for intercept of test sections nested within site j and u section-specific adjustment for intercept of test section i nested within site j. The site-level and section-level variance for intercept (model-based as-built IRI) is 0.0801 and 0.0222, respectively. There are much more site-level variation than section-level variation on intercept. Similarly, the slope of TIME for pavement section i ^ 1ij þ u ^ 1j . u ^ 1j is within experimental site j is estimated as 0:0297 þ u site-specific adjustment for slope of test sections nested within site ^ 1ij is section-specific adjustment for slope of test section i j and u nested within site j. Similar to intercept, there are also a lot of variation on the slope of TIME. The site-level and section-level variance for slope (model-based IRI growth rate) is 0.0004 and 0.0005,
Model
Intercept TIME THICKNESS(T) MATERIAL(M) TIME*T T*M
MLM (Model 8)
OLS
Estimate
P-value
Estimate
P-value
0.8608 0.0297 0.0391 0.0622 0.0145 0.1120
0.0000 0.0001 0.3109 0.0933 0.0012 0.0324
0.9447 0.0040 0.0136 0.0787 0.0006 0.1297
0.0000 0.0841 0.6928 0.0020 0.8421 0.0003
respectively. It is evident that there are slightly less site-level variation than section-level variation on slope. In addition, sectionlevel random slopes and random intercepts have a correlation of 0.35, indicating that pavement sections with large intercept adjustment within the same sites tend to have a small slope adjustment. That is to say, within the same experimental sites, IRI value of pavement sections with relatively large as-built IRI value tends to increase more slowly. Taken together, the mean of section-specific linear growth rates is 0.0224 m/km/year, with a standard deviation of 0.0193 m/km/year while the mean of model-based as-built IRI values is 0.8836 m/km, with a standard deviation of 0.1360 m/km. Table 9 presents a comparison between the results of multilevel model (Model 8) and OLS regression. As expected, the estimates of OLS regression deviate considerably from those of multilevel model. For example, the effect of TIME is estimated to be 0.0040 (p = .0841) according to the results of OLS regression. When using multilevel model, this effect is estimated to be 0.0297 (p = .0001). Theoretically, if the clustered longitudinal structure can be ignored, multilevel model and OLS regression should generate similar results. The great difference between the results obtained by multilevel model and OLS regression further emphasizes the necessity for using multilevel model to account for the clustered longitudinal structure of the SPS-5 pavement performance data.
Y. Yu, L. Sun / Construction and Building Materials 162 (2018) 192–201
6. Conclusions This study examined the effect of overlay thickness, overlay material, and pre-overlay treatment on evolution of asphalt overlay roughness in LTPP SPS-5 experiment. Roughness data were measured and collected repeatedly on test sections nested within experimental sites. To account for the clustered longitudinal structure of the LTPP SPS-5 roughness data, a multilevel model were established using a step-up model-building strategy. Both measurement correlation within the same test section and roughness evolution correlation within the same experimental site are simultaneously taken into account in the framework of the proposed multilevel model. The study revealed that significant variations exist on roughness across both test sections and experimental sites. Site effect can attribute as much as 63.5% of total variation on IRI values, while section-level factors can explain only 20.9% of total variation. These results justified the necessity of using multilevel models to analyse the clustered longitudinal pavement performance data. The multilevel model developed in this study assumed that, for specific test section nested within a specific experimental site, IRI value changes linearly with time elapsed after overlay. This assumption, which was supported by extensive previous studies, was tested and validated statistically in this study using inservice pavement performance data. The multilevel model discovered that apart from time elapsed after overlay, overlay thickness and overlay material influence roughness evolution. Two interaction terms (i.e., time by overlay thickness, and overlay thickness by overlay material) were found to be significant. While as-built IRI is influenced by both overlay thickness and overlay material, IRI growth rate is only impacted by overlay thickness. There was no evidence that pre-overlay treatment has a significant effect on roughness evolution. Regardless of overlay material, IRI of thin overlay (50.8 mm) tends to grow 0.0297 m/km per year while IRI of thick overlay (127 mm) only grows 0.0152 m/km per year, indicating that overlay thickness greatly impacts IRI deterioration rate. There are no significant difference between the deterioration rates of IRI when two test sections only differ in overlay material (virgin vs. recycled). For as-built IRI, it is evident that using recycled material increases the as-built IRI for thin overlay while decreases the asbuilt IRI for thick overlay. There are a lot of random variations on roughness evolution across both experimental sites and test sections. The site-level and section-level variance for intercept (model-based as-built IRI) is 0.0801 and 0.0222, respectively. It is evident that there are much more site-level variation than section-level variation on intercept. The site-level and section-level variance for slope (model-based IRI growth rate) is 0.0004 and 0.0005, respectively. Site-level variation is only slightly less than section-level variation on slope. It should be noted that accounting for random effects can greatly change the estimation of fixed effect parameters, thereby influencing the interpretation of the effects of various factors (e.g., overlay thickness) on roughness evolution. The methodology developed in this study can also be employed to analyse other performance measures of pavement (e.g., rutting and cracking) and other infrastructure. Further studies can be conducted to reveal the cause of site effect, such as pavement
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structure, climate, and traffic loads, and explore their effects on roughness evolution. Acknowledgements This study is supported by the National Science Foundation grants CMMI-0408390 and CMMI-0644552; the National Natural Science Foundation of China grants 51250110075 and U1134206; and by the Chinese Overseas Study Abroad Scholarship. The authors are grateful to FHWA LTPP program for their tremendous effort in quality data collection and public release, which made this analysis possible. The authors thank anonymous reviewers for their insightful comments and constructive suggestions, which help us improve the content and presentation of the original manuscript. References [1] G.E. Elkins, T. Thompson, B. Ostrom, A. Simpson, B. Visintine, Long-Term Pavement Performance Information Management System User Guide, 2016. [2] A. Ahmed, S. Labi, Z.Z. Li, T. Shields, Aggregate and disaggregate statistical evaluation of the performance-based effectiveness of long-term pavement performance specific pavement study-5 (LTPP SPS-5) flexible pavement rehabilitation treatments, Struct. Infrastruct. Eng. 9 (2) (2013) 172–187. [3] R. West, J. Michael, R. Turochy, S. Maghsoodloo, Use of data from specific pavement studies experiment 5 in the long-term pavement performance program to compare virgin and recycled asphalt pavements, Transp. Res. Rec. 2208 (2011) 82–89. [4] Q. Dong, B.S. Huang, Evaluation of influence factors on crack initiation of LTPP resurfaced-asphalt pavements using parametric survival analysis, J. Perform. Constr. Facil 28 (2) (2014) 412–421. [5] J.D. Singer, J.B. Willett, Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence, Oxford University Press, New York, 2003. [6] J. Hox, Multilevel Analysis: Techniques and Applications, second ed., Routledge, New York, 2010. [7] F. Hong, D.H. Chen, Effects of surface preparation, thickness, and material on asphalt pavement overlay transverse crack propagation, Can. J. Civ. Eng. 36 (9) (2009) 1411–1420. [8] F. Hong, D.-H. Chen, M.M. Mikhail, Long-term performance evaluation of recycled asphalt pavement results from texas: pavement studies category 5 sections from the long-term pavement performance program, Transp. Res. Rec.: J. Transp. Res. Board 2180 (2010) 58–66. [9] R.L. Carvalho, H. Shirazi, M. Ayres, O. Selezneva, Performance of recycled hotmix asphalt overlays in rehabilitation of flexible pavements, Transp. Res. Rec.: J. Transp. Res. Board 2155 (2010) 55–62. [10] Q. Dong, B. Huang, Evaluation of effectiveness and cost-effectiveness of asphalt pavement rehabilitations utilizing LTPP data, J. Transp. Eng. 138 (6) (2012) 681–689. [11] U.A. Mannan, R.A. Tarefder, Evaluation of Long-Term Pavement Performance Based on New Mexico LTPP SPS5 Data, Transportation & Development Congress, American Society of Civil Engineers, Orlando, Florida, 2014, pp. 269–279. [12] Y.H. Wang, The effects of using reclaimed asphalt pavements (RAP) on the long-term performance of asphalt concrete overlays, Constr. Build. Mater. 120 (2016) 335–348. [13] Q. Dong, X. Jiang, B. Huang, S.H. Richards, Analyzing influence factors of transverse cracking on LTPP resurfaced asphalt pavements through NB and ZINB models, J. Transp. Eng. 139 (9) (2013) 889–895. [14] Strategic Highway Research Program, Construction Guidelines for Experiment SPS-5, Rehabilitation of Asphalt Concrete Pavements, 1990. [15] C.M. Raymond, S.L. Tighe, R. Haas, L. Rothenburg, Analysis of influences on asbuilt pavement roughness in asphalt overlays, Int. J. Pavement Eng. 4 (4) (2003) 181–192. [16] J.L. Peugh, A practical guide to multilevel modeling, J. School Psychol. 48 (1) (2010) 85–112. [17] D. Glaser, R.H. Hastings, An introduction to multilevel modeling for anesthesiologists, Anesth. Analg. 113 (4) (2011) 877–887. [18] S.W. Raudenbush, A.S. Bryk, Hierarchical Linear Models: Applications and Data Analysis Methods, second ed., SAGE Publications, London, 2001. [19] J. Fox, Applied Regression Analysis and Generalized Linear Models, third ed., SAGE Publications, London, 2015.
