LTPP Data Analysis: Influence of Design and Construction Features on the Response and Performance of New Flexible and Rigid Pavements (2005)

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133 CHAPTER 4 - ANALYSIS METHODS 4.1 INTRODUCTION The purpose of this chapter is to provide a summary of analysis methods that were used to perform this research. Some of the previous studies analyzed LTPP data (GPS and SPS experiments) based on engineering criteria (using basic statistics) and subjective judgment [1-4] . For example, the engineering criteria may include the rate of growth, severity levels and impact of distress on the functionality of the pavement. Several statistical methods were employed for establishing performance criteria to study the effect of design and construction features on pavement performance in this research. The statistical methods range from trend plotting to complex multivariate analysis. This research focuses on evaluating the effects of specific design and construction features on the response and performance of the flexible and rigid pavements (SPS-1 and SPS-2 Experiments). The selection of statistical methods was founded on the specific objectives of this study and performance data extent/occurrence. These methods, as well as the concept of Performance Index (PI) developed and employed in the analysis, are explained in this chapter. 4.2 PERFORMANCE INDICATORS The performance of a pavement is an accumulation of damage over time. All pavement sections within each SPS-1 and SPS-2 site were monitored over time; however, the monitoring of these sections is staggered with age (i.e., the distresses data were collected at different times for individual sections), and the performance measures (cracking, rutting and roughness) have shown a variable trend with time. Therefore, it was felt necessary to develop a measure that can quantify the overall performance of a pavement section over time. Figure 4-1 through Figure 4-4 show various performance curves for twelve test sections within two sites of the SPS-1 experiment. These figures show the measurement variability with time. The following discussion presents various options that were considered to transform the time series data of a section into a single performance indicator. The options considered are listed below: • Maximum distress at the latest age/survey. • Area under the performance curve. • Area under the performance curve normalized to the latest age. • Performance Index.

134 Maximum distress at the latest age is one of the options used for time series data analysis. This performance indicator only considers the maximum distress that was recorded for the test section in its monitored lifetime. Also, this performance indictor will not capture the performance trend over time. In addition, the measurement variability over time is not taken into account. Area under the curve represents the actual pavement performance for a distress; larger area indicates poorer performance. The area under the curve can be calculated using the trapezoidal rule by using Equation (1). ( ) 11 2i ii ii y yArea t t ++ +  = −     ∑ (1) The shortcoming of “area under the curve” is that this indicator cannot discriminate the performance of two sections having the same area but with different times for distress occurrence. For example, the performance curves in Figure 4-5 and Figure 4-6 may have similar “area under the curve” but the curve in Figure 4-6 shows better performance than that in Figure 4-5. Area under the curve normalized to the latest age can be another alternative which can eliminate the discrepancy of using “area” alone (as mentioned above). This indicator can also be calculated based on the trapezoidal rule and can be represented mathematically by Equation (2). ( ) 11 2i ii ii age age y yt t Area L L ++ +  −     = ∑ (2) Where; “Lage” is the latest age used to normalize the “area”. This indicator distributes the performance of a section (area) evenly over all years. However, performance curves can exhibit highly variable trends with time (see Figure 4-1) and may have gaps in the data for some years. Therefore, an alternative indicator was selected, where the performance is weighted with age.

135 0 20 40 60 80 100 120 140 160 1 2 3 4 5 6 7 8 9 Age (years) Al lig at or C ra ki ng ( sq m ) 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 Figure 4-1 Fatigue cracking with age— AL (1) 0 20 40 60 80 100 120 140 160 180 1 2 3 4 5 6 7 8 9 Age (years) Lo ng . Cr ac ks W P (m ) 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 Figure 4-2 Longitudinal cracking-WP with age — AL (1) 0 10 20 30 40 50 60 70 80 0 2 6 8 9 Age (years) Tr an s. C ra ck in g (m ) 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 Figure 4-3 Transverse cracking with age — IA (19) 0 2 4 6 8 10 12 -1 0 2 3 6 7 8 9 Age R ut , m m 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 Figure 4-4 Rutting with age — IA (19) Figure 4-5 Poor Performance Figure 4-6 Good Performance t5 t6 t7 t8 t9 Cracking Area Years t1 t2 t3 t4 t5 Cracking Area Years

136 The Performance Index (PI) is defined as: i i i i i y t PI t ⋅ = ∑ ∑ (3) Where: ti = the age at distress measurement year i yi = distress measured at year i (for example alligator cracking in. sq-m, rut depth in mm and IRI in m/km) Note that only the ages at which distress measurements were taken are included in the calculation of PI. Equation (3) can be further simplified to the form of a series as shown by Equation (4). 3 31 1 2 2 . .. . ...... i i i i i i i i i i y t y ty t y tPI t t t t = + + + +∑ ∑ ∑ ∑ (4) It can be seen from Equation (4) that higher weights will be given to the performance measured at the later ages (as ti+1 > ti and Σ ti is constant for a given pavement section). This makes the performance index more applicable to the SPS-1 and SPS-2 experiments which stipulate that no maintenance or rehabilitation action should be taken during the life of the pavement. The following hypothetical example illustrates the difference between various performance indicators discussed above. Figure 4-7 shows the performance curves for five different pavement sections. The best and the worst performing sections are to be identified from the time series data. Three of the performance indicators were calculated for all five sections and the results are summarized in Table 4-1. It is clear from the results that section D is best performing because the distress remains at the same level over the years and all indicators are capturing this well. The second best section according to “Area” and “Area/Lage” is section B; however according to “PI” section A is second best. By visual comparison of the performance curves for sections A & B, it can be said that section B will deteriorate at a faster rate compared to section A, given the performance history of the sections (see Figure 4-7). As higher weights are given for later years in the calculation of the Performance Index (PI), it is expected that this indictor will be more suitable to capture the present

137 and relative future performance of each section. Therefore, PI was selected from among various performance indictors for this study. The performance indices (PIs) were calculated for each section and for the different performance measures such as cracking, rutting and roughness. This was calculated by summing the product of distress and age for all available surveys and dividing it by the sum of ages for available surveys, as shown by Equation (3). All analyses (overall and site level) were performed using PIs for test sections. Although PI seems to be the best option among all the performance indicators considered, it has some inherent limitations. These limitations are mainly because PI is dependent on the number and timing of the distress surveys. For two pavement sections of the same age and performance, with one monitored each year and the other monitored on alternate years, the PI for the former section will be slightly lower. For the same sections if the monitoring were not performed at a regular time interval, the section with more surveys towards the later age will have a slightly inflated PI. However, this limitation may not have considerable impact in the case of the SPS-1 and SPS-2 experiment as all the pavement sections were monitored with a regular time interval of 1 to 2 years. In SPS-1 and SPS-2 experiments the pavement sections at different sites have different ages. Among pavement sections with different ages and similar performance, the PI of younger sections will be lower than that of older sections. To address this issue, the age of test sections was considered as a covariate in all statistical analyses of PI. This will adjust the PIs according to the age of pavement sections. The statistical methods used in the study are briefly explained next.

138 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 Age (years) M ea su re d D is tre ss Section A Section B Section C Section D Section E Figure 4-7 Comparing different performance curves — An Example Table 4-1 Calculated performance indicators Sections Performance Indicator A B C D E Area 39.75 31 67.5 19 53 Area/Lage 4.0 3.1 8.4 2.1 5.9 PI 5.5 5.9 10.9 2.0 7.5

139 4.3 OVERALL STATISTICAL ANALYSIS METHODS Two types of methods were used for overall statistical analysis. One is based on the magnitude of the performance, i.e. comparison of mean performances between the levels of various factors. The other type of methods is based on the frequency of occurrence of distresses i.e. probability of occurrence or non-occurrence. The ANOVA (one-way and multivariate) method belongs to the first type. The Linear Discriminant Analysis (LDA) and the Binary Logistic Regression (BLR) belong to the second type. 4.3.1 Analysis of variance (ANOVA) The ANOVA is a tool that allows for better understanding of how the independent variables (categorical) influence the dependent variable (continuous). Using the General Linear Model (GLM) univariate procedure, various hypotheses can be tested about the mean of a single dependent variable when cases are classified into groups based on one or more factors (independent variables). For example, the effects of different base types or asphalt thickness (factors as independent variables) on the amount of cracking (dependent variable) are ideal candidates for such an analysis. Moreover, some of these independent variables may be considered to be having a fixed or a random effect on the dependant variable. Also, any other continuous variables (independent) for which the dependent variable is to be adjusted can be included in the model as a covariate. Both balanced and unbalanced models can be tested by ANOVA. A design is considered as a balanced design if each cell in the model contains the same number of cases. ANOVA can be performed by considering one factor at a time, or by considering more than one factor at a time. ANOVA is “one-way” when the effect of a single factor is studied on a dependant variable, whereas, ANOVA is “multivariate” when the effect of more than one factor is studied on a dependant variable. Also, multivariate ANOVA is more efficient as it adjusts for the effects of various factors at a time. Moreover, interaction effects, if any, between various factors can be studied by multivariate ANOVA. To apply ANOVA, the observations must be independent random samples from a normally-distributed population with equal variances. The residuals can be used to check these assumptions to have confidence on the observed significance levels. Generally, two common departures from ANOVA model— non-constancy of the error term and non-normality of the

140 distribution of the error terms, are found in the data. The following frequently recommended remedial measures are found in the literature [5-7]: • Often, non-constancy of the error variance is accompanied by non-normality of the error term. A standard remedial measure here is to transform (e.g., log, natural log or square root etc.,) the response variable (dependent variable). • If the error terms are normally distributed but the variance of the error term is not constant, a standard remedial measure is to use weighted least squares. • When there are major departures from the ANOVA model and even transformations are not successful in stabilizing the error variance and error normality, a non-parametric test for the equality of the factor level means may be used instead of ANOVA. All the assumptions of the ANOVA models used in this research were checked and appropriate remedial measures as discussed above were adopted where ever necessary. Statistical significance of an effect of a factor implies that there exists a significant mean difference between the performances (in this study) of any two levels within the factor. For example, a statistically significant effect of HMA surface thickness on fatigue cracking implies that there is a significant (statistical) mean difference between fatigue cracking on sections with 4- inch (102 mm) HMA thickness and sections with 7-inch (178 mm) HMA thickness. Moreover, in simple terms, a statistical significance indicates that the effect is not a happenstance. However, it is important to confirm the practical or operational difference between the means of various levels of a factor, if a factor has a statistically significant effect. An attempt was thus made in this study to gauge the practical or operational significance of statistically significant differences in the analysis. The operational significance adopted for various performance measures is discussed next. Practical Significance The statistical significance of difference between the marginal means for various levels of design and site factors needs to be judged from practical point-of-view. This practical significance is dependent on the magnitude of the mean difference of levels for a particular factor and will vary for each performance measure. For example, if the means for alligator cracking are significantly (statistically) different for pavement sections constructed on DGAB and on ATB, one should check whether this difference has any practical or operational meaning from an engineering point

141 of view. The practical significance therefore depends on the subjective judgment of actual pavement performance observed in the field. To determine reasonable levels of practical significance for different distress types (fatigue cracking, rut depth, transverse cracking and roughness), the performance curves developed based on the engineering judgment of expert panels were used. These curves for various distress types were developed under two studies [1, 8]. The criteria for fatigue cracking, rut depth, roughness and transverse cracking performances are shown in Figures 4-8, 4-10, 4-12, 4-14 and 4-15, respectively. As mentioned before, the ANOVA was conducted on PI for all performance measures except roughness. For roughness the change in IRI (Latest IRI- Initial IRI) was used as dependent variable in ANOVA. Because the marginal means from ANOVA are in terms of PI, the performance curves from the expert panel were converted to PI, assuming 1 year monitoring interval. These curves, in terms of PI, for fatigue cracking, rut depth and transverse cracking are shown in Figures 4-9, 4-11 and 4-13, respectively. It can be seen from these curves that the slopes of the individual performance curves vary with age. For example, the slope of the IRI curve is the same up to year 5 and later can be separated into two parts. From these two slopes, change in IRI per year can be calculated for the first five years and for the next five years (see Figure 4-14). The weighted average of these slopes was used to calculate the change in IRI per year. Furthermore, the above described curves define the boundaries between good and poorly performing pavements for interstate and non-interstate highways, respectively. For SPS-1 experiment, it was estimated that 80% of the designs corresponded to the interstate highway class, while the remaining 20% were non-interstate, based on the asphalt layer thicknesses. Therefore, the slope (change per year) was further weighted for the proportions of the pavement class within the SPS-1 experiment. Table 4-2 shows the threshold values for practical or operational significance for the various distress types.

142 Table 4-2 Operationally significant differences for various performance measures Performance measure Weighted slope per year Remarks Fatigue cracking (%) 0.20 This will translate into 1.0 sq-m of area per year. Rut depth (mm) 0.80 The operational significant difference for rut depth is 0.8 mm per year. Transverse cracking (m) 3.50 This will translate into 75 m of crack spacing per year. Longitudinal Cracking (m) 4.50 The weighted slope was calculated based on 5000 ft/mile failure criterion used in AASHTO 2002. The failure criterion is thus 144 m for a SPS-1 test section. Operational value is based on the slope of the performance curve between 0 and 10 years, assuming zero cracking up to 5 years and failure at 20 years. Roughness ∆IRI(m/km)-Flexible ∆IRI(m/km)-Rigid 0.13 0.10 The change in IRI was calculated based on initial IRI and latest IRI

143 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 Age (years) F a t i g u e C r a c k i n g ( % ) Interstate Non-Interstate Figure 4-8 Performance criteria for fatigue cracking [1] 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 10 Age (years) P I o f F a t i g u e C r a c k i n g ( % ) Interstate Non-Interstate Figure 4-9 Performance criteria for PI of fatigue cracking 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 Age (years) R u t D e p t h ( m m ) Interstate Non-Interstate Figure 4-10 Performance criteria for rut depth [1] 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 Age (years) P I o f R u t D e p t h ( m m ) Interstate Non-Interstate Figure 4-11 Performance criteria for PI of rut depth

144 0 20 40 60 80 100 120 140 160 0 2 4 6 8 10 Age (years) C r a c k S p a c i n g ( m ) 0 5 10 15 20 25 30 35 40 45 C r a c k L e n g t h ( m ) Figure 4-12 Performance criteria for transverse cracking [1] 0 20 40 60 80 100 120 140 160 0 2 4 6 8 10 Age (years) C r a c k S p a c i n g ( m ) 0 5 10 15 20 25 30 35 P I o f C r a c k L e n g t h ( m ) Figure 4-13 Performance criteria for PI of transverse cracking 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 8 9 10 Age (years) I R I ( m / k m ) Interstate Non-Interstate Figure 4-14 Performance criteria for roughness-Flexible [1] 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 8 9 10 Age (years) I R I ( m / k m ) Figure 4-15 Performance criteria for roughness-Rigid [1, 8]

145 The analysis of variance (ANOVA) is a powerful method; however under certain conditions (limited available data) the application of this method has some restrictions. These issues are briefly summarized below: • The un-balanced data makes it difficult to meet the equal variance assumption. Therefore, an appropriate transformation of the response variable may be adopted to address this issue. • In case of fractional factorial design, the higher order interactions (between more than two factors) cannot be studied [9]. • Replication within each cell of the experiment design plays an essential role in determining power of hypothesis testing. The power of a hypothesis test is the probability of correctly rejecting the null hypotheses when the null hypothesis is not true. Lower number of replications within experiment design will reduce the power of detecting a mean difference between levels of a factor for a given variance. • Time series ANOVA with repeated measures seems to be an appropriate choice of analysis for this type of experiment where each section is monitored over time. However, this type of analysis requires a more balanced data i.e., all pavement sections should be monitored at the same interval and up to an age long enough (about 15 years) for capturing long term pavement performance. The SPS-1 and SPS-2 experiments were designed as fractional factorials. Further, as same number of sites was not constructed in each zone-subgrade combination and as all the sections did not exhibit distress, the experiment is unbalanced. Thus only two-way interactions may be reliable in the analysis. In addition, transformation of the response variables becomes an essential choice to fulfill requirements of ANOVA. When natural logarithmic transformation is applied to response variables, due to the nature of the transforming function (natural logarithm of zero or a negative value is not defined), only data pertaining to those test sections that have distressed (i.e. non-zero positive data) were considered in ANOVA. Hence, ANOVA results are based only on distressed sections. In the SPS-1 and SPS-2 experiments, each SHRP ID represents a unique design and thus there are 24 designs in each experiment. The performance of the designs with respect to each other

146 was evaluated using the deviation from mean performance, which is the standard deviate. The designs were evaluated based on their performance (PI), considering one distress at a time. The standard deviate was calculated for each of the twelve designs within each site. shows a sample calculation of standard deviate with respect to alligator cracking for sections in the AL (1) site, which is calculated by using the following equation. ( ) ( )site given for the PIsof DeviationStandard site given for the PIAverage - design givena of PI DeviateStandard = As this measure was calculated for each section, considering one site at a time, it indicates the relative standing of the section compared to other sections. It thus helps nullify the variation in performance (due to site conditions) among sites, as the sections are weighed with respect to companion sections in each site. The standard deviate will show the relative comparison of various designs for a specific performance measure. This value can be interpreted in the following three possible ways: • Lower value indicates better performance than the mean • Zero value indicates the mean performance • Higher value indicates worse performance than the mean. The standard deviate for a particular performance can also be used to compare the effects of design factors, and for this one-way ANOVA was performed on the standard deviates of the sections. The analyses were performed on data from all sections and also on subsets of data stratified by different subgrade types, climates and combinations of these. This helps identify the effects of design factors under different site conditions. The standard deviate values of each design were averaged from the various sites to study the overall as well as the interaction effects of design factors with climate and subgrade soil type. To consider all available sections, the test sections were categorized as “distressed” and “non-distressed” for frequency based methods (LDA and BLR). The frequency-based analyses methods (discussed below) will help in identifying the significant factors that discriminate between the two categories.

147 Table 4-3 Calculation of standard deviate for alligator cracking - Alabama (1) Section ID Performance Index Average Standard deviation Standard deviate 0101 23.08 -0.70 0102 90.69 1.36 0103 25.43 -0.62 0104 3.83 -1.28 0105 95.90 1.52 0106 16.12 -0.91 0107 21.97 -0.73 0108 70.45 0.75 0109 75.47 0.90 0110 52.74 0.21 0111 65.33 0.59 0112 10.22 45.93 32.82 -1.09 4.3.2 Extent of distress The effect of the key experimental factors on performance, through the relationship between the magnitude and relative occurrence of the observed distresses, can be observed from the data. Simple bivariate plots between the percentage of test sections that have exceeded various levels of distress for the key performance measures, categorized by experimental design and site factors were plotted to display and explore the data. Note that the effect of climatic zone will only be shown for the wet regions because of the limited number of sites (4 sites) in the dry regions. 4.3.3 Linear Discriminant Analysis Linear Discriminant Analysis (LDA) allows for distinguishing between two or more groups of data. This is done by identifying variables that are significant in classifying the data into various groups. The procedure for predicting membership is to initially analyze pertinent variables where group membership is already known. The details of theoretical background of LDA is available in relevant literature [6, 10, 11]. For example, groups of observations can include one group of pavements with cracks and the second group with no cracks. The method allows for determining which variables discriminate between cracked and non-cracked pavements.

148 4.3.4 Binary Logistic Regression Binary Logistic Regression (BLR) is used often in the case where the outcome variable is discrete (dichotomous). The difference between logistic and linear regression is reflected both in the choice of a parametric model and in the assumptions. This method is based on the maximum likelihood method for determining the parameters of interest. The details of theoretical background of BLR are available in relevant literature [12]. The interpretation of effects for various levels of the categorical variables (independent) is very convenient in terms of the odds ratio when this type of model is used. Logistic regression models are also very useful for discrimination analysis (of various groups) when categorical variables are used as independent variables. 4.4 SITE-LEVEL ANALYSIS METHODS In the site level analysis each section is evaluated based on the performance in comparison with similar designs of a site (state). It is assumed that within each site, climatic conditions, subgrade soil type and traffic volume are identical for all test sections. Thus the main advantage of this analysis is that comparisons are made among those sections that were subjected to similar loading and environmental conditions. Furthermore, construction methods, material sources and surveys are also assumed to be identical within each site. All site-level analyses were conducted using the Performance Indices (PIs) of the sections for various performance measures. The difference in performance is assessed based on average values. The details of analysis are discussed below. Comparisons by Design Factors The site-level analysis consisted of series of comparisons, each focusing on the effect of a particular design/construction factor, for SPS-1 and SPS-2 experiments. Such comparisons are not possible for SPS-8 sections because of the limited number of sections in the experiment. For the site level analysis, each section’s performance was analyzed in terms of its performance index (PI). Comparisons were done at two levels—A and B. In level-A analyses, all designs (0101 through 0112, or 0113 through 0124) at a given site were compared such that only one factor is held common within the sections of each group. For example, in level-A analysis, the effects of

149 HMA thickness [102 mm (4-inch) vs. 178 mm (7-inch)] were studied, within a site, by ignoring base type & thickness, and drainage. In level-B analyses, most of the factors are ‘controlled’ for comparisons. In other words, individual sections within a given site are paired such that all but one design parameter are the same. This parameter is the factor being studied. Comparing a given pair of sections will allow for determining the effect of the particular design factor, with the highest possible level of constraint (level-B). In this case, there are four factors being studied, so the highest possible number of constraints is three. For example, comparing sections 0111 and 0112 (SPS-1) allows for determining the effect of base thickness [203 mm (8-inch) ATB versus 305 mm (12-inch) ATB], while comparing sections 0216 and 0220 (SPS2) allows for determining the effect of base type (DGAB versus LCB). Table 4-4 and Table 4-5 show possible comparisons within a given site in SPS-1 and SPS-2 experiments, respectively. The relative effects of levels within each design factor were studied based on the ratio of mean performance of the sections corresponding to a level over the mean performance of all levels of the factor. A sample calculation of relative performance is presented in Table 4-6. In the table, the comparison of relative performance indicates that pavement sections with 178 mm (7-inch) HMA surface thickness are performing better than those with 102mm (4-inch) HMA surface thickness, since the relative performance is lower for sections with 178 mm (7-inch) HMA surface thickness (0.8 versus 1.2). For factors with two levels (such as HMA surface thickness, PCC thickness, and drainage), the relative performance of each level can range from 0 to 2, a value of 1 indicating no effect of the factor [i.e., the amount of distress (performance) corresponding to the two levels of the factor is the same]. A value less than 1 indicates better performance compared to mean performance of sections corresponding to both the levels of a factor. Consequently, a value higher than 1 indicates worse performance. The best possible performance translates to 0, and the worst possible performance translates to 2. For cases where there is no distress or same level of distress, each level of a given factor will have relative performance of 1 indicating no difference in performance. For factors with more than two levels, similar logic can be extended. For the effect of base type, the relative performance of each base type ranges from 0 to 5, since there are five base types

150 in SPS-1 experiment. In the case of the SPS-2 experiment, for the effect of base type, the relative performance of each base type ranges from 0 to 3, since there are three base types under comparison. A value of 1 for all base types indicates that the amount of distress is the same for all base types. Values close to 1 for all the base types being compared indicate that there is no significant effect of the base type. A higher value indicates more distress (worse performance) for a particular base type. For SPS-1, the worst possible performance translates to 5 (all other base types would show 0, indicating no distress), and the best possible performance translates to 0 (no distress). The relative performance for various levels of the main factors was calculated for all the sites in SPS-1 and SPS-2 experiments, and for each performance measure. The concept of relative performance can be utilized across the sites without considering traffic or age variability because it is calculated at site-level.

151 Table 4-4 Site Level Comparisons for the SPS-1 Experiment Site with Sections 101 to 112 Site with Sections 113 to 124 Effects Level Comparisons Comments Comparisons Comments A (101,102) vs.(103,104) vs. (105,106) vs. (107,108,109) vs. (110,111,112) Ignoring other factors (113,114) vs.(115,116) vs. (117,118) vs. (119,120,121) vs. (122,123,124) Ignoring other factors I. Effect of Base Type DGAB vs. ATB vs. ATB/DGAB vs. PATB/DGAB vs. ATB/PATB B (103 vs. 105) (104 vs. 106) All other factors controlled (116 vs. 118) (115 vs. 117) All other factors controlled A (101,103,105,107,110) vs. (102,104,106,108,111) vs. (109,112) Ignoring other factors (113,115,117,119,122) vs. (114,116,118,110,123) vs. (121,124) Ignoring other factors II. Effect of Base Thickness 203 mm vs. 305 mm vs. 406 mm B (111 vs. 112) (108 vs. 109) All other factors controlled (120 vs. 121) (123 vs. 124) All other factors controlled A (102,103,105,101,104,106) vs. (107,111,112,108,109,110) Ignoring other factors (113,116,118,114,115,117) vs. (120,121,122,119,123,124) Ignoring other factors III. Effect of Drainage B (103 vs. 111) (101 vs. 108) Ignoring base thickness (113 vs. 120) (115 vs. 123) Ignoring base thickness A (102,103,105,107,111,112) vs. (101,104,106,108,109,110) Ignoring other factors (113,116,118,120,121,122) vs. (114,115,117,119,123,124) Ignoring other factors IV. Effect of AC Thickness 102 mm vs. 178 mm B (101 vs. 102) (103 vs. 104) (105 vs. 106) Ignoring the base thickness (113 vs. 114) (116 vs. 115) (118 vs. 117) Ignoring the base thickness

152 Table 4-5 State Level Comparisons for the SPS-2 Experiment Sites with Sections 101 to 112 Sites with Sections 113 to 124 Effects Level Comparisons Comments Comparisons Comments A (201, 202, 203, 204) vs.. (209, 210, 211, 212) Ignoring other factors (213,214,215,216) vs. (221,222,223,224) Ignoring other factors Effect of Drainage DGAB vs. PATB B (201 vs. 209), (202 vs. 210), (204 vs. 212), and (203 vs. 211) All other factors controlled (214 vs. 222) (213 vs. 221) (215 vs. 223) (216 vs. 224) All other factors controlled A (201, 202, 203, 204) vs. (205, 206, 207, 208) vs. (209, 210, 211, 212) Ignoring other factors (213,214,215,216) vs. (217,218,219,220) vs. (221,222,223,224) Ignoring other factors Effect of Base Type DGAB vs. LCB vs. PATB B (201 v. 205 v. 209), (202 v. 206 v. 210), (203 v. 207 v. 211), and (204 v. 208 v. 212) All other factors controlled (213 v. 217 v. 221) (214 v. 218 v. 222) (215 v. 219 v 223) (216 v. 220 v. 224) All other factors controlled A (201, 202, 205, 206, 209, 210) vs. (203, 204, 207, 208, 211, 212) Ignoring other factors (214,215,218,219,222,223) vs. (213,216,217,220,221,224) Ignoring other factors Effect of PCC Thickness 203 mm vs. 279 mm B (201 vs. 204), (202 vs. 203), (205 vs. 208), (206 vs. 207), (209 vs. 212), and (210 vs. 211) By ignoring flexural strength only (213 vs. 216) (214 vs. 215) (217 vs. 220) (218 vs. 219) (221 vs. 224) (222 vs. 223) By ignoring flexural strength only Effect of PCC Strength 3.8 MPa vs. 6.2 MPa A (201, 203, 205, 205, 207, 209, 211) vs. (202, 204, 206, 208, 210, 202) By ignoring only lane width (213, 215, 217, 219, 221) vs. (214, 216, 218, 220, 222, 224) By ignoring only lane width Effect of Lane Width 3.7 m vs. 4.3 m A (201, 204, 205, 208, 209, 212) vs. (202, 203, 206, 207, 210, 211) Ignoring other factors (213,216,217,220,221,224) vs. (214,215,218,219,222,223) Ignoring other factors

153 Table 4-6 Example calculation of relative performance (State 1-Alligator Cracking) 4” AC Thickness 7” AC Thickness Section ID Performance Index Section ID Performance Index 102 90.69 101 23.08 103 25.43 104 3.83 105 95.90 106 16.12 107 21.97 108 70.45 111 65.33 109 75.47 112 10.22 110 52.74 Average 51.59 Average 40.28 Mean Performance (51.59+40.28)/2 = 45.93 Relative performance 51.59/45.93=1.12 Relative performance 40.28/45.93=0.88

154 4.5 METHODS FOR INVESTIGATING APPARENT RELATIONSHIP BETWEEN PAVEMENT RESPONSE AND PERFORMANCE This analysis is aimed at investigating the relationship between the pavement responses (deflections) and performance measures (cracking, rutting, roughness, etc.). The usefulness of such relationships can be further divided in two ways: • To provide an explanatory information for a given performance trend. For example, a relationship between AC pavement rutting and the farthest FWD sensor would indicate that rutting is related to the subgrade. • To predict the future performance. For example, a high initial deflection of a pavement may help predict its future cracking and rutting performance. Relationships were sought by directly relating commonly collected pavement response data to the development of specific distresses, using statistical analyses. This analysis was conducted at the site level as well as for the overall experiment. The following describes statistical techniques used to investigate the apparent relationships between response and performance measures. 4.5.1 Univariate Analysis Univariate and Bivariate analyses are simple statistical methods for data analysis. These methods include determination of data statistics such as mean, standard deviation and data frequencies. Simple histograms and box plots can also be generated to determine data distribution. These methods also allow for determining the degree of dependence between variables. The results of such an analysis can be graphically illustrated. Such an analysis can also provide summary statistics such as the coefficient of correlation. Bivariate analysis can also assist in identifying outliers. This analysis was applied at the site-level for identifying predictive relationships. 4.5.2 Multiple Regression Analysis Regression analyses attempt to explain a dependent variable in terms of many independent (explanatory) variables. The model form (equation) can be either linear or non-linear, and with actual, transformed, or interaction clusters of variables. The model coefficients are estimated using best (least squares) fitting techniques. The objective of this method is to develop models explaining the apparent relationships between pavement performance measures and responses. This analysis was used for investigating explanatory relationship by using the data from the overall experiment.