Long-Term Field Performance of Warm Mix Asphalt Technologies (2017)

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109 is a widely used statistical method for analyzing data using two categorical responses. Instead of providing a yes or no answer to the predictions for crack initiation, the probability of a pavement to crack under a particular condition (material, environment, structure, etc.) will be determined. Depending on the probability results, engineers and/or local agencies can set up different threshold values as a limit of crack initia- tion to aid decision-making. In general, the development of statistically based perfor- mance prediction models involves four steps: • Data collection. Potential data that can be incorporated into the analysis may include but not be limited to the following: – Dependents: pavement performance data, such as crack area, crack length, and rut depth. – Independents: potential influencing factors for a partic- ular cracking distress, such as climate, material proper- ties, traffic, pavement structures, etc. These data should be included based on engineering experience and could vary due to data availability. • Data preprocessing. The existence of collinearity, the ran- domness of data distribution, and other assumptions for the statistical analysis must be checked first to determine the type of regression method to be used, the needs of data transformation, and other data preprocessing needs. • Model development. Statistical analysis is performed to select the optimum number of independents, develop model parameters, and calibrate the models. This step usually can be performed using commercial statistical soft- ware such as SPSS or Minitab. Both crack initiation models and crack propagation models are constructed. • Review of model structure. The reasonableness of the models must be reviewed according to their engineering meanings (influencing factors, trend of relationships, etc.) and vali- dated by extensive field data. Sensitivity analysis also should be performed to determine the effect of individual factors on the overall performance. Introduction A number of statistical methods can be used to determine the relationship between predictor variables and responses, among which multiple linear regression (MLR) is widely used in pavement engineering. However, if collinearity exists between the variables, MLR could result in an over-fitting model that cannot predict new responses well (Hawkins 2004). Even worse, MLR could give incorrect signs for parameters (Yeniay and Göktas 2002). Here, collinearity is defined as a high level of correlation between two predictor variables. Although collinear data can be removed manually from the database, some meaningful data could be discarded accidentally (Darwish et al. 2013). Alternatively, the partial least squares (PLS) method can be used. The PLS method is able to solve collinearity problems and ensure that only the parameters that contribute strongly to the prediction model are used. In addition, the PLS method is suitable for a relatively small dataset, which is practically use- ful for pavement performance predictions because obtaining large amounts of field performance data and laboratory data is usually time-consuming and costly. Specifically, the PLS regression method first determines the number of predictor variables using a combination of leave one out cross validation (LOOCV) and the prediction sum of squares (PRESS) method. This step is important because if more than the required number of predictor variables is selected, more noise would be added to the data and result in over-fitting. If the number of predictor variables is too small, meaningful data for model calibration might be discarded. Next, PLS regression selects the predictor variables accord- ing to standardized coefficients. The standardized coeffi- cients identify the importance of each predictor variable in the model. The higher the standardized absolute value of the coefficients, the greater their role in the prediction model. For crack initiation, a probabilistic-based model is more suitable than a deterministic-based model. This study sug- gests using Binary logistic (BL) regression to develop the probabilistic-based crack initiation model. The BL regression A P P E N D I X G A Framework for Development of Performance Predictive Models Based on Statistical Methods

110 Details of each step are provided below using transverse cracking model development as an example. Data Collection The potential data that could correlate with transverse cracking are given in Chapter 3. Table G.1 presents a sum- mary of all the collected data to be considered as predictor variables for transverse cracking model development. Data Preprocessing Prior to modeling, it is necessary to ensure that the condi- tions of linear regression or normality hold for the data and to determine if any transformations of the responses or predictor variables are needed. For these purposes, a plot of standardized residuals versus fitted values (predicted responses) was used. Figure G.1 (a) shows the residual plot without data transfor- mation. As can be seen, a strong pattern of predicted responses (field cracks) was obtained, which indicates the need for data transformation. Different transformations were tried using the statistical software Minitab, and eventually a natural logarith- mic transformation was selected for its highest prediction qual- ity based on the Box-Cox procedure. Figure G.1 (b) shows the residual plot with transformation. No violation of the assump- tion of constant variance is suggested and no transformation of predictor variables is warranted for the data presented. Model Development The development of the crack initiation model and the propagation model is similar except that the crack initiation model requires additional BL regression analysis. Thus, the development of the crack propagation model is discussed first and then the BL regression analysis of the crack initiation model is explained. Check of Multicollinearity In this study, a variance inflection factor (VIF) was used to check the multicollinearity among the predictor variables. Equation (G-1) was used to calculate the VIF for the ith pre- dictor variable Xi that was listed in Table G.1: = − VIF R 1 1 (G.1)i i 2 where Ri2 = coefficient of multiple determination when Xi is regressed on the other predictor variables. A threshold value of 10 typically is used for the VIF. That is to say, when VIFi is greater than 10, the ith predictor variable Predictor Variables Unit Range IDT strength, 14°F Mpa 2.17-5.56 Creep compliance (D1), -4°F 1/Gpa 0.04-0.16 Creep compliance (D2), 14°F 1/Gpa 0.05-0.18 Creep compliance (D3), 32°F 1/Gpa 0.07-0.71 m-value, creep compliance N/A 0.11-0.46 Work density, 14°F Mpa 0.02-0.13 Air void content % 1.8-9.1 Binder low PG °C -6.5 to -28.4 Binder stiffness, BBR Pa 21.5-414.2 m-value, BBR, -6°C N/A 0.23-0.48 Asphalt content % 4.2-10.0 Effective binder content % 6.7-14.4 Passing #200 sieve % 2.8-11.9 Pavement age year 2-7 Average yearly low-temperature hour hour 0.1-1269.8 HMA thickness inch 2.0-14.3 Overlay thickness inch 1.0-6.0 AADTT N/A 10-3380 Note: The temperatures shown after some predictor variables indicate the test temperature. Table G.1. Predictor variables and their ranges considered in transverse cracking models. (a) (b) St an da rd iz ed R es id ua l Fitted Value St an da rd iz ed R es id ua l Fitted Value Figure G.1. Standardized residual versus fitted values: (a) without transformation of field cracks and (b) with natural logarithmic transformation of field cracks.

111 is considered to be highly correlated (multicollinear) with the other predictor variables. The VIF values calculated in this study indicate that many of the predictor variables hold high VIF values (greater than 10). For example, Figure G.2 shows the multicollinearity between the creep compliance and low-temperature hour, as well as between work density and the bending beam rheometer (BBR) m-value. Therefore, MLR is not suitable for this analysis. A method such as PLS regression that can handle high multicollinearity must be applied. Identification of the Optimum Number of Predictor Variables One of the most critical steps for PLS regression is to deter- mine the number of predictor variables. The number of pre- dictor variables controls the complexity of the model and its predictive ability. The cross-validation selection criterion for the predictor variables used in this study is PRESS. Equa- tion (G.2) defines PRESS. ∑( )= − ( ) = PRESS y yˆ (G.2)i i i n 2 1 where yi = field transverse crack for the ith observation; and yˆ(i) = predicted responses when the regression model is fitted to a sample of n-1 observations with the ith observa- tion omitted. Smaller PRESS values indicate a better predictive quality. Therefore, the number of variables that gives the minimum PRESS should be selected. Figure G.3 shows the PRESS cal- culation results for crack propagation based on the data. As shown, the number of predictor variables was determined to be six because this value corresponds to the lowest PRESS. (a) Cr ee p Co m pl ia nc e, 1 /G pa Low Temperature Hour (<15°F) (b) Fr ac tu re W or k of D en sit y, M pa m-value, BBR Figure G.2. Examples of multicollinearity: (a) creep compliance and low-temperature hour (<15çF) and (b) fracture work density and BBR m-value. Figure G.3. Summary of PRESS results at different numbers of predictor variables for crack propagation. Number of Predictor Variables PR ES S 1.8 1.6 1.4 1.2 1 0.8 0.6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

112 Determination of Model Coefficients Standardized coefficients for each predictor variable were determined using Minitab software to perform PLS regres- sion analysis. Standardized coefficients identify the impor- tance of each predictor variable in the model. The higher the standardized absolute value of the coefficients, the greater their role in the prediction model. For the crack propagation model based on 22 data points (22 pavements with transverse cracking), six predictor variables with the highest standard- ized coefficients (absolute values) were selected and are shown in Table G.2 with their corresponding trend. The positive trend indicates that high values correlate with high transverse crack distress and vice versa. The negative trend indicates that high values correlate with low transverse crack distress and vice versa. Review of Model Structure Post-Model Analysis Based on Engineering Judgment Once a model has been developed, a review of the model variables and coefficients is critical to ensure that the math- ematical model is also compatible with engineering expe- rience. For this example, the trend of the pavement age in the model for development of transverse cracking is negative, which does not match engineering judgment. The reason could be that the crack amounts used for the analysis are different from those in the projects. Some relatively new projects have very high amounts of cracking (e.g., the MN 169 project, with a pavement age of 2 years) due to a cold climate and other possible reasons (poor mix design, etc.), whereas other proj- ects have very few cracks even after a long time of service (e.g., the MD 925 project, with a pavement age of 7 years) because of a warm climate, low traffic counts, or a proper mix design, etc. Furthermore, almost no relationship was found between transverse cracking length and pavement age. In fact, as can be seen from the crack initiation model in Chapter 3, the pavement age, combined with other factors such as cli- mate, has more influence on crack initiation than on crack propagation. Once the crack has started, other factors, such as material properties and pavement thickness, have more impact on the development of cracking and crack length. To address this problem, the pavement age variable was manually excluded from consideration for the crack propa- gation model. Then, the PRESS was calculated again and the optimum number of predictor variables was still six. Next, PLS regression was performed without pavement age. The crack propagation model with predictor variables with the six highest standardized coefficients was selected. The final pre- dictor variables selected for the crack propagation model are listed in Table G.3. All the selected variables seem to be reason- able based on engineering judgment. The crack propagation model developed by the PLS method using the six predictor variables is shown in Equation (G.3). = ( )− − + − − +Y e (G.3)X X X X X X8.825 11.665 9.587 0.0033 0.267 1.047 0.00061 2 3 4 5 6 where Y = transverse crack length, ft/200 ft; e = base of natural logarithm, approximately 2.718; X1 = fracture work density (14°F), MPa; X2 = creep compliance (32°F), 1/GPa; X3 = average yearly low-temperature hour, hr (from AASHTOWare Pavement ME); X4 = percentage passing #200 sieve, %; X5 = overlay thickness, in.; and X6 = AADTT. Model Validation The reasonableness of the model must be validated, pref- erably with an external dataset that is different from the one used for model development. However, procurement of con- sistent field and laboratory data for long-term performance model development is extremely difficult and costly. In this study, the LOOCV method was used because it is always com- plete and every single data point of the limited field data can be used. LOOCV repeatedly divides data into two sets: a training data set and a testing data set. The training data set is used to construct the model, and the testing data set is used to vali- date the model. In statistical software Minitab, the LOOCV can be performed at the same time as the PLS regression. Specifically, for each potential model, the LOOCV omits one response and recalculates the model without including Positive Trend Predictor Variables Negative Trend Predictor Variables Thickness of HMA total layer Fracture work density AADTT Percentage passing #200 sieve Thickness of HMA overlay Pavement age Table G.2. Initial predictor variables selected for crack propagation. Positive Trend Predictor Variables Negative Trend Predictor Variables Average yearly low-temperature hour Fracture work density AADTT Creep compliance Percentage passing #200 sieve Overlay thickness Table G.3. Final predictor variables selected for crack propagation.

113 the omitted response. The LOOCV then predicts the omit- ted response using the recalculated model and calculates the residual value. Such steps are repeated until all the responses are omitted and fitted exactly once. Figure G.4 (a) shows the relationship between field- measured and predicted transverse cracking according to Equation (G.3), with the HMA and WMA results separated. This model has a coefficient of determination (R2) value of 0.82, standard error of the estimate of 0.47, and a Mallow’s Cp of 7.0, all of which indicate good prediction quality. The regression model has the capacity to predict transverse crack- ing for both HMA and WMA pavements. Figure G.4 (b) presents the validation of the crack propagation model using the LOOCV method. As shown, most of the validated data are located fairly close to the line of equality. The R2 value of 0.6 and standard error of the estimate of 0.79 illustrate a rela- tively good validation result. Sensitivity Analysis Sensitivity analysis was performed to test the robustness of the model prediction results considering the possible pres- ence of uncertainty. The prediction results (not extremely high or low) were evaluated when the variables were varied within specific ranges. Many methods have been developed to carry out sensitivity analysis, and the one used in this study is the one-at-a-time (OAT) method. For this method, one fac- tor at a time is varied while the others are kept at their base- line values. By using OAT analysis, the effect of an individual input on output change can be clearly evaluated. In contrast to the OAT method, two-variable analysis also can measure the output variation by considering the interaction effect of two variables. This analysis was also used in this study. In terms of the OAT method, a 10 percent increase and decrease of input variables (±10%) was applied, as recommended (Schwartz et al. 2011). As an example, sensitivity analysis results for the crack prop- agation prediction model are shown in Figure G.5. Figure G.5 (a) through (f) indicate that the changes in the amount of transverse cracking are acceptable with the variations (±10%) of the fracture work density, creep compliance, hour of low temperature, percentage passing #200 sieve, thickness of the overlay, and AADTT, respectively. Two-variable sensitivity analysis also shows that the prob- ability changes for transverse cracking are within a reason- able range with the variation of two variables at the same time. Therefore, the prediction ability of the crack propagation model is robust and no uncertainty was found. Crack Initiation Model Development and Validation For the crack initiation model, a PLS procedure that is sim- ilar to the one used for developing the crack propagation model was applied in conjunction with the BL regression method to develop a probabilistic-based predictive model. BL regression is a widely used statistical method for ana- lyzing data with two categorical responses. A BL regression model allows prediction of the probability of crack initiation under different scenarios. By comparison, linear regression techniques (MLR and PLS regression) are used with a con- tinuous response. The BL crack initiation model is unique, however, in that instead of simply providing a binary result of “yes” or “no” for crack initiation, the BL model estimates the probability that the pavement will initiate a crack under the current condition. A higher probability will indicate a higher change of crack initiation. Figure G.4. Crack propagation model development and validation: (a) relationship between predicted and field-measured transverse cracks and (b) validation of transverse crack propagation model (SEE = standard error of the estimate). (a) 0 2 4 6 8 0 2 4 6 8 Pr ed ic te d Tr an sv er se C ra ck (L n) , ft /2 00 ft Field-Measured Transverse Crack (Ln), ft/200 ft HMA WMA Line of Equality R2 = 0.82 SEE=0.47 0 2 4 6 8 0 2 4 6 8 V al id at ed T ra ns ve rs e Cr ac k (L n) , ft /2 00 ft Field-Measured Transverse Crack (Ln), ft/200 ft Validated Line of Equality R2 = 0.6 SEE=0.79 (b)

114 (a) (c) (e) 0 20 40 60 80 100 0.00 0.03 0.06 0.09 0.12 Density of Fracture Work, Mpa Tr an sv er se C ra ck , ft /2 00 ft Tr an sv er se C ra ck , ft /2 00 ft 0 20 40 60 80 100 0.0 0.2 0.4 0.6 Creep Compliance, 1/Gpa Tr an sv er se C ra ck , ft /2 00 ft 0 20 40 60 80 100 0 200 400 600 Hour of Low Temperature, Hour Tr an sv er se C ra ck , ft /2 00 ft 0 20 40 60 80 100 0.0 2.0 4.0 6.0 8.0 10.0 Percentage Passing #200 Sieve, % Tr an sv er se C ra ck , ft /2 00 ft 0 20 40 60 80 100 0.0 1.0 2.0 3.0 4.0 5.0 Thickness of Overlay, in. Tr an sv er se C ra ck , ft /2 00 ft 0 20 40 60 80 100 0 500 1000 1500 AADTT (f) (d) (b) Figure G.5. Sensitivity of field transverse crack amount to variable changes: (a) fracture work density, (b) creep compliance, (c) hour of low temperature, (d) percentage passing #200 sieve, (e) thickness of overlay, and (f) AADTT.

115 Arbitrary values were assigned to two groups of pave- ment transverse cracking: 0.02 for pavement sections with- out cracking (yi = 0.02) and 1.0 for pavement sections with recorded cracking (yi = 1). The probability model is shown in Equation (G.4), where P indicates the probability of the initiation of transverse cracking, and therefore 1-P means the probability of no crack initiation. ( )= = + ( )− − + − + − P y e ˆ 1 1 1 (G.4)i 8.42 0.0019X 0.284X 1.52X 0.867X1 2 3 4 where Pˆ = probability of initiation of transverse cracking, %; yi = ith pavement section; e = base of natural logarithm, approximately 2.718; X1 = low-temperature hour, hr; X2 = percentage passing #200 sieve, %; X3 = IDT strength (14°F), MPa; and X4 = pavement age, year. Using the crack initiation model, the probability of crack- ing for each project was estimated; Figure G.6 (a) shows these results as the solid bars. Of the projects with transverse cracks, 15 out of 22 pavement projects were predicted to have higher than 50 percent probability for crack initiation. In the without transverse cracking group, shown in Figure G.6 (b), 36 of 39 pavement projects were predicted to have less than 50 percent probability for crack initiation. These findings indicate that the prediction results match the field conditions well. To validate the model, the LOOCV method was used. Each sample data item was validated once using LOOCV; Figure G.6 (b) presents the results as the bars with grids. The cross-validated data have almost the same probability range distribution as the predicted data, indicating the model’s good prediction power. Furthermore, when new validation data are introduced, the model should still work well. Sensitivity analysis was conducted for the crack initiation model as well and the results are shown in Figure G.7. It appears that for sections both with and without cracks, the change in the probability of transverse crack initiation are acceptable within the variation (±10%) of IDT strength, hour of low temperature, percent passing the #200 sieve, and pave- ment age (age). Two-variable sensitivity analysis also shows that the changes in the probability of transverse crack initiation are within a reasonable range. Therefore, the prediction ability of the crack initiation model is robust and no uncertainty is found. It is worth noting that although the crack initiation probability is not very sensitive to low temperature hour and percent passing the #200 sieve, the combined effect of varying, for example, IDT strength and low temperature hour together can greatly affect the predicted probability. (a) 0 10 20 30 0-25 25-50 50-75 75-100 3 4 4 11 5 4 2 11 N um be r o f P av em en t Se cti on s Probability Range, % Predicted Validated 0 10 20 30 0-25 25-50 50-75 75-100 28 8 1 2 26 10 1 2 N um be r o f P av em en t Se cti on s Probability Range, % Predicted Validated (b) Figure G.6. Validation of transverse crack initiation model: (a) with transverse cracks and (b) without transverse cracks.

116 (a) (c) (d) 0 20 40 60 80 100 100 150 200 250 Hour of Low Temperature, Hour With Cracks Without Cracks Pr ob ab ili ty o f T ra ns ve rs e Cr ac k, % 0 20 40 60 80 100 2.0 3.0 4.0 5.0 IDT Strength, Mpa With Cracks Without Cracks Pr ob ab ili ty o f T ra ns ve rs e Cr ac k, % 0 20 40 60 80 100 2 4 6 8 Percent Passing #200 Sieve, % With Cracks Without Cracks Pr ob ab ili ty o f T ra ns ve rs e Cr ac k, % 0 20 40 60 80 100 2 3 4 5 Pr ob ab ili ty o f T ra ns ve rs e Cr ac k, % Service Life (Age), year With Cracks Without Cracks (b) Figure G.7. Sensitivity of field transverse crack probability to variable changes (a) IDT strength; (b) hour of low temperature; (c) percent passing #200 sieve, and (d) pavement life (age).

Abbreviations and acronyms used without definitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FAST Fixing America’s Surface Transportation Act (2015) FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TDC Transit Development Corporation TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S.DOT United States Department of Transportation

TRA N SPO RTATIO N RESEA RCH BO A RD 500 Fifth Street, N W W ashington, D C 20001 A D D RESS SERV ICE REQ U ESTED N O N -PR O FIT O R G . U .S. PO STA G E PA ID C O LU M B IA , M D PER M IT N O . 88 Long-Term Field Perform ance of W arm M ix A sphalt Technologies N CH RP Research Report 843 TRB ISBN 978-0-309-44633-4 9 7 8 0 3 0 9 4 4 6 3 3 4 9 0 0 0 0