Statistical Modeling for the Characteristics of Open Graded Friction Course Asphalt

An open-graded friction course (OGFC) is a special type surface layer of traditional Dense Graded Hot Mix Asphalts (DGHMA) pavement that is increasingly being used around the world due to its various benefits, such as, frictional, safety and environmental, etc. In this research, selective laboratory OGFC properties were statistically modeled depends on mix design inputs for two purposes or aims; mix inputs significant and prediction the OGFC properties according mix inputs. Principally, Indirect Tensile Strength (ITS), water sensitivity (TSR), and permeability (K) were selected from mechanical, durability, and volumetric properties, respectively as an output property; they represent the dependent variables for each model. While, fillers as conventional mineral filler or Ordinary Portland Cement (CMF, or OPC), binder content (BC), and polymer content (SBS) are represented inputs or the independent variables for all models. The generated models offered a vital achievable tool for prediction (e.g., their R2 are 0.781, 0.82 1 and 0.820, respectively, for the mentioned model’s properties), also it helped to scale the significant of each independent variable (e.g., filler type significantly affect water sensitivity properties, its correlation was 0.752). This study reveals that the statistical modeling is achievable and offers a dynamic tool to describe the characteristics and performance of OGFC mixture in term volumetric, mechanical and durability properties.

Durability can identify as the resistance of the mixture to subsequent failures and distresses within the lifespan of the pavement layers under different loading and weather conditions. Raveling was reported as the most important distresses in OGFC in addition to the common distresses such as rutting (due to studded tires), reflective cracking, and delamination (which is principally caused by construction problems) [14].
Numerous causes for raveling development like hardening due to high rate of oxidation as a result of elevated air voids [15] [16], deficiency in compaction [17], insufficient temperature during construction [18], and volumetric properties problems (e.g., incorrect calculation of binder content and/or air void content or lack of control of these properties during construction ) [19] [20]. Numerous numerical and experimental models have been recommended to enhance understanding and predicting of raveling occurrence. The conclusion of these efforts is that raveling is mostly influenced by the total air voids content in the mixture and its binder content [21], however different parameters like the number of cold days at the project site and the course aggregate fraction also showed to influence both the appearance and magnitude of this distress [22] [23].
However, the main purpose of this study is to develop statistical models for predicting some volumetric, mechanical, and durability properties according to the variation in some main mix parameters. This prediction process could facilitate the understanding of the role of these parameters in general mix characteristics. Therefore, this paper will discuss the analysis process for built and validate the prospective models.

Raw material.
Limestone aggregates were supplied from local quarries, which is located to the west of Karbala. The physical properties of the aggregates present in Table (1). They were crushed limestone aggregate with a degree of crushing exceed 90%. The ASTM D7064 proposed gradation range for OGFC and the middle range of each size was selected to prepare the mixes in this research work. Figure (1) displays the particle size distribution, which falls within the suggested lower and upper limits in ASTM D7064 gradation. The type and quantity of filler have an important role on the overall mixture performance and have a direct effect on mechanical properties for the OGFC. Two types of fillers were used in this research; namely, Ordinary Portland Cement (OPC), and Conventional Mineral Filler (CMF). Table (2) identifies physical and chemical properties for used fillers. The used bitumen was nominated with penetration grade (40-50), it was supplied from Al-Neasseria in the South of Iraq. The selected neat bitumen cement meet the specification in ASTM D946 [27]. Also, it was modified with SBS polymer called Kraton D1192 ESM. the properties of the neat and modified bitumen are presented in Table (3). while Table (4) illustrates the SBS polymer properties. The process of polymer-modified asphalts is not common procedure in Iraq. Thus, the SBS polymer and asphalt cement were prepared in the university of Kerbala laboratory.  Mixture design and analysis.
Two OGFC mix types were included in this study i.e., traditional and modified mixes. The traditional mixture contained neat binder grade 40-50 type, virgin Coarse and fine aggregates, with CMF, OPC filler types. The selected of aggregate gradation was based on ASTM D7064 [32] as cleared previously in Figure (1). Therefore, to determinate the characteristics of this mix, six different asphalt contents ranging between 5%-7.5% in increments of 0.5 % is introduced. The bitumen contents 6%-7% were found, corresponding to best durability and volumetric properties that satisfy limitations of ASTM D7064 criteria; i.e., cantabro, air-voids, and draindown test results.
In this study, only three parameters where selected from mechanical, volumetric and durability properties to develop statistical models. However, the volumetric properties of OGFC mixes with twofiller types and four polymer content and six-asphalt content were characteristic. Main indexes like bulk density, air void, effective Porosity, VFB, and VMA, permeability, draindown, were determined and analyzed according to ASTM D7064 [32], while the permeability was selected to represent the volumetric properties. The mechanical properties of OGFC were characterized by many tests; i.e., Indirect Tensile strength, Marshall Stability and flow, wheel truck test, skid resistance with the same mix design inputs. While, Indirect tensile strength (IDT) test according to AASHTO T283 [33] was selected as an important test to represent the mechanical properties of the OGFC. Similarly, the durability properties were evaluated by tensile strength ratio (TSR) test according to AASHTO T283 [33]. It is worth mentioned that in details models for each volumetric, mechanical, and durability properties will present in future publication.

Collected Data.
The input data (results) of permeability (as an average of four samples results), ITS (as an average of three samples results), and TSR (as an average of three set results) each set comprised two conditioned and unconditioned samples). A total of 639 test results were collected and analyzed in (SPSS) software to extract the averaged results which used to build the model, the input averaged data are as presented in Table (

Model preparation.
Model preparation from the outcomes that obtained in the experimental work is an essential in this research. Empirical modeling was achieved using analysis tools of SPSS software. The variables involved in the empirical modeling were filler types, binder content, and percent of SBS. The collected averaged results are 72,40, and 37 for each test of permeability, tensile strength ratio, and indirect tensile strength, respectively, consequently, a total of 639 test result were collected and analysis. The results were divided randomly into 49, 30, 28 result to generate the model and the other 23, 10, 9 for each test of permeability, TSR, and ITS, respectively, were used to validate the model. The first step to model preparations is to the correlation between the variables using SPSS Pearson's correlation. Many combinations of variables were used starting from only constant to quadratic form of the variables with the incorporation of multiple terms of the various variables discussed above.
To achieve the obligations for the built models, program testing needs to determine dependent and independent variables of the developed models. The variables and the code adopted for calculation are presented in Table (

Result and Discussion for The Prediction Models.
SPSS software was used to build and analysis the models. For the simplification the linear models were tried first, unfortunately, the trials that made for linear models were unsuccessful to represent the observations. However, it was found that all prediction models were nonlinear, as will see hereafter.

Building the permeability model.
As mentioned previously the Permeability was selected to build a model from many volumetric parameters. This selection is established on the believe that it is the most important character. Modeling permeability to filler type, binder content, and polymer content was conducted. Many models were tried (linear, multiple and nonlinear models). It was observed that all linear models were failed to estimate accurate predicted values of permeability. Tables (7) demonstrates samples of the tried models, whereas low values of (R²) are the predominant for both regression and model validation. It is worth mentioned that other testing parameters than R² were conducted to test the validity of the models, but the values of R² are only presented for simplification and prevent dilatation.
On the other hand, after many trials a nonlinear model was determined with reasonable accuracy. The analysis results of adopted nonlinear model is shown in Tables (8), (9), and (10). The model's analysis consists of the analysis of goodness fitting and variance for observed and predicted result. The model adequacy is illustrated in figure (2). The following can be recognized from the analysis process: 1.  (8) demonstrates that the filler type has the most significant correlation to permeability, then binder content and lastly polymer content. Although, binder content is believed to be the most important, but we have to remember that the used ranges of building the model is limited. 3. Table (10) states that the MSE is low, which is good for the significant of the model. 4. Table (9) shows the parameter of the developed model and its limitation with Confidence Interval of 95%. 5. Table (10) discloses that the sum of regression is higher that sum of residue which is sustained the significant of the model. While, from the same table, the high value of the R-Square (0.781) indicates an acceptable prediction. 6. Figure (2) indicates that acceptable scatter can recognized between predicted and observed K values, furthermore, almost all value within the significant level boundaries.

Figure 2comparisons between the experimental and predicted values of permeability.
Building the Tensile strength ratio modal.
As mentioned previously the TSR was selected to build a model from many durability parameters. This selection is established on the believe that it is the most important durability character. Modeling TSR to filler type, binder content, and polymer content was conducted. Many models were tried (linear, multiple and nonlinear models). It was observed that all linear models were failed to estimate accurate predicted values of TSR. Tables (11) demonstrates samples of the tried models, whereas low values of (R²) are the predominant for both regression and model validation. It is worth mentioned that other testing parameters than R² were used to test the validity of the models, but the values of R² are only presented for simplification and prevent dilatation.
On the other hand, after many trials a nonlinear model was determined with reasonable accuracy. The analysis results of adopted nonlinear model are shown in Tables (12), (13), and (14). The model's analysis consists of the analysis of goodness fitting and variance for observed and predicted result. Figure (3) demonstrates the adequacy of model. The following can be recognized from the analysis process: 1. Table (12) explains the bivariate Pearson Correlation between variables. The same table shows that the independent variables have very low to absent of correlation between each other, which is good for the accuracy of the model. 2. Table (12) demonstrates that the filler type has the most significant correlation to TSR, then polymer content and lastly binder content.
Confidence interval 95% 3. Table (14) states that the MSE is low, which is good for the significant of the model. 4. Table ( 13) shows the parameter of the developed model and its limitation with Confidence Interval of 95%. 5. Table (14) discloses that the sum of regression is higher that sum of residue which is sustained the significant of the model. While, from the same table, the high value of the R-Square (0.821) indicates a good prediction, thus from this value a conclusion can draw that the developed model for Tensile strength ratio is acceptable. 6. Figure (3) indicates that acceptable scatter can recognized between predicted and observed operability values, furthermore, almost all value within the significant level boundaries.

Figure 3comparisons between the experimental and predicted values of TSR.
Building the Indirect tensile strength model.
As mentioned previously the ITS was selected to build a model from many Mechanical parameters. This selection is established on the believe that it is the most important mechanical character. Modeling ITS to filler type, binder content, and polymer content was conducted. Many models were tried (linear, multiple and nonlinear models). It was observed that all linear models were failed to estimate accurate predicted values of ITS. Tables (15) demonstrated samples of the tried models, whereas low values of (R²) are the predominant for both regression and model validation. It is worth mentioned that other testing parameters than R² were used to test the validity of the models, but the values of R² are only presented for simplification and prevent dilatation.
On the other hand, after many trials a nonlinear model was determined with reasonable accuracy. The analysis results of adopted nonlinear model are shown in Tables (16), (17), and (18). The model's analysis consists of the analysis of goodness fitting and variance for observed and predicted results. Figure (4) demonstrates the adequacy of model. The following can be recognized from the analysis process: 1.  (16) demonstrates that the polymer content has the most significant correlation to ITS, then filler type and lastly binder content. 3. Table (18) states that the MSE is low, which is good for the significant of the model. 4. Table (17) shows the parameter of the developed model and its limitation with Confidence Interval of 95%. 5. Table (18) discloses that the sum of regression is higher that sum of residue which is sustained the significant of the model. While, from the same table, the high value of the R-Square (0.820) indicates a perfect prediction, thus from this value a conclusion can draw that the developed model for ITS is acceptable. 6. Figure (4) indicates that acceptable scatter can recognize between predicted and observed operability values, furthermore, almost all value within the significant level boundaries.

Conclusion.
From the statistical analysis of this research study, the following can be concluded: 1. General well-known linear and nonlinear model offered by available software could not represent the resulted values of mechanical, volumetric and durability properties in acceptable models.
2. Modeling the OGFC volumetric, mechanical, and durability characteristics with reference to mix design inputs is achievable and satisfactory in terms of prediction and the significant of input parameters with more complicated multi-variable non-liner models. 3. Permeability model is proven to be predictive from filler type, polymer content, and binder content.
At the same time and within models' boundaries, the filler type has the most significant correlation to permeability, then binder content and lastly polymer content.
4. Moisture sensitivity model is proven to be predictive from filler type, polymer content, and binder content. At the same time and within models' boundaries, filler type has the most significant correlation to TSR, then polymer content and lastly binder content 5. ITS model is proven to be predictive from filler type, polymer content, and binder content.
Simultaneously and within models' boundaries, polymer content has the most significant correlation to ITS, then filler type and lastly binder content.

CONFLICT OF INTERESTS.
-There are no conflicts of interest.