This article was submitted to Construction Materials, a section of the journal Frontiers in Built Environment
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Asphalt pavements are subjected to major distresses like fatigue, rutting, and lowtemperature cracking due to repeated traffic loading and climatic conditions. The modification of the asphalt binder (a major component of an asphalt paving mixture) using additives helps in minimizing the possibility of pavement distresses. The cement additive was used in this study at cementtoasphalt (C/A) percentages of 0, 10, and 20% by volume. The main objective of the study was to investigate the impact of C/A percentage, temperature, and loading frequency on the rutting resistance of asphalt binders using statistical analysis. Two aging conditions were also used: unaged condition and shortterm aging condition in the rolling thinfilm oven (RTFO). The dynamic shear rheometer (DSR) test was used to characterize the asphalt binders at ten loading frequencies (0.1, 0.3, 0.6, 1, 1.59, 3, 5, 7, 8, and 10 Hz) and four temperatures (58, 64, 70, and 76°C). These combinations were used to cover a wide range of combined conditions and to follow the hightemperature range for the Superpave performance grade (PG) system. Multiple statistical analyses [the oneway analysis of variance (ANOVA) and correlation tests] were performed to identify the relation between the tested variables and the rutting parameter (G*/sinδ). Findings of the study have shown that the loading frequency has a significant effect on the rutting parameter for unaged and RTFOaged asphalt binders under different temperatures and using different C/A percentages. Regression analysis was conducted to depict an accurate model that can predict the rutting parameter (G*/sinδ) for each aging condition. Based on the regression analysis, nonlinear power models were developed for the rutting parameter of four groups: unaged unmodified, unaged cementmodified, RTFOaged unmodified, and RTFOaged cementmodified asphalt binders with the coefficient of determination (
Stresses develop inside the pavement structure as a result of repeated traffic loading and climatic conditions. Therefore, the utilized mixtures need to sustain several distress stimuli throughout their service life (
One of the main modifications was made to the cement asphalt concrete mix, to help withstand the variation in temperatures without showing failure under the existing distresses. Multiple studies were conducted to assess the effect of filler additives (in general) on the performance of asphalt mixtures under high temperatures. One study tested the effect of changed filler materials in the mix on the mechanical performances through the resilient modulus, dynamic creep, and indirect tensile tests (
Based on the previous studies of the literature, it is clear that CMA binders significantly enhance pavement resistance against common distresses, such as rutting. However, no previous studies have been conducted to assess the impact of loading frequency on the behavior of cementmodified asphalt binders. Therefore, the present study aims at evaluating the impact of changing the C/A percentage on the rheological properties of CMA binders at different temperatures and loading frequencies. Additionally, all investigations were carried out for both unaged (fresh) asphalt binders and asphalt binders aged for a shortterm in the rolling thinfilm oven (RTFO). The data were collected using experimental testing, namely, using the dynamic shear rheometer (DSR) test. Following this, statistical analysis was performed to assess the impact of each mentioned parameter on the rheological behavior of the CMA binders. The oneway analysis of variance (ANOVA) and correlation tests were used to depict the relationship between all parameters and the binder performance. Finally, a regression analysis was conducted to predict the rutting resistance parameter using the abovementioned parameters for both aged and unaged binders.
The study approach has been divided into two major parts: laboratory work was presented by testing the different CMA binder samples using the dynamic shear rheometer (DSR) test and statistical analysis was presented by the ANOVA test, correlation test, and regression model development.
The original (fresh) asphalt binder used in this study is a 60/70penetration grade asphalt binder (PG 64–10 based on the Superpave Performance Grading System). The Portland cement material used in the study was obtained from a local source. The ordinary Portland cement is the type of cement used in this study. The properties of the asphalt binder and cement are shown in
Properties of materials.
Asphalt binder  Cement  

Property  Value  Property  Value 
Penetration (0.1 mm)  60/70  Type  Ordinary Portland cement 
Specific gravity  1.01  Specific gravity  3.12 
Softening point (°C)  50  
Ductility (cm)  115  
Flash and fire points (°C)  300 and 305  
Performance grade (PG)  PG 6410 
Cementmodified asphalt binders were prepared at three percentages: 0%, 10%, and 20% by volume. The 0% represents the control asphalt binder where no cement is added to the asphalt binder. The specific gravities of the asphalt binder and the cement material were obtained (1.01 and 3.12, respectively) to be used in estimating accurately the amount of cement to be added to the asphalt binder at each C/A percentage. A highshear mixer was used to mix the cement with the asphalt binder at a high rotational speed of 2000 rpm for 15 min at a high temperature ranging between 160°C and 170°C.
The dynamic shear rheometer (DSR) shown in
Dynamic shear rheometer (DSR) used in the study.
Schematic diagram of the DSR test.
The DSR test is carried out by applying shear force on the binder set between upper and lower oscillation plates, with an oscillation angle of 10 rad/s. The DSR test provides measurements of the complex shear modulus (G*) value and the phase angle (δ) of the asphalt binder. The complex modulus value represents the stiffness of the asphalt binder, while the phase angle represents the lag in the response of the asphalt binder (viscoelastic behavior). For instance, at 0°, 90°, and 0°–90° phase angles, the asphalt binder shows elastic, viscous, and viscoelastic behavior, respectively (
To resist rutting in asphalt pavements, an asphalt binder with high stiffness and elastic behavior is needed. For this reason, in the criteria of the Superpave system, minimum requirements were set for the rutting parameter (G*/sinδ) values of 1.0 and 2.2 kPa for the unaged (fresh) and RTFOaged asphalt binders, respectively. On the other hand, to resist fatigue cracking in asphalt pavements, an asphalt binder with low stiffness (soft) and high elastic parts is required. Therefore, the Superpave system specifies a maximum limit for the fatigue parameter (G*sinδ) value of 5,000 kPa for the PAVaged asphalt binders.
The present study included multiple statistical analyses in order to enhance the knowledge regarding the effect of varying the surrounding conditions such as temperature and loading frequency on different C/A percentage samples. The conducted statistical analyses were ANOVA and correlation tests. Furthermore, a regression model was established to come up with a model that can predict the rutting parameter depending on the C/A percentage used in the mix, temperature, and the expected loading frequency on the pavement. The obtained data set from the experimental testing included the following:
• 10 loading frequencies (0.1, 0.3, 0.6, 1, 1.59, 3, 5, 7, 8, and 10 Hz)
• 4 temperatures (58, 64, 70, and 76°C)
• 3 CMA binder percentages (0%, 10%, and 20%)
• 2 Aging levels; unaged (fresh) binders and short (RTFO)aged binders
• Total of 240 DSR tests, 120 for each aging level
There are two major types of the ANOVA test: oneway ANOVA and twoway ANOVA. Oneway ANOVA is a statistical test implemented to compare the variance in the means group with one independent variable. Therefore, oneway ANOVA gives two possible descriptions for the tested groups: null hypothesis in which there is no difference between the groups and equality between means or alternative hypothesis in which there is a difference. Conducting multiple ttests by evaluating the tested groups together is the same as conducting the oneway ANOVA test. However, oneway ANOVA assumes that the tested sample follows a normal distribution behavior and variance obtained from the data in the different tested groups is the same. On the other hand, twoway ANOVA is a more advanced form of oneway ANOVA in which it tests the significance of two independent variables with the other dependent variables. Moreover, twoway ANOVA assumptions are the same as those of oneway ANOVA; however, it assumes that the tested independent variables should be in categorical independent groups.
In this study, to evaluate any significant differences between the three factors considered in the study (C/A percentage, temperature, and loading frequency), the oneway ANOVA statistical test was performed. The
The study implemented the correlation test in order to determine if one of the testing factors had an effect on the outcome rutting parameter of the CMA binders. The correlation test could measure the strength of two numerically measured and continuous parameters. The indicator parameter is defined as the correlation coefficient and ranges between −1 and 1, depending on the strength of the relationship between the tested variables (
There are several types of regression analyses depending on the complexity of the relation between the dependent variable and the independent variables and the number of independent variables affecting the dependent variable. The two main types of regression analyses are linear and nonlinear regression analyses. Nonlinear regression is used when the existing data are presented using a scatter plot, and the data show a form of a curvilinear line. The nonlinear regression analysis predicts the best possible function of independent variables to predict the dependent variable in the following form:
However, linear regression is implemented when the scatter plot shows a straight line between the dependent and independent variables. Therefore, the regression analysis is performed to check the multiple possibilities of nonlinear relations such as polynomial of higher than the 2nd order, exponential, or logarithmic relationships. The regression analysis gives an indication of the accuracy of the estimated relationship between the tested independent variables and dependent variables. Rsquared (
The
In this study, the tested dependent variable was set to be the rutting parameter and the independent variables were set to be the C/A percentage, temperature, and loading frequency. Therefore, scatter plots were utilized to check the type of relation between the dependent variables and independent variables in order to identify the best fitting shape of the model. In this test, the provided set of data is a total of 120 points for each aging criterion with a testedtochecked ratio of 70/30.
The effect of the addition of cement to the asphalt binder on the rheological properties of asphalt binders is discussed in this part. The cementmodified asphalt binders at percentages of 0%, 10%, and 20% were evaluated using the DSR test at different temperatures and loading frequencies for the unaged and RTFOaged conditions. Moreover, the strength of the relationship between changing the temperature and loading frequency was assessed using multiple statistical analysis methods such as the correlation test, the oneway ANOVA test, and the regression modeling test using SPSS software.
The oneway ANOVA test checked whether there were any significant differences between the 3 C/A percentages at once in both the unaged and RTFOaged samples. The
Oneway ANOVA test results.
Asphalt binder  The ANOVA test outputs  ANOVA results for rutting 

Unaged asphalt binders  0% variance  4,570,041 
10% variance  10,328,754  
20% variance  2,263,504  

0.01316  
RTFOaged asphalt binders  0% variance  26,992,970 
10% variance  66,818,096  
20% variance  10,171,406  

0.00434 
In this study, the correlation test was conducted on the unaged as well as RTFOaged cementmodified asphalt using different C/A percentages under different loading frequencies for each of the tested temperatures. The effect of adding cement to asphalt binders on the performance of CMA binders was investigated under different loading frequencies (0.1, 0.3, 0.6, 1, 1.59, 3, 5, 7, 8, and 10 Hz) and at the temperatures of 58, 64, 70, and 76°C using the DSR test. The shear complex modulus (G*) and phase angle (δ) values after shortterm aging for each asphalt binder were used for pavement performance prediction against rutting distress.
A histogram for shear complex modulus (G*) and phase angle (δ) values versus loading frequency (sample: RTFOaged 10% cementmodified asphalt binder at 64°C).
Correlation test results between the temperature and C/A percentage variables for the unaged and RTFOaged CMA binders.
Asphalt binder aging classification  C/A percentage (%)  Temperature (°C)  

58  64  70  76  
Unaged CMA  0  0.998  0.994  0.994  0.995 
10  0.997  1.000  0.999  0.999  
20  0.996  0.998  0.996  0.999  
RTFOaged CMA  0  0.996  0.998  0.999  0.999 
10  0.995  0.998  0.995  0.974  
20  0.996  0.999  0.999  0.999 
The correlation results show a minimum value of the Pearson R coefficient of 0.974 for the unaged CMA using a 10% C/A percentage under 76^{o}C. Hence, the Pearson R coefficient ranges between 0.994 to 1.000 and 0.974 to 0.999 for the unaged and RTFOaged CMA; the correlation is considered almost perfect which indicates that changing the temperature has a significant impact on the performance of the rutting parameter in which all the results tend to approach one, that is, very strong (almost perfect) correlation.
As per the previously conducted statistical analysis which had shown that changing the C/A percentage and loading frequencies have a significant effect on the rutting parameter and the data are correlated, the regression model analysis was conducted to develop an accurate model that can predict the rutting parameter. The regression analysis was conducted using binderbased hypotheses.
This testing hypothesis was conducted on two main criteria based on modification and aging criteria which provided a total number of 40 points for each unmodified group and 80 points for each modified group. As the tested C/A percentages are 0%, 10%, and 20%, the unaged and RTFOaged CMA points were divided into 40 unmodified CMAs (0% C/A percentage) and 80 points for the modified CMAs (10% and 20% C/A percentages). The temperature and C/A variables were tested separately with the rutting parameter to account for the behavior of the existing relation between each variable with the rutting parameter. Scatter plots have been implemented to investigate the relationship between each variable against the rutting parameter for each aging group. As shown in
Nonlinear regression models of rutting parameter for the unaged and RTFOAged CMA binders.
Modification condition  Aging criteria  Adjusted 
Sum of squares ratio  ANOVA results  Prediction model  

Residual  Regression  
Unmodified asphalt binders  Unaged  0.986  0.992  2.761×10^{8}  2.2875×10^{6}  Y = 1.103 × 10^{13} F^{0.979} T^{−5.719} 
RTFOaged  0.996  0.998  3.749×10^{6}  1.7155×10^{9}  Y = 5.343×10^{1}°F^{−29.290} T^{0.820}  
Modified CMAs  Unaged CMA  0.986  0.991  7.314×10^{6}  8.1492×10^{8}  Y = 4.210×10^{14} (C/A)^{−1.153} F^{0.894} T^{−5.809} 
RTFOaged CMA  0.992  0.995  2.515×10^{7}  5.0046×10^{9}  Y = 5.083×10^{11} (C/A)^{−1.393} F^{−26.931}T^{−1.393} 
Here, Y is the rutting parameter, C/A is the CMA binder percentage (%), T is the tested temperature (°C), and F is the loading frequency (Hz). Since the models in
Measured and predicted G*/sinδ value versus loading frequency for the unaged unmodified asphalt binder at 58°C.
Measured and predicted G*/sinδ value versus loading frequency for the unaged 20% cementmodified asphalt binder at 64°C.
Predicted vs. experimental rutting parameter for the unaged unmodified CMAs: Modeling points.
Predicted vs. experimental rutting parameter for the unaged unmodified CMAs: Testing (validation) points.
Predicted vs. experimental rutting parameter for the unaged modified CMAs: Modeling points.
Predicted vs. experimental rutting parameter for the unaged modified CMAs: Testing (validation) points.
Predicted vs. experimental rutting parameter for the aged unmodified CMAs: Modeling points.
Predicted vs. experimental rutting parameter for the aged unmodified CMAs: Testing (validation) points.
Predicted vs. experimental rutting parameter for the aged modified CMAs: Modeling points.
Predicted vs. experimental rutting parameter for the aged modified CMAs: Testing (Validation) points.
The comparisons have shown an accurate prediction of the acquired model from SPSS with slight variation in the estimated rutting parameter in the 10 and 16 testing points for both unaged and RTFOaged CMAs, respectively. However, some consistent variation existed for rutting parameters at loading frequencies between 7 and 10 Hz. Therefore, those points were excluded from the regression analysis. It is worth mentioning that rutting distress becomes more pronounced on asphalt pavements at high temperatures and low loading frequencies (low truck speeds).
The study aimed at evaluating the effect of C/A percentage, temperature, and loading frequencies on unaged and RTFOaged CMAs using the DSR test which assessed the rutting parameter under combined conditions. Moreover, multiple statistical analyses were conducted to evaluate the relation between the rutting parameter and the tested variables using the oneway ANOVA and correlation test in order to come up with a regression model using SPSS to predict the rutting parameter. Based on the analysis and results of this study, the following main findings and conclusions are drawn:
1) The oneway ANOVA test performed in the analysis of this study showed that there is a significant difference between the tested unaged and RTFOaged CMAs by the DSR test with regard to the C/A percentage.
2) Conducting the correlation test has shown that changing the loading frequencies affects the rutting parameter significantly under different temperatures and C/A percentages. The Pearson R coefficient of the tested samples ranged between 0.994 to 1.000 and 0.974 to 0.999 for the unaged and RTFOaged asphalt binders, respectively.
3) Scatter plots were tested to identify the type of the relationship between each variable and the rutting parameter (G*/sinδ). As a result of the nonlinear behavior of the three variables with the rutting parameter, multiple nonlinear forms have been tested in order to get the most accurate form that would contribute to forming a model for both the unaged and RTFOaged cementmodified asphalt binders (CMAs).
4) A regression analysis has been conducted using SPSS in order to build a model for each group based on aging and modification conditions that can predict the rutting parameter precisely. The collected data from experiments have been grouped according to the modification condition and aging criteria in order to accommodate the need to predict the rutting parameter in a variety of conditions. Therefore, the nonlinear regression analysis has been conducted on 4 groups, namely, unaged modified and unmodified, and RTFOaged modified and unmodified CMAs.
5) The model with the highest
In addition to the main findings of this study, it is also recommended to conduct further research in the future related to field data to fully investigate the impact of temperature, loading frequency, and the C/A percentage on pavement performance against rutting distress in the field.
The data used to support the findings of this study are included within the article. Any additional data related to the article may be requested from the corresponding author.
GAK: Paper writing, data reduction, analysis of results, and experimental testing. KG: Paper writing, data reduction, and analysis of results. MI: Paper writing, data reduction, and analysis of results. AS: Paper writing, data reduction, and analysis of results. MN: Data reduction and analysis of results. YE: Data reduction and analysis of results.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
The authors of the paper would like to acknowledge and thank the University of Sharjah and Ajman University for their support.