Reliability of Calculation of Dynamic Modulus for Asphalt Mixtures Using Different Master Curve Models and Shift Factor Equations

Abstract

To develop a mechanistic-empirical pavement design system for Norwegian conditions, this paper evaluates the influence of the adoption of different models and shifting techniques on the determination of dynamic modulus master curves of asphalt mixtures. Two asphalt mixture types commonly used in Norway, namely Asphalt Concrete (AC) and Stone Mastic Asphalt (SMA) containing neat bitumen and polymer-modified bitumen, were prepared by the roller compactor, and their dynamic moduli were determined by the cyclic indirect tensile test. The dynamic modulus master curves were constructed using the standard logistic sigmoidal model, a generalized logistic sigmoidal model and the Christensen–Anderson–Marasteanu model. The shifting techniques consisted of log-linear, quadratic polynomial function, Arrhenius, William–Landel–Ferry and Kaelble methods. The absolute error, normalised square error and goodness-of-fit statistics encompassing standard error ratio and coefficient of determination were used to appraise the models and shifting methods. The results showed that the standard logistic sigmoidal model and the Williams–Landel–Ferry equation had the most suitable fits for the specimens tested. The asphalt mixtures containing neat bitumen had a better fit than the ones containing polymer-modified bitumen. The Kaelble equation and log-linear equation led to similar results. These findings provide a relevant recommendation for the mechanistic-empirical pavement design system.

Study on the Phase Angle Master Curve of the Polyurethane Mixture with Dense Gradation

“…A strain limitation of 75-125 µε was used during the test procedure to keep the specimens within the elastic range. The phase angle of the PU mixture was measured in the experiment at six temperatures (5,15,25,35,45,55 • C) and eight loading frequencies (0.1, 0.5, 1, 2, 5, 10, 20, 25 Hz). The average phase angle values of four replicates were used for fitting the master curve.…”

“…To evaluate five phase angle model's fitting divergence and minimize the error between the predicted and measured phase angle, four different error minimization methods were applied to determine the "goodness of fit" [55]: (1) Se/Sy minimization, as in Equations ( 14) and ( 15), (2) R 2 maximization as in Equation ( 16), (3) the Sum of Square Error (SSE) minimization as in Equation ( 17), and (4) Error 2 minimization as in Equation (18).…”

Study on the Construction of Dynamic Modulus Master Curve of Polyurethane Mixture with Dense Gradation

“…To evaluate the divergence of fit between the five dynamic modulus models and minimize the error between predicted and measured dynamic modulus, "goodness-offit" is used in this study. Four different solver methods were applied to determine the "goodness-of-fit" [33]: the first (1) used Se/Sy (the ratio of the standard error (Se) to the standard deviation (Sy)) minimization, the second (2) used R 2 maximization, the third (3) used the Sum of Square Error (SSE) minimization, and the fourth (4) used Error 2 minimization.…”

“…The study [32] employed five distinct master curve models to predict the dynamic modulus and corresponding phase angle for three different kinds of asphalt mixture, and recommended a model that combined the CAM model and sigmoidal model. Reference [33] adopted three master curve models and five kinds of shift equation factors to compare the prediction accuracy for four kinds of asphalt mixtures, and the SLS model and the Williams-Landel-Ferry equation produced the best-fitting results. Study [29] adopted two master curve models and three kinds of shift factor equations to construct the master curve model of the dynamic modulus, and the GLS model was proved to predict more precisely.…”

“…Reference [32] compared five different shift factor equations for fitting and predicting the experimental dynamic modulus and phase angle, and recommended a proper shift factor equation for generating the master curve. Study [33] adopted three shift factor equations and provided recommendations for the selection of the proper master curve model. References [43][44][45] utilized the Polynomial shift factor equation to construct the master curve of the asphalt mixture.…”