Differential Scheme Effective Medium Theory for Hot-Mix Asphalt $\left|{\mathit{E}}^{\ast }\right|$ Prediction

An empirical $\left|{\mathit{E}}^{\ast }\right|$ predictive equation, known as Witczak’s $\left|{\mathit{E}}^{\ast }\right|$ predictive model, has been adopted in the Mechanistic-Empirical Pavement Design Guide. However, empirical approaches have significant drawbacks, particularly with application of the model for materials that vary from those used in the calibration of the model and their reliance on large calibration data sets. In order to overcome the limitations of an empirical approach, a fundamental micromechanics modeling framework based on the differential scheme effective medium theory has been developed and introduced in this paper. The proposed modeling framework herein takes a sequential approach, using a series of two-phase differential particulate composite models to predict the effective tensile complex modulus $\left(\left|{\mathit{E}}^{\ast }\right|\right)$ of a three-phase HMA mixture, which consists of the asphalt binder, aggregate particles, and air voids. The model prediction results were compared with experimentally measured $\left|{\mathit{E}}^{\ast }\right|$ of five dense graded HMA mixtures across a range of low temperatures. In general, the model was found to predict $\left|{\mathit{E}}^{\ast }\right|$ with a very reasonable level of accuracy. Additional work to extend the applicability of the modeling framework to higher temperature regimes and the need to develop a more general and systematic approach for practical implementation are discussed.