HIRSCH MODEL FOR ESTIMATING THE MODULUS OF ASPHALT CONCRETE

The purpose of this paper is to present a new, rational and effective model for estimating the modulus of asphalt concrete using binder modulus and volumetric composition. The model is based upon an existing version of the law of mixtures, called the Hirsch model, which combines series and parallel elements of phases. In applying the Hirsch model to asphalt concrete, the relative proportion of material in parallel arrangement, called the contact volume, is not constant but varies with time and temperature. Several versions of the Hirsch model were evaluated, including ones using mastic as the binder, and one in which the effect of film thickness on asphalt binder modulus was incorporated into the equation. The most effective model was the simplest, in which the modulus of the asphalt concrete is directly estimated from binder modulus, voids in mineral aggregate, and voids filled with asphalt binder. Models are presented for both dynamic complex shear modulus and dynamic complex extensional modulus. Semi-empirical equations are also presented for estimating phase angle in shear loading and in extensional loading. The proposed model was verified by comparing predicted modulus and phase angles to values reported in the literature for a range of mixtures.