Other prediction models of asphalt stiffness

Ever since the development of Bonnaure s and Brown s models, several other researchers, primarily in the United States, developed relationships for predicting asphalt stiffness, using the equivalent term dynamic modulus, l l. A list of all predictive models until 2003 can be found in Bari and Witczak (2006). 

Originally, the most wildly used predictive equation was Witczak s equation (Andrei et al. 1999 Witczak 2005), also known as the original Witczak equation. The dynamic modulus was determined with respect to percentage passing through certain sieves, binder viscosity, air voids, effective binder content and loading frequency. 

Witczak s original predictive model was reformulated to include the dynamic shear modulus of the bitumen IG li, and the binder phase angle associated with IG I, (Bari 2005 Bari and Witczak 2006, 2007). The new equation developed is know as the modified Witczak equation (model) and is as follows  

Another commonly used equation is the Hirsch predictive equation (Christensen et al. 2003). In this case, the dynamic modulus is determined with respect to voids in the mineral aggregate, voids filled with binder and dynamic shear modulus of bitumen. The equation developed is as follows  

The phase angle, 0, can be calculated from the following equation e = -21(logP,P-55 logP,. 

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