The Dynamic Shear Modulus of Paving Asphalts as a Function of Frequency

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Abstract
The deformation response of paving asphalts to small‐amplitude sinusoidal loading in shear is linear and thermorheologically simple so that master curves relating the dynamic shear modulus to the (reduced) frequency can be constructed. A simple analytical expression which gives a good fit to these master curves is proposed. Data were obtained for the response of 14 different asphalts over a range of frequencies and temperatures, and master curves relating the absolute value of the modulus to the reduced frequency were constructed. These were found to fit closely to an equation which is one arm of an hyperbola whose asymptotes represent the purely viscous and purely elastic behavior expected at infinitely low and infinitely high frequencies, respectively. The rapidity with which an asphalt changes from a viscous to an elastic response as the frequency of loading increases (shear susceptibility parameter) is indicated by the distance between the point at which the hyperbola crosses its “modulus” axis and its origin. The phase angle is approximately proportional to the slope of the hyperbola, and the equation relating the phase angle with reduced frequency obtained using this relationship gave an adequate fit to the data. From this equation, and that of the hyperbola, the relaxation spectra of the materials were calculated. Shear susceptibility parameters, limiting viscosities, and moduli at a very high frequency of the materials are given and the increase of these parameters when a Kuwait asphalt was air blown in the refinery is indicated. The method used to fit the hyperbola equation to the data and an indication of the precision of fit are given in the Appendix.

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