Optimal time-frequency equivalency factor for approximate interconversion between the dynamic and relaxation moduli

The viscoelastic stiffness of asphalt concrete is commonly represented using relaxation modulus and dynamic modulus, which are functions of loading time and loading frequency, respectively. They are typically measured via experimental testing whereby only one of the moduli is determined, and interconversion techniques can be used to obtain the other modulus if needed. Although exact approaches exist for pavement modulus interconversion, they can be difficult to implement in practice, and approximate conversion techniques have therefore been developed for conventional use. A popular approach is to approximate a direct relationship between the time and frequency domains via an equivalency factor, but there is no apparent consensus on its proper value. In this paper, a new numerical technique is applied to experimental data to ascertain the optimal value of the time-frequency equivalency factor. Approximate conversions from dynamic modulus to relaxation modulus are conducted using the optimal factor, and results are compared to popular alternative approaches. The optimal factor is determined to be 0.0673±0.0009 with 95% confidence. Using the mean value of 0.0673 produced conversion errors of 1.41% on average among 30 samples of hot mix asphalt.