Critical evaluation of unit response function interconversions for asphalt concrete linear viscoelastic modeling using discrete spectrum

It is well-known that asphalt concrete has three unit response functions (URFs): complex modulus, relaxation modulus, and creep compliance. The interconversions among these three URFs are generally done through discrete relaxation/retardation spectrum. Since different methods of determining discrete spectrum have been developed in the past, this study focused on systematically comparing and evaluating three classical methods: collocation, multidata, and windowing methods, with four relaxation/retardation time selections. Additionally, considering theoretical requirement and practical preference, both wide and narrow relaxation/retardation time ranges are evaluated to quantify their influences on the result qualities. After multiple sets of result comparisons, it has been found that all three methods can lead to reasonable results as long as wide and appropriate relax-ation/retardation time range is given. However, since in practice shorter time range may be used more often, in this scenario attention needs to be paid to the solution quality including the spectrum values and shape, and the characterized function accuracy. Overall, the windowing method causes fewer solving issues than the other two methods due to its optimization nature, which prohibits the negative relaxation/retardation strength values. Despite that, the collocation and multidata methods occasionally lead to more reasonable results when narrower relaxation/retardation time range is used. From these observations, a hybrid procedure, which takes advantage of each interconversion method, is proposed in this study to optimize the discrete spectrum determination for asphalt concrete.

Automated summary

It is known that asphalt concrete has three unit response functions: complex modulus, relaxation modulus, and creep compliance. This study systematically compares and evaluates three classical methods for interconverting these functions. The results show that all three methods can provide reasonable results with wide and appropriate relaxation/retardation time range. However, the windowing method is found to have fewer solving issues and is recommended for asphalt concrete determination.