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The objective of this research study was to evaluate several mathematical models to be used in calculating the onset of tertiary flow [referred to as the flow number (FN) parameter] for asphalt mixtures. The FN indicates the onset of shear deformation in asphalt mixtures, which is a significant parameter in evaluating rutting in the field. The FN is obtained from the repeated load permanent deformation (RLPD) laboratory test. Current modeling techniques in determining the FN use a polynomial model fitting approach, which works well for most conventional asphalt mixtures. However, analysis and observations on the use of this polynomial model for rubber-modified asphalt mixtures showed problems in identifying the true FN values. The scope of the work included the collection and analysis of more than 300 RLPD test data files, which comprised more than 40 mixtures, a wide range of test temperatures, and several stress levels. A new comprehensive mathematical model was recommended to accurately determine the FN. The results and analysis were evaluated through manual calculations and found to be accurate, rational, and applicable to all mixture types, whether a tertiary stage was reached or not.

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