Sine versus Haversine Displacement Waveform Comparison for Hot Mix Asphalt Four-Point Bending Fatigue Testing

An experimental study was conducted to determine the effect of haversine and sine displacement waveforms on four-point flexural beam fatigue test results for hot mix asphalt. Seven asphalt mixtures with different gradations, binder types, and binder contents were tested for this study. Four of the mixes were tested in California and three in Australia. The mixes were tested at different strain levels under both waveforms in displacement-controlled mode without rest periods. The comparison showed no differences between haversine and sine testing modes for six of the seven mixtures. Fatigue life, the shape of the stiffness reduction curves, initial dynamic moduli and phase angles, and Black diagrams were essentially the same for both testing modes. This similarity was attributed to the viscoelastic nature of the asphalt mix. Because of asphalt's viscoelasticity, the beam at-rest position in haversine testing will rapidly move to halfway between zero and maximum displacement, and so the same stress is produced by haversine and sine displacement waveforms as soon as the peak-to-peak amplitudes are equal. For one of the seven mixes, sinusoidal testing produced considerably longer fatigue lives, although it is believed this mix is an outlier and can be ignored. Based on these results, it was concluded that there is no compelling reason to recommend sinusoidal over haversine testing mode, or vice versa. A practical reason to recommend the sine testing mode is that the stress in the haversine alternative becomes sinusoidal after a small number of load repetitions.