Empirical formulas for near-bed wave orbital velocity parameters involved in maximum wave load in random wave trains

This paper presents empirical methods utilizing recently developed formulas (Kawamata and Kobayashi., 2022; Kawamata et al., 2018) to predict the maximum wave forces on near-bed structures and wave-induced movement ratios of isolated rocks in random wave trains. The methods assume that the maximum wave load occurs when the velocity semi-amplitude defined as half the difference between successive negative and positive peaks of the near-bed wave orbital velocity is maximized. The empirical formulas for the velocity-waveform parameters at the maximum velocity semi-amplitude in a random wave train were derived from the near-bed velocities and surface elevations measured in laboratory wave flumes. The laboratory formula for the maximum velocity semi-amplitude was reviewed and improved with near-bed wave orbital velocities and surface elevations estimated from pressure measurements under a wider range of wave conditions in the field. The newly developed formulas for the velocity-waveform parameters at velocity semi-amplitude maxima, combined with the previously developed formulas, showed reasonable agreement with the maximum wave forces measured on the artificial reef models under random waves in a laboratory wave flume as well as with the movement ratio of quarry rocks (median mass = 0.40 t) observed in a field test. •Formulas for velocity parameters involved in maximum wave load in random wave trains are presented.•Formulas were derived from lab and field data of near-bed velocities and surface elevations.•Maximum wave forces on near-bed objects in random wave trains were reasonably predicted.•Movement ratios of quarry rocks in a field test were reasonably predicted.•Formulas are applicable if common wave parameters are available.