Clear-water span shoulder migration beneath pipelines in wave-plus-current conditions on a flat sea bed

• Nineteen new cases are provided which includes 16 clear water cases and an additional three live bed cases as a check of the experimental setup. • A complete rational model is proposed for predicting the wave-plus-current induced span shoulder migration rate in both the clear water and live bed regimes. • Dependence of the relative current strength on the span shoulder migration rate under clear water conditions was explained. • A contradiction stating Shields parameter’s “weak dependence” is resolved which indicates it still has a significant impact despite at a narrow range around incipient sediment motion. The present study investigates the wave-plus-current induced span shoulder migration rate beneath pipelines in the clear-water regime. Eighty-five cases from present and previous experiments are collected, covering three scenarios: pure current, pure wave, and wave plus current. Among these, 19 new cases are provided in the present study, which includes 16 clear-water cases and an additional three live-bed cases as a check of the experimental setup. Effects of the relative current strength, Keulegan–Carpenter number, Shields number, and embedment depth on the span shoulder migration rate are examined. It is found that, increasing Keulegan–Carpenter number will decrease the span shoulder rate; however, its dependence is weak when it is sufficiently small. Through dimensional analysis, a complete rational model is proposed for predicting the wave-plus-current induced span shoulder migration rate in both the clear-water and live-bed regimes. A contradiction that the Shields parameter has “weak dependence” in the clear-water regime according to a previous study, is likewise resolved. The complete model shows that the Shields parameter still has a significant impact despite having weak dependence in a narrow range around incipient sediment motion.