A general formula for non-cohesive bed load sediment transport

A bed load transport formula for non-cohesive sediment, based on the bed-shear concept of Meyer-Peter and Müller, was developed and validated for steady flows, oscillatory flows, and combined steady and oscillatory flows. The bed load formula introduced in this study was examined using data from experimental and field measurements for a wide range of flows and sediment conditions, as occurring in river, coastal, and marine environments. More than 1000 steady and 500 oscillatory flow cases were used in the study. The relationship between the bed load transport and the total Shields parameter to the power 1.5 was first confirmed for the steady flows. An exponential factor to take into account the effect of the critical Shields parameter was introduced. The proposed formula for the steady current was expanded and generalized to take into account the effects of oscillatory flows as well as oscillatory flows with a superimposed current at an arbitrary angle. The time-dependent bed load transport was treated in a “quasi-steady” manner using the quadratic value of the instantaneous Shields parameter for the two half-periods of the wave (when the total instantaneous velocity u is in the direction of the wave, u > 0, or in the opposite direction, u < 0). A good correlation was found between the bed load formula and the measurements for colinear oscillatory and steady flows when no phase-lag occurred in the experiments. However, a marked scatter was observed since the Shields parameter had to be estimated and not derived directly from measured data. Finally, the validity and limitations of the obtained bed load transport formula are discussed.