1 GENERAL When the stream flows over a sediment bed, the hy- drodynamic drag and lift forces act on the sediment grains at the bed surface. As the stream velocity en- hances, a state is ultimately reached when the sedi- ment grains at the bed surface are entrained intermit- tently if the hydrodynamic forces overcome the stabilising force arising from the submerged weight of the sediment grains, called the entrainment threshold of sediment. Different feasible modes of entrainment threshold of sediment are rolling, slid- ing and lifting modes, as depicted schematically in Figure 1. In rolling mode, the overturning moment on the sediment grain about the pivot point exceeds the stabilising moment about that point, whereas in sliding mode, the drag force on the sediment grain exceeds the frictional resistance at the contacts of the grains. On the other hand, in lifting mode, the lift force exceeds the submerged weight of the sediment grain. The complexity of the interaction between the sediment grains and the turbulent flow renders the problem of sediment transport intricate. Thus, the complex phenomenon impedes to achieve a compre- hensive theoretical analysis. Regarding the applica- tions of the knowledge of sediment transport, it plays an important role in analysing the stability and ex- tending the lifetime of important riverine structures, such as bridge, barrage, culvert, reservoir dam, etc. Figure 1. Schematic of bedload transport with the motion of sediment grains in rolling, sliding and saltating (or lifting) modes. The study on entrainment threshold of sediment by the streamflow was pioneered by Shields (1936). He did a semi-theoretical analysis to recommend the famous Shields diagram. His diagram represents a curve (well-known as Shields curve) of threshold Shields function Θ c versus shear Reynolds number R * and is commonly used to determine the threshold bed shear stress for a given median size of sediment Hydrodynamics of sediment transport: grain scale to continuum scale Subhasish Dey & Sk Zeeshan Ali Department of Civil Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India ABSTRACT: A theory of sediment transport, describing the entrainment phenomenon from the grain scale to the continuum scale, under a steady-uniform flow over a sediment bed is presented. The sediment grains, as- sumed as discrete spherical grains, are subjected to turbulent wall-shear flows. At the grain scale, the forces acting on a sediment grain resting over three compact spherical grains are analysed to determine the criteria for entrainment threshold in rolling, sliding and lifting modes taking into account the turbulence effects. Comparison of the theoretical results with the experimental data shows that the entrainment threshold lies within the sliding and lifting modes. Then, at the grain scale, using the log-normal probability density function for the near-bed instantaneous horizontal velocity, the entrainment probabilities in rolling, sliding and lifting modes for a given grain size are derived. The rolling and sliding probabilities increase with an increase in Shields function and after attaining their individual maximum values, they reduce, whereas the lifting proba- bility increases with Shields function. The maximum value of entrainment probability in rolling mode is close to the threshold Shields function in rough flow, whereas the entrainment probability in lifting mode initiates from the value of the threshold Shields function. In a continuum scale, the bedload flux is derived by hypothe- sising the saltating mode of sediment transport incorporating the lifting probability obtained at the grain scale. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by HR Wallingford Ltd.: ePrints at HR Wallingford