Entrainment, incipient motion, initiation of motion and threshold velocity are terms often used for the beginning of motion of particles in a bed under the influence of flow. In dredging applications this can occur as erosion phenomena in rivers, channels and on the sea floor, but also around bottom founded structures, submerged pipelines, during the loading process of TSHD’s and during hydraulic transport of sands and gravels. In 1936 Shields carried out research resulting in the famous Shields curve, giving a relation between the non-dimensional shear stress on the bed and the boundary Reynolds number. A Shields value above the Shields curve means that there is erosion, belowmeans negligible erosion. The advantage of the Shields approach is, that the resulting curve is independent of grain density and fluid properties, but the disadvantage is that the so called friction velocity and grain diameter occur both in the non-dimensional shear stress and in the boundary Reynolds number, making it an implicit graph. Hjulstrømcarried out his research in the same period as Shields and came up with a dimensional graph with the erosion velocity on the vertical axis and the grain diameter on the horizontal axis. The advantage of this graph is that it is explicit, but the disadvantage that a new graph has to be constructed for each combination of fluid properties and water depth. Since 1936 many researchers have carried out research on this subject, however non has found a complete fundamental explanation of the Shields curve.
The paper will give an overview of the research and the models as developed by many researchers until now and show the basics of a new model developed by the author giving a full fundamental explanation of the Shields curve, including protrusion, stages of entrainment, laminar main flow and non-uniform grain distributions. The new model has been verified with numerous data from many researchers and the correlation is very good in general.