Shields' entrainment criterion in bridge hydraulics

Two related problems of sediment hydraulics are addressed: (1) Inception of sediment transport for nearly uniform flow of both uniform and nonuniform sediment beds for two different sediment densities and grain sizes ranging from sand to gravel, and (2) generalized inception conditions if elements are inserted in a plane sediment bed. The Shields' criterion is formulated with basic quantities involving gravity. viscosity, and densities of the two-phase flow. The results of the analysis relate to the viscous, the transition, and the fully turbulent regimes. The transition regime is verified with extended laboratory experiments. Then, these conditions are used as a basis for formulating a general stability criterion for loose bed hydraulics, and compared to detailed experiments involving pier and square elements located either at the channel side or at its axis. In addition, a generalized densimetric particle Froude number is introduced that accounts for both uniform sediments and mixtures. The engineering application of the present results is straightforward, given that basic parameters of hydraulics, sediment, and fluid are involved.