The critical shear stress (τc) for grain entrainment is a poorly constrained control on bedload transport rates in rivers. Direct calculations of τc have been hindered by the inability to measure the geometry of in situ grains; i.e., the shape and location of each grain relative to surrounding grains and the bed surface. We present the first complete suite of three-dimensional (3-D) grain geometry parameters for 1055 water-worked grains, and use these to parameterize a new 3-D grain entrainment model and hence estimate τc. The 3-D data were collected using X-ray computed tomography scanning of sediment samples extracted from a prototype scale flume experiment. We find that (1) parameters including pivot angle and proportional grain exposure do not vary systematically with relative grain size; (2) τc is primarily controlled by grain protrusion, not pivot angle; and (3) larger grains experience larger forces as a result of projecting higher into the flow profile, producing equal mobility. We suggest that grain protrusion is a suitable proxy for assessing gravel-bed stability.

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