Low-Submergence Effect on Incipient Sediment Motion

Low submergence is usually observed over a channel bed of a steep slope. It is equivalent to large-scale roughness characterized by high ratios of grain diameter to flow depth, $d_{50}/h$. This study shows that the critical Shields stress ${\theta }_c$ for incipient sediment motion can be theoretically formulated either as a function of $d_{50}/h$ or the channel bed slope $S$ for fully rough beds. Different from previous studies, the derivation is conducted by involving the friction factor that applies for open-channel flows subjected to large-scale roughness. The analysis also takes into account other factors including grain density, sediment uniformity, and intergrain friction. The results show that for natural gravel beds, if $d_{50}/h<1$ or $S<0.6$, the incipient sediment motion is controlled by the bed resistance and therefore ${\theta }_c$ increases with increasing $d_{50}/h$ or $S$. Otherwise, the incipient motion is dominantly driven by the streamwise component of the grain gravity, which causes a reduction in ${\theta }_c$ with increasing $d_{50}/h$ or $S$. The theoretical formula agrees reasonably with experimental data collected from eight sources in the literature.