Data compiled from eight decades of incipient motion studies were used to calculate dimensionless critical shear stress values of the median grain size, t* c 50 . Calculated t* c 50 values were stratified by initial motion definition, median grain size type (surface, subsurface, or laboratory mixture), relative roughness, and flow regime. A traditional Shields plot constructed from data that represent initial motion of the bed surface material reveals systematic methodological biases of incipient motion definition; t* c 50 values determined from reference bed load transport rates and from visual observation of grain motion define subparallel Shields curves, with the latter generally underlying the former; values derived from competence functions define a separate but poorly developed field, while theoretical values predict a wide range of generally higher stresses that likely represent instantaneous, rather than time-averaged, critical shear stresses. The available data indicate that for high critical boundary Reynolds numbers and low relative roughnesses typical of gravel-bedded rivers, reference-based and visually based studies have t* c50 ranges of 0.052-0.086 and 0.030-0.073, respectively. The apparent lack of a universal t*50 for gravel-bedded rivers warrants great care in choosing defendable t* c50 values for particular applications.

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A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers

The performance is tested of 12 bed load sediment transport formulae developed for use in gravel bed channels. The formulae are applied in the manner intended by the original authors. To this end, the test data are restricted to ones obtained in approximately steady flow when the material in motion was similar to that present on the bed; that is, transport was not size selective. This represents the nearest approach to “equilibrium sediment transport” that can be realized with available data. Four sets of river data and three sets of flume data were chosen for the test, covering a range of eight orders of magnitude in unit bed load transport rate. The test data were not used in the development of the formulae. The analysis separates mean bias and local bias. No formula performs consistently well. Limitations of the test data, the constraints imposed by an operationally realistic test, and reasons based upon the physics of the transport phenomenon all may be adduced for this. To estimate the magnitude of transport with limited hydraulic information, stream power equations should be used because they provide the most straightforward scale correlation of the phenomenon. In particular, the approach of Bagnold deserves further study. When local hydraulic information is available, a formula should be selected that is sensitive to bed state or grain size distribution and, in this context, the formulae of Einstein, Parker, and Ackers-White-Day bear continued examination.

An assessment of bed load sediment transport formulae for gravel bed rivers

Incubating salmonid eggs in streambeds are often threatened by deposition of fine sediment within the gravel. To relate sedimentation of spawning gravel beds to sediment transport, infiltration of fine sediment (<2 mm in diameter) into clean gravel beds, bed material size distributions, scour-fill depths, and sediment transport during 10 storm flow events were measured in three streams of north coastal California. Although suspended sediment comprised most (75–94%) of the clastic load during storm flows, bed load material (0.25–2 mm) accounted for most (70–78%) of the fine sediment accumulated in experimental gravel implanted in the streambeds. Sand trapped in the interstices of the top several centimeters formed a seal that impeded deeper deposition of very fine sand and finer material. The seal was responsible at least in part for a decrease in the rate of fine-sediment accumulation with increasing cumulative bed load transport. Areas of the streambeds commonly scoured or filled 0.1 m or more during storm flows, and thus scour and fill commonly created a sandy layer at least as thick as the seal formed by sediment infiltration. Scour could erode eggs laid in the bed and expose deeper levels of the bed to infiltration by fine sediment, but at the same time could allow fine sediment to be winnowed away. Great temporal and spatial variation in sedimentation in these streams suggests that individual storms of moderate size pose a threat to eggs in many but not all areas selected by fish for spawning.

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Sediment Transport and Resulting Deposition in Spawning Gravels, North Coastal California

Stable reticulate structures, which we call “stone cells,” have been observed in cobble-gravel channel beds with low bed material transport rates. Experiments show that such structures develop simultaneously with the armor layer during an extended period when flows do not exceed the Shields threshold by more than ∼2 times, so that bed material transport is low. They are constructed by particles moving from less stable positions into more stable configurations against each other. Intermediate developments include clusters and stone lines. They reduce sediment transport by orders of magnitude and are evidently a major stability-promoting mechanism in gravel channels. The timescale for their development suggests that the boundaries of many gravel-bed channels are not in equilibrium with recent competent flows but reflect the history of recent “dominant” flows.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98WR00484

Stabilizing self-organized structures in gravel-bed stream channels: Field and experimental observations

Bed scour, egg pocket depths, and alteration of stream-bed surfaces by spawning chum salmon (Onchorhynchus keta) were measured in two Pacific Northwest gravel-bedded streams. Close correspondence between egg burial depths and scour depths during the incubation period suggests an adaptation to typical depths of bed scour and indicates that even minor increases in the depth of scour could significantly reduce embryo survival. Where egg burial depths are known, expressing scour depth in terms of bed-load transport rate provides a means for predicting embryo mortality resulting from changes in watershed processes that alter shear stress or sediment supply. Stream-bed alteration caused by mass spawning also may influence embryo survival. Theoretical calculations indicate that spawning-related bed surface coarsening, sorting, and form drag reduce grain mobility and lessen the probability of stream-bed scour and excavation of buried salmon embryos. This potential feedback between salmon spawning and bed mobility implies that it could become increasingly difficult to reverse declines in mass-spawning populations because decreased spawning activity would increase the potential for bed scour, favoring higher embryo mortality. Further analysis of this effect is warranted, however, as the degree to which spawning-related bed loosening counteracts reduced grain mobility caused by surface coarsening, sorting, and redd form drag remains uncertain.

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Stream-bed scour, egg burial depths, and the influence of salmonid spawning on bed surface mobility and embryo survival

A continuous record reveals that the incidence of bedload in a coarse-grained river channel changes from flood to flood. Long periods of inactivity encourage the channel bed to consolidate sufficiently so that bedload is largely confined to the recession limb of the next flood-wave. But when floods follow each other closely, the bed material is comparatively loose and offers less resistance to entrainment. In this case, substantial amounts of bedload are generated on the rising limb. This is confirmed by values of bed shear stress or stream power at the threshold of initial motion which can be up to five times the overall mean in the case of isolated floods or those which are the first of the season. This produces a complicated relationship between flow parameters and bedload and explains some of the difficulties in establishing bedload rating curves for coarse-grained channels. Besides this, the threshold of initial motion is shown to occur at levels of bed shear stress three times those at the thresholds of final motion. This adds further confusion to attempts at developing predictive bedload equations and clearly indicates at least one reason why equations currently in use are unsatisfactory. Bedload is shown to be characterized by a series of pulses with a mean periodicity of 1.7 hours. In the absence of migrating bedforms, it is speculated that this well-documented pattern reflects the passage of kinematic waves of particles in a slow-moving traction carpet. The general pattern of bedload, including pulsations, is shown to occur more or less synchronously at different points across the stream channel.

John T Layman

Papers

The incidence and nature of bedload transport during flood flows in coarse‐grained alluvial channels