Formulas for Bed-Load transport
07 Jun 1948-Iss: 3, pp 39-64
TL;DR: In this article, an attempt is made to derive an empirical law of bed-load transport based on recent experimental data and the results and interpretation of tests already made known in former publications of the Laboratory for Hydraulic Research and Soil Mechanics at the Federal Institute of Technology, Zurich.
Abstract: In the following paper, a brief summary is first of all given of the results and interpretation of tests already made known in former publications of the Laboratory for Hydraulic Research and Soil Mechanics at the Federal Institute of Technology, Zurich. After that, an attempt is made to derive an empirical law of bed-load transport based on recent experimental data. We desire to state expressly that by bed-load transport is meant the movement of the solid material rolling or jumping along the bed of a river; transport of matter in suspension is not included.
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TL;DR: In this article, a method is presented which enables the computation of the bed-load transport as the product of the saltation height, the particle velocity and the bed load concentration.
Abstract: A method is presented which enables the computation of the bed-load transport as the product of the saltation height, the particle velocity and the bed-load concentration. The equations of motions for a solitary particle are solved numerically to determine the saltation height and particle velocity. Experiments with gravel particles (transported as bed load) are selected to calibrate the mathematical model using the lift coefficient as a free parameter. The model is used to compute the saltation heights and lengths for a range of flow conditions. The computational results are used to determine simple relationships for the saltation characteristics. Measured transport rates of the bed load are used to compute the sediment concentration in the bed-load layer. A simple expression specifying the bed-load concentration as a function of the flow and sediment conditions is proposed. A verification analysis using about 600 (alternative) data shows that about 77% of the predicted bed-load-transport rates are within 0.5 and 2 times the observed values.
1,653 citations
Cites methods from "Formulas for Bed-Load transport"
...The typical bed-load formula of Meyer-Peter and Miiller (28) was also used....
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TL;DR: Several different erosion and sediment and sediment-associated nutrient transport models with regard to these factors are reviewed, limited to those models with explicit considerations of either the sediment generation or transport process.
Abstract: Information on sediment and nutrient export from catchments and about related erosive processes is required by catchment managers and decision-makers. Many models exist for the consideration of these processes. However, these models differ greatly in terms of their complexity, their inputs and requirements, the processes they represent and the manner in which these processes are represented, the scale of their intended use and the types of output information they provide. This paper reviews several different erosion and sediment and sediment-associated nutrient transport models with regard to these factors. The review of models is limited to those models with explicit considerations of either the sediment generation or transport process.
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TL;DR: In this article, the authors used data compiled from eight decades of incipient motion studies to calculate dimensionless critical shear stress values of the median grain size, t* c 50.
Abstract: 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.
919 citations
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TL;DR: The relative importance of various processes and the nature of the interplay between them are inferred from detailed observations of the morphology of erosional forms on channel bed and banks, and their spatial distributions.
Abstract: Improved formulation of bedrock erosion laws requires knowledge of the actual processes operative at the bed. We present qualitative field evidence from a wide range of settings that the relative efficacy of the various processes of fluvial erosion (e.g., plucking, abrasion, cavitation, solution) is a strong function of substrate lithology, and that joint spacing, fractures, and bedding planes exert the most direct control. The relative importance of the various processes and the nature of the interplay between them are inferred from detailed observations of the morphology of erosional forms on channel bed and banks, and their spatial distributions. We find that plucking dominates wherever rocks are well jointed on a submeter scale. Hydraulic wedging of small clasts into cracks, bashing and abrasion by bedload, and chemical and physical weathering all contribute to the loosening and removal of joint blocks. In more massive rocks, abrasion by suspended sand appears to be rate limiting in the systems studied here. Concentration of erosion on downstream sides of obstacles and tight coupling between fluid-flow patterns and fine-scale morphology of erosion forms testify to the importance of abrasion by suspended-load, rather than bedload, particles. Mechanical analyses indicate that erosion by suspended-load abrasion is considerably more nonlinear in shear stress than erosion by plucking. In addition, a new analysis indicates that cavitation is more likely to occur in natural systems than previously argued. Cavitation must be considered a viable process in many actively incising bedrock channels and may contribute to the fluting and potholing of massive, unjointed rocks that is otherwise attributed to suspended-load abrasion. Direct field evidence of cavitation erosion is, however, lacking. In terms of the well-known shear-stress (or stream-power) erosion law, erosion by plucking is consistent with a slope exponent ( n ) of ∼2/3 to 1, whereas erosion by suspended-load abrasion is more consistent with a slope exponent of ∼5/3. Given that substrate lithology appears to dictate the dominant erosion process, this finding has important implications for long-term landscape evolution and the models used to study it.
679 citations