Nonlinear Bedload Transport Trajectory Angle Expressed in a Traditional Form: Derivation and Application
Publication: Journal of Hydraulic Engineering
Volume 145, Issue 8
Abstract
The most common bedload transport calculation methods use an equation for the vector direction that is a linear function of the transverse slope. Existing theoretical formulations that account for nonlinear effects when transverse slopes are steep (such as noncohesive stream banks) are not widely used in practice, due largely to the complexity of their implementation. In this analysis, a single equation for the bedload transport rate direction is derived that accounts for the nonlinearity. The equation is cast in the same form as most linear formulations, but with the constant replaced by a function that requires the equation to be solved numerically. Negligible streamwise slopes are assumed, which allows the simplified expression; otherwise, the derivation follows past rigorous theoretical treatments that are valid for transverse slopes up to the angle of repose. A direct comparison is made between linear and nonlinear derivations that highlights the approximations inherent in the linear form. Application of the equation to two different types of past experiments illustrates the degree of error associated with evaluating bedload data involving steep transverse slopes using a traditional linear form for the vector direction.
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Acknowledgments
This work was an extension of a project originally funded by the Illinois Water Resources Center (Grant: Streambank Erosion in the Mackinaw River, Illinois) when the first author was a graduate student at University of Illinois at Urbana-Champaign. Thanks are extended to Davide Motta for assistance with the mathematics during the early stages of the analysis. Thanks are also extended to two anonymous reviewers for helpful comments.
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Published In
Journal of Hydraulic Engineering
Volume 145 • Issue 8 • August 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jul 9, 2018
Accepted: Jan 23, 2019
Published online: Jun 6, 2019
Published in print: Aug 1, 2019
Discussion open until: Nov 6, 2019
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