TY - JOUR

T1 - Nonlinear Bedload Transport Trajectory Angle Expressed in a Traditional Form

T2 - Derivation and Application

AU - Waterman, David M.

AU - García, Marcelo H.

N1 - Funding Information:
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.
Publisher Copyright:
© 2019 American Society of Civil Engineers.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - 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.

AB - 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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U2 - 10.1061/(ASCE)HY.1943-7900.0001619

DO - 10.1061/(ASCE)HY.1943-7900.0001619

M3 - Article

AN - SCOPUS:85066927722

VL - 145

JO - American Society of Civil Engineers, Journal of the Hydraulics Division

JF - American Society of Civil Engineers, Journal of the Hydraulics Division

SN - 0733-9429

IS - 8

M1 - 04019028

ER -