1
Cheng, N. S. (2002). "Exponential formula for bedload transport." Journal of
Hydraulic Engineering, ASCE, 128(10), 942-946.
EXPONENTIAL FORMULA FOR BEDLOAD TRANSPORT
Nian-Sheng Cheng1
Abstract: An exponential formula that does not involve the concept of the critical shear stress
is derived in this study for computing bedload transport rates. The formula represents well
various experimental data sets ranging from the weak transport to high shear conditions.
Comparisons of the present study are also made with many previous bedload formulas
commonly cited in the literature.
Keywords: Bedload, sediment transport, transport rate, shear stress, critical shear stress, weak
transport, high shear.
INTRODUCTION
Most of the formulas available in the literature for computing bedload transport rates
can be expressed in terms of shear stress excess or its equivalents. Typical examples are those
proposed by Meyer-Peter and Mueller (1948) and Yalin (1977), respectively, which include
the term of (Θ - ΘC), where Θ = u*
2
/[(ρS/ρ -1)gD] = the dimensionless shear stress, u* = shear
velocity, ρS = density of particle, ρ = density of fluid, g = gravitational acceleration, D =
diameter of particle, and ΘC is its corresponding critical value at the threshold condition of
bed particles. Another example is the theoretical expression derived by Bagnold (1973) who
reported that the transport rate was proportional to ( )
C
Θ
Θ . Obviously, all the formulas
1
Asst. Professor, Environmental Engineering Research Centre, School of Civil and Structural Engineering,
Nanyang Technological University, Nanyang Avenue, Singapore 639798. cnscheng@ntu.edu.sg
2
of this kind can be used to predict bedload transport rates only for Θ > ΘC or the conditions of
moderate to high shear stresses.
On the other hand, for practical purposes, sediment transport rates can also be

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