Sediment transport for nonuniform sediment mixtures: the Egiazaroff equation and its application in a canyon river in Brazil

Understanding the sediment yield and transport is one of the major topics of hydrosedimentology today. Although there are several methods to evaluate the incipient movement, the Shields model is mostly-used. However, the model proposed by Shields assumes that the sediments are uniform in an homogeneous and non-cohesive mixture. As such conditions are not easily found in nature, Egiazaroff proposed a sheltering coefficient, which considers the sediments in a non-homogeneous mixture in a wide range of granulometry. This coefficient allows correcting the Shields critical shear stress for nonuniform mixtures and can be used in mountain rivers, where the sediment size varies in several orders of magnitude. The equation proposed by Egiazaroff has been neglected for so many years in Brazil, and it is not mentioned in hydraulics or hydrosedimentology books . Thus, the present paper aimed to introduce the model proposed by Egiazaroff. Applying this equation to one natural river in a canyon, southern Brazil, the paper shows the good performance of this equation and recommends its use in mountain rivers in Brazil.

Two Stochastic Fraction Bedload Transport Rate Models for Nonuniform Sediment

Based on a method stochastic processes, two new bedload transport models for the ith size fraction nonuniform sediment are theoretically developed by using a stochastic model of sediment exchange and the probabilistic distribution of fractional bedload transport rates. The relations, proposed recently by Yang, for the probability of fractional incipient motion and for the average velocity of particle motion are introduced to bedload formulas. Plenty of experimental data for the bedload transport rate of uniform sediment are used to determine parameters. Finally, the two models are verified with natural data expressing the transport of nonuniform sediment under full motion in laboratory flume. The result shows that the experimental observations agree well with the predicted fractional bedload transport rates. Comparison of the theory with field data shows that the proposed formula still applies to uniform sediment transportation condition as long as the relevant parameters for uniform sediment are taken into account.

A MULTIPLE-SIZED TRANSPORT FORMULA FOR NONUNIFORM SEDIMENTS UNDER CURRENT AND WAVES

Nonuniform sediment transport exhibits difference from uniform sediment, even when the mean grain size is the same for both cases. The hiding, exposure, and armoring among different size fractions in the nonuniform bed material may significantly affect sediment transport, morphological change, bed roughness, wave dissipation, etc. It is necessary to develop multiple-sized sediment transport capacity formula to improve the accuracy and reliability of coastal analysis tools. The Wu et al. (2000) formula, which was developed for river sedimentation, is herein extended to calculate multiple-sized sediment transport under current and waves for coastal applications. This formula relates bed-load transport to the grain shear stress and suspended-load transport to the energy of the flow system. It considers the effect of bed material size composition in the hiding and exposure correction factor, which is omitted in many other existing formulas. Methods have been developed in this study to determine the bed shear stress due to waves only and combined current and waves, and in turn to compute the bed-load and suspended-load transport rates using the Wu et al. (2000) formula without changing its original formulation. The enhanced bed-load formula considers the effect of wave asymmetry on sediment transport, calculates the onshore and offshore bed-load transport rates separately and then derives the net transport rate, whereas the enhanced suspended-load formula calculates only the net transport rate due to the limit of available data. The formula has been tested using the single-sized and multiple-sized sediment transport data sets. The formula provides reliable predictions in both fractional and total transport rates. More than half of the test cases are predicted within a factor of 2 of the measured values, and more than 90% of the cases are within a factor of 5. This accuracy is generally reasonable for sediment transport under current and waves, which is very complex and little understood.