Abstract
A nonhomogeneous discrete-time three-state Markov chain model is developed in this study to quantify the bedload and suspended load discharge under unsteady flow for mixed size sediment particles. When flow is subject to sudden changes, the particle holding time, defined as the amount of time for a sediment particle staying on the bed or in the moving state, needs to be carefully evaluated. The time step used in this study for single-step motion in the discrete-time Markov chain is represented by a characteristic timescale for particle motion. The transition probabilities are functions of flow conditions and particle properties. Specifically, the likelihood of particle movement between the bedload layer and the bed surface is evaluated by the entrainment probability. Exchange of sediment particles between the bedload layer and suspended load layer is quantified by the suspension probability. A nonhomogeneous Markov chain ensures the transition probabilities are time dependent as they are a function of local conditions. The proposed sediment transport model can be used to calculate both bedload and suspended load as a function of time for any size fraction of mixed size sediment particles. The proposed sediment transport relation is compared with a classic sediment transport formula. The comparison shows that the proposed model performs better for particles of smaller grain size. It is also demonstrated that the quasi-steady assumption normally adopted in flow-sediment modeling appears to be a valid approximation when the time for the sediment transport rate to reach an equilibrium state is sufficiently small. The proposed model is also validated against unsteady bedload transport flume data, as well as flume data containing both bedload and suspended load.
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Acknowledgments
The writers gratefully acknowledge the financial support from the National Science Foundation under grant number #0748787.
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Published In
Journal of Hydrologic Engineering
Volume 21 • Issue 11 • November 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Dec 21, 2014
Accepted: Feb 2, 2016
Published online: Jun 30, 2016
Published in print: Nov 1, 2016
Discussion open until: Nov 30, 2016
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