Abstract
Sediment transport in natural rivers usually originates as results of erosion, landslides, debris flow and other sources which during high pulses or floods move along the river from highest to lowest altitude by altering river’s geomorphology. This paper investigates sediments transport in laboratory condition considering the same size of sediments but different hydraulic regimes. The main objective of the experimental work presented in this paper is to recall and to give another prospect of well-known Meyer-Peter and Müller approach for estimation of Shields number in laboratory conditions, and calibration of dimensionless Meyer-Peter and Müller number at different hydraulic regimes. For this purpose, two different experiments were conducted. During the first experiment, the water amount flushed on the flume and bed slope were altered simultaneously until the equilibrium state was achieved. Meanwhile, the critical Shields number was estimated. While, during the second experiment, the water amount remained constant, only the bed slope of the flume was continuously tilted. Both experiments were conducted under the same sediments size. Meanwhile, sediments discharge and Shields number were measured and computed for given hydraulic conditions. Also, calibration of the dimensionless Meyer-Peter and Müller number was performed, where several iterations were considered until equilibrium was reached (\(A = 3.42)\); measured sediments were almost equal with sediments discharge computed by using Meyer-Peter and Müller formula. After these experiments, it was concluded that Meyer-Peter and Müller formula can also be applied for other hydraulic conditions and similar procedure may be adopted to calibrate the dimensionless Meyer-Peter and Müller number at other cases.
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Abbreviations
- \(\varepsilon\) :
-
Average difference (error) (%)
- \(g_{vco}\) :
-
Computed sediments discharge (m3/s/m)
- \(\tau_{c}\) :
-
Critical shear stress (Pa)
- \(\theta_{C}\) :
-
Critical Shields number (-)
- \(K\) :
-
Dimensionless coefficient of the shape of the grains
- Q :
-
Flow discharge (m3s−1)
- \(S\) :
-
Flume slope (%)
- \(i\) :
-
Flume’s bed slope (%)
- g :
-
Gravitational acceleration (ms−2)
- \(l\) :
-
Length of channel (m)
- \(x\) :
-
Longitudinal coordinate (m)
- \(d_{m}\) :
-
Mean particle’s diameter (mm)
- \(g_{vme}\) :
-
Measured sediments discharge (m3/s/m)
- \(MPM\) :
-
Meyer-Peter and Müller
- A :
-
Meyer-Peter and Müller (MPM) number
- \(\rho_{s}\) :
-
Particles’ density (kg/m3)
- \(F\) :
-
Resisting force (N)
- \(g_{v}\) :
-
Sediment discharge (l/s/m)
- \(h_{s}\) :
-
Sediment’s layer depth
- \(\tau\) :
-
Shear stress (Pa)
- \(\theta\) :
-
Shields number (-)
- \(h\) :
-
Total depth (m)
- \(\rho\) :
-
Water density (kg/m3)
- \(h_{w}\) :
-
Water depth
- \(b\) :
-
Width of channel (m)
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Acknowledgements
Authors would be grateful to Aristeidis Mikroutsikos and Hayssam Abdalsalam for their valuable contribution to conduct these experimental works. Authors are grateful to the Editor’s and the Reviewers comments, which signifcantly improved the current version of the paper.
Funding
Alban Kuriqi was supported by a PhD scholarship granted by Fundação para a Ciência e a Tecnologia, I.P. (FCT), Portugal, under the PhD Programme FLUVIO–River Restoration and Management, grant number: PD/BD/114558/2016.
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Kuriqi, A., Koçileri, G. & Ardiçlioğlu, M. Potential of Meyer-Peter and Müller approach for estimation of bed-load sediment transport under different hydraulic regimes. Model. Earth Syst. Environ. 6, 129–137 (2020). https://doi.org/10.1007/s40808-019-00665-0
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DOI: https://doi.org/10.1007/s40808-019-00665-0