Abstract
Purpose
Bedload transport discharge is important in river engineering and morphodynamics. The Meyer-Peter and Müller (MPM) equation for determining bedload transport rates that was introduced in 1948 is still widely used in basic and applied engineering practise. An employment of the MPM equation for sand bed rivers is rarely observed as it usually performs well for gravel-bed rivers. The MPM equation was improved by introducing a correction factor considering the effects of the bedform and sediment mixture.
Materials and methods
Field measurements of bedload transport rates at 64 cross sections of different sites along the Nile River in Egypt were collected and employed to enhance the prediction of bedload transport rates based on the MPM formula. Furthermore, independent laboratory experiments were executed in a straight sand bed flume to verify the modified form of the MPM equation and to extend its application range.
Results and discussion
The MPM equation was improved by introducing a correction factor considering the effects of the bedform and sediment mixture. The accuracy of several sediment transport formulas (Meyer-Peter and Müller 1948; Frijlink 1952; Wong and Parker J Hydraul Eng 132:1159–1168, 2006; van Rijn 1984; modified Abdel-Fattah 2004; Huang Water Resour Res 46 W09533, 2010) was also evaluated using cumulative field measurements. Results suggest that the modified MPM equation is more suitable for the Nile River conditions than are the other tested equations.
Conclusions
The study results indicate that the modified MPM equation can predict the bedload transport rates under the Nile River conditions with high accuracy.
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Change history
08 August 2022
A Correction to this paper has been published: https://doi.org/10.1007/s11368-022-03306-9
Abbreviations
- λ a, λ b, η, and ξ :
-
correction factors
- B :
-
river width (m)
- C :
-
overall Chezy coefficient (m0.5 s−1)
- C′ :
-
grain-related Chezy coefficient (m0.5 s−1)
- d 10 :
-
size at which 10% by weight is finer (m)
- d 35 :
-
size at which 35% by weight is finer (m)
- d 50 :
-
size at which 50% by weight is finer (m)
- d 90 :
-
size at which 90% by weight is finer (m)
- d m :
-
arithmetic mean diameter of the sediment (m)
- D * :
-
dimensionless particle diameter (–)
- g :
-
gravitational acceleration (m s−2)
- k s :
-
effective bed roughness (m)
- q b :
-
bedload transport rate (g m−1 s−1)
- R b :
-
hydraulic radius of the bed region (m)
- R h :
-
hydraulic radius (m)
- S :
-
energy gradient (–)
- s :
-
relative density (–)
- T :
-
dimensionless transport stage parameter (–)
- u :
-
mean flow velocity (m s−1)
- u * :
-
the bed shear velocity (m s−1)
- y :
-
flow depth (m)
- ϕ :
-
dimensionless bedload transport rate (–)
- θ :
-
Shields parameter (–)
- θ cr :
-
critical mobility parameter
- ρ s :
-
sediment density (kg m−3)
- ρ :
-
water density (kg m−3)
- σ g :
-
standard deviation of sediment mixture (–)
- τ o :
-
bed shear stress (N m−2)
- μ :
-
bedform factor or efficiency factor
- τ o′:
-
effective bed shear stress (N m−2)
- τ cr :
-
critical bed shear stress according to Shields (N m−2)
- ν :
-
kinematic viscosity (m2 s−1)
References
Abdelhaleem FS (2019) Roughened bridge piers as a scour countermeasure under clear water conditions. ISH J Hydraul Eng 25(1):94–103
Abdelhaleem FS, Helal EY (2015) Impacts of grand Ethiopian renaissance dam on different water usages in upper Egypt. Brit J Appl Sci Tech 8(5):461–483
Abdel-Fattah S, Amin AM, van Rijn LC (2004) Sand transport in Nile River, Egypt. J Hydraul Eng 130(6):488–500
Ackers P, White WR (1973) Sediment transport: a new approach and analysis. J Hydraul Eng 99:2041–2060
Amin AM (1999) Experimental approach to bed load transport of slightly non-uniform sediment. Dissertation, International Institute for Hydraulic and Environmental Engineering, IHE, Delft
Bagnold RA (1966) An approach to the sediment transport problem from general physics. US Geol Surv Prof Pap 422-I:1–42
du Boys MP (1879) Le Rhone et le rivieres a lit affoillable. Mem Doc Ann Pont et Chaussees Ser 5(18):141–195
Einstein HA (1950) The bed load function for sediment transportation in open channel flows. Tech Bull 1026 Soil Conserv Serv US Dept. of Agric Washington DC
Frijlink HC (1952) Discussion of bed load movement formulas. Report No, X2344/LV, Delft Hydraulics. Delft
Gaweesh MT, van Rijn LC (1994) Bed load sampling in sand-bed rivers. J Hydraul Eng 120(12):1364–1384
Gaweesh MT, Gasser MM (1991) Geomorphic and hydraulic response of the Nile River to the operation of High Aswan Dam. Water Sci. Magazine 9 National Water Research Centre Egypt
Gomez B, Chruch M (1989) An assessment of bed load sediment transport formulae for gravel bed rivers. Water Resour Res 25:1161–1186
Helal E (2019) Experimental evaluation of changes in channel bed morphology due to a defective pressure flow pipe. J Irrig Drain Eng 145(10):04019022
Huang HQ (2010) Reformulation of the bed load equation of Meyer-Peter and Müller in light of the linearity theory for alluvial channel flow. Water Resour Res 46:W09533. https://doi.org/10.1029/2009WR008974
Huang HQ, Chang HH (2006) Scale independent linear behaviour of alluvial channel flow. J Hydraul Eng 132:722–730
Hunziker RP, Jaggi MNR (2002) Grain sorting processes. J Hydraul Eng 128:1060–1068
HRI (2000) Field measurements of sediment load transport in the Nile river at Aswan, Qena, Sohag, Beni-Suef and Cairo. Technical Rep No.101/2000 Hydraulics Research Institute, HRI, Delta Barrages
Kuriqi A (2019) Recalling Meyer-Peter and Müller approach for assessment of bed-load sediment transport. Preprints 2019:2019040050. https://doi.org/10.20944/preprints201904.0050.v1)https://www.preprints.org/subject/browse/engineering/civil_engineering
Meyer-Peter E, Müller R (1948) Formulas for bed load transport, Proc. 2nd IAHR congress Stockholm, Sweden
Nielsen P, Callaghan DP (2003) Shear stress and sediment transport calculations for sheet flow under waves. Coast Eng 47(3):347–354
Ota JJ, Nalluri C (2003) Urban storm sewer design: approach in consideration of sediments. J Hydraul Eng 129(4):291–297
Parker G (1991) Selective sorting and abrasion of river gravel. II: applications J Hydraul Eng 117:150–171
Qi M, Li J, Chen Q (2018) Applicability analysis of Pier-scour equations in the field: error analysis by rationalizing measurement data. J Hydraul Eng 144(8):1–12
Recking A, Liebault F, Peteuil C, Jolimet T (2012) Testing bedload transport equations with consideration of time scales. Earth Surf Process Landf 37:774–789
Smart GM (1984) Sediment transport formula for steep channels. J Hydraul Eng 110:267–276
Singh AK, Kothyari UC, Ranga Raju KG (2004) Rapidly varying transient flows in alluvial rivers. J Hydraul Res 42(5):473–486
Tritthart M, Schober B, Habersack H (2011) Non-uniformity and layering in sediment transport modelling 1: flume simulations. J Hydraul Res, IAHR 49(3):325–334
van Rijn LC (1984) Sediment transport, Part I: bed load transport. J Hydraul Eng 110(10):1431–1456
van Rijn LC, Gaweesh MT (1992) New total sediment load sampler. J Hydraul Eng 118(12):1686–1691
Vanoni VA, Brooks NH (1957) Laboratory studies of the roughness and suspended load of alluvial streams. Sedimentation laboratory. California Institute of Technology, Pasadena, Report E-68, USA
Wong M (2003) Does the bed load transport relation of Meyer-Peter and Müller fits its own data. 30th Congress Int. Assoc. for Hydro-Environ Eng and Res, Madrid
Wong M, Parker G (2006) Reanalysis and correction of bed load relation of Meyer-Peter and Müller using their own database. J Hydraul Eng 132:1159–1168
Yalin MS (1963) An expression for bed load transportation. J Hydraul Eng 89:221–250
Yalin MS, Scheuerlein H (1988) Friction factors in alluvial rivers. Tech Univ München, Munich, Germany, Rep 59:76 (in German)
Yang SC (2005) Prediction of total bed material discharge. J Hydraul Res IAHR 43(1):12–22
Yang CT (1984) Unit stream power equation for gravel. J Hydraul Eng 110:1783–1797
Zanke CE (2001) On the physics of flow-driven sediments (bed load). Int J Sediment Res 16:1–18
Acknowledgements
The authors are very grateful to the Hydraulics Research Institute staff for their collaboration and facilitating the field measurements data.
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Abdelhaleem, F.S., Amin, A.M., Basiouny, M.E. et al. Adaption of a formula for simulating bedload transport in the Nile River, Egypt. J Soils Sediments 20, 1742–1753 (2020). https://doi.org/10.1007/s11368-019-02528-8
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DOI: https://doi.org/10.1007/s11368-019-02528-8