Determination of Form Friction Factor of Armored Gravel-Beds Rivers ‎

Document Type : Research Article


1 Department of Water Engineering, College of Agriculture, Bu-Ali Sina University, 3869565178, ‎Hamadan, Iran‎

2 Department of Water Engineering, College of Agriculture, Bu-Ali Sina University, 3869565178, ‎Hamadan, Iran‎


Friction factor plays a substantial role in hydraulic computations. In coarse-bed rivers, friction ‎factor depends on grain size and bed forms. A wide range of particle sizes and developing ‎armor layer have great effects on friction factor. Therefore, determination of form friction ‎factor of armored river beds has been investigated in this study and, a friction equation was ‎developed based on computing grain friction factor of the total friction factor. Analysis of ‎obtained equation showed that the friction factor is rather independent of grain-size ‎distribution of the material forming the bed and the maximum grain size of this material. The ‎major controlling parameter is the slope of the energy grade line. These results are explained by ‎the coupling of the friction factor with the incipient motion problem and the rearrangement of ‎the grains of the coarsest fraction in the armor coat. To verify the equation, Keulegan method ‎was used which results 80% agreement between two methods‏.‏‎ Also, including the major part of ‎total friction factor to form friction factor (40%) shows the great effects of bed form on flow ‎resistance. The results of the current study showed that making and development of armor ‎layer increase bed roughness and friction factor and decrease average flow velocity causing a ‎reduction in threshold Shields parameter and augmentation in bed stability. Field observations ‎are employed to test the methods.‎


اخروی، س.س.، افضلی‌مهر، ح.، نظیری، د. و شهرکی، ن. (۱۳۹۲). "ویژگی‌های پروفیل سرعت در توالی برآمدگی و فرورفتگی‌ها- منطقه مورد مطالعه: اردل از توابع شهرکرد". دوازدهمین کنفرانس هیدرولیک ایران، پردیس کشاورزی و منابع طبیعی دانشگاه تهران، تهران.
Acaroglu, E.R. (1972). "Friction factors in solid material systems". J. Hydr. Div. 98(HY4), 681-699.
Ackers, P. and White, W.R. (1973). "Sediment transport: New approach and analysis." J. Hydr. Div. 99(HY11), 2041-2060.
Afzalimehr, H. (2010). "Effect of flow non-uniformity on velocity and turbulence intensities in flow over a cobble-bed". Hydrol. Process. 24, 331-341.
Afzalimehr, H., Singh, V.P. and  Fazel Najafabadi, E. (2010). "Determination of Form Friction Factor". J. Hydrol. Eng. 15(3):237-243.
Billi, P. (1988). "A note on cluster bedform behaviour in a gravel-bed river". Catena. 15(5):473-481.
Brayshaw, A.C., Frostick, L.E. and Reid, I. (1983). "The hydrodynamics of particle clusters and sediment entrainment in coarse alluvial channels". Sedimentology. 30(1):137-143.
Bathurst J.C. (2002). "At-a-site variation and minimum flow resistance for mountain rivers". J. Hydrol. 269, 11-26.
Brownlie, W.R. (1983). "Flow depth in sand-bed channels". J. Hydraul. Eng. 109(7):959-990.
Carling, P.A. (1991). "An appraisal of the velocity-reversal hypothesis for stable pool-riffle sequences in the river severn, England". Earth Surf. Processes Landforms. 16(1):19-31.
Church, M. and Hassan, M.A. (2002). "Mobility of bed material in Harris Creek". Water Resour. Res. 38(11):1237, doi:10.1029/2001WR000753.
Coleman, N.L. (1967). "A theoretical and experimental study of drag and lift forces acting on a sphere resting on a hypothetical stream bed". Proc., 12th Congress of the Int. Association for Hydraulic Research, Vol. 3, Fort Collins, Colo., 185-192.
Constantinescu, G., Garcia, M. and Hanes, D. (2016). River Flow. ISBN 9781138029132- CAT# K27572.
Dey, S. (2014). "Fluvial hydrodynamics (hydrodynamic and sediment transport phenomena)". Springer, pp. 508-511.
Diplas, P. (1987). "Bed load transport in gravel-bed streams". J. Hydraul. Eng. 113(3):277-291.
Fedele, J.J. and Garcia, M.H. (2001). "Alluvial roughness in streams with dunes: A boundary-layer approach". River, coastal and estuarinemorphodynamics, G. Seminara and P. Blondeaux, eds., Springer, Berlin, 37-60.
Fenton, J.D. and Abbott, J.E. 1977. "Initial movement of grains on a stream bed: The effect of relative protrusion". Proc. R. Soc. London, Ser. A, 352, 523-537.
Froehlich, D.C. (1995). "Armor-limited clear-water contraction scour at bridges". J. Hydraul. Eng. 21(6):490-493.
Garcia, M.H. (2008). "Section 2: Sediment transport and morphodynamics". ASCE manual of practice 110: Sedimentation engineering, M. H. Garcia, Reston, Va., 2.21-2.63.
Gessler, J. (1990). "Friction factor of armored river beds". J. Hydraul. Eng. 116(4):531-542.
Graf, W.H. and Suszka, L. (1987). "Sediment transport in steep channels". J. Hydrosci. Hydr. Eng. 5(1):11-26.
Griffiths, G.A. (1989). "Flow resistance in gravel channels with mobile beds". J. Hydraul. Eng. 115(3):340-355.
Hammond, F.D., Heathershaw, A.D. and Langhorne, D.N. (1984). "A comparison between shields threshold criterion and the Henderson movement of loosely packed gravel in a tidal channel". J. Sedimentology. 31:51-62.
Hendrick, R.R., Lisa, L. and Papanicolaou, A.N. (2010). "The role of hydrologic processes and geomorphology on the morphology and evolution of sediment clusters in gravel-bed rivers". Geomorphology, 114:483-496.
Jarrett, R. D. (1991). "Hydraulic of mountain rivers". Channel flow resistance: Centennial of Manning’s formula, B. C. Yen, ed., Water Resources, Littleton, Colo., 287-298.
Julien P.Y. (1995). "Erosion and Sedimentation". Cambridge University Press, UK.
Julien, P.Y., Klaassen, G.J., Ten Brinke, W.B.M. and Wibers, A.W.E. (2002). "Case study: Bed resistance of Rhine river during 1008 flood". J. Hydraul. Eng. 128(12):1042-1050.
Keulegan, G. H. (1938). "Laws of turbulent flow in open channel". J. Res. Natl. Bur. Stand. 1151(21): 707-741.
Knighton, D.A. (1998). "Fluvial forms and processes: a new perspective". Arnold, London.
Lamb, M.P. Dietrich, W.E. and Venditti, J.G. (2008). "Is the critical Shields stress for incipient sediment dependent on channel-bed slope? ". J. Geophy. Res. 113, F02008.
Meyer-Peter, E. and Muller, R. (1948). "Formulas for bed-load transport". Proc., 3rd Meeting of IAHR, Stockholm, Sweden, 39-64.
Namaee, M.R., Sui, J. and Whitcombe, T. (2017). "A revisit of different models for flow resistance in gravel-bed rivers and hydraulic flumes". Intl. J. River Basin Management. 15(3):277-286.
Oreizi, Z., AfzaliMehr, H., Singh, V.P. and Okhravi, S.S. (2014). "Investigation of Particle-Size Distribution and Friction Factor for a Gravel-Bed river: Marbar". J. River Eng. 2(3):1-38.
Petit, F. (1989). "The evaluation of grain stress from experiments in a pebble-bedded flume". Earth Surf. Processes Landforms, 14:499-508.
Prestegaard, K.L. (1983). "Bar resistance in gravel bed streams at bankfull stage". Water Resour. Res. 19:472-476.
Proffitt, G.T. (1980). "Selective transport and armoring of nonuniform alluvial sediments," thesis presented to the University of Canterbury, Christchurch, New Zealand, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Robert, A. (1997). "Characteristics of velocity profiles along riffle-pool sequences and estimates of bed shear stress". J. Geomorphology, 19,89-98.
Simons, D.B. and Richardson, E.V. (1966). "Physiographic and hydraulic studies of rivers: resistance to flow in alluvial channels". U. S. Geol. Surv, Page, 422-J.
Strom, K., Papanicolaou A.N., Evangelopoulos, N. and Odeh, M. (2004). "Microforms in gravel bed rivers: formation, disintegration, and effects on bed load transport". J. Hydraul. Eng. 130(6):554–567.
Van Rijn, L.C. (1982). "Equivalent roughness of alluvial bed". J. Hydr. Div., 108HY10, 1215-1218.
Van Rijn, L.C. (1984). "Sediment transport. Part III: Bed forms and alluvial roughness". J. Hydraul. Eng. 110(12): 1733-1754.
Wolman, M.G. (1954). "A method of sampling coarse river-bed material". EOS, Transactions American Geophysical Union 35, 951-956.
Yalin, M.S. (1972). Mechanics of sediment transport, 2nd Ed., Pergamon, Oxford, N.Y.
Yen B. C. (2002). "Open channel flow resistance". J. Hydraul. Eng. 128:20-39.
Yen, B.C. (1991). "Hydraulic resistance in open channels". Channel flow resistance: Centennial of Manning’s formula, B. C. Yen, ed., Water Resource, Highlands Ranch, Colo., 1-135.
Yang, S.-Q., Tan, S.-K. and Lim, S.-Y. (2005). "Flow resistance and bed form geometry in a wide alluvial channel". Water Resour. Res. 41, W09419, doi:10.1029/2005WR004211
  • Receive Date: 17 October 2017
  • Revise Date: 19 June 2018
  • Accept Date: 19 June 2018
  • First Publish Date: 22 November 2018