Analytical and Empirical Regime Relationships in Alluvial Rivers

Document Type : Research Paper


1 M. Sc. Student of River Engineering, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Iran.

2 Assistant of Professor, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Iran,

3 Assistant of Professor, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Iran.


It is vitally important that rivers reach an equilibrium state (regime). To be more precise, determination of stable hydraulic geometry is one of the most important factors on which designing, planning and training of rivers is based. In this research, an analytical model was proposed initially by using extremal hypotheses and then multivariate hydraulic geometry relationships were applied to the rivers under dominant bed load. Thereafter, field study was carried out on several gravel bed rivers in Khuzestan and Chaharmahal provinces. A total of 24 hydrometeorological stations in 17 river reaches were sampled to characterize bed material gradation curve. With regards to bed structure of gravel bed rivers, samplings were made by surface and volumetric methods. Then, sediment samples were put into two categories of surface and armor layers. The collected field data was originally applied to derive regime relationships by using multivariate regression analysis. The effect of bed structure was directly studied to better understand it in the regime relationships. A reasonable agreement was observed between the developed analytical and empirical exponents of the hydraulic geometry relationships in this study and those by other researchers. Finally, the developed model was calibrated using the field data of Iran and the mean relative error of the bankfull width and depth calculation were 26% and 24%, respectively.


Main Subjects

1-    Brownlie, W. R., 1983. Flow depth in sand-bed channels. Journal of Hydraulic Engineering, ASCE109, pp. 959–990.
2-    Bunte, K. and Abt, S. R., 2001. Sampling surface and subsurface particle‐size distributions in wadable gravel‐ and cobble‐bed streams for analyses in sediment transport, hydraulics, and stream‐bed monitoring. USDA Forest Service Rocky Mountain Research Station, General Technical Report RMRSGTR‐74.
3-    Chow, V.T., 1959. Open Channel Hydraulics. New York, McGraw-Hill Book Company, Inc.
4-    DuBoys, P., 1879. River Rhone and tributaries of unconsolidated sediments. Annales de ponts et chausses18 (5), pp. 141–195.
5-    Engelund, F. and Skovgaard, O., 1973. On the origin of meandering and braiding in alluvial streams. Journal of Fluid Mechanics57, pp. 289-302.
6-    Hey, R.D. and Thorne, C.R., 1986. Stable channels with mobile gravel beds. Journal of the Hydraulic Engineering, ASCE, 112 (8), pp. 671- 689.
7-    Huang, H.Q., 2010. Reformulation of the bed load equation of Meyer-Peter and Müller in light of the linearity theory for alluvial channel flow. Water Resources Research46 (9), pp. 1-11.
8-    Huang, H.Q. and Nanson, G.C., 2000. Hydraulic geometry and maximum flow efficiency as products of the principle of least action. Earth Surface Processes and Landforms, 25, pp. 1–16.
9-    Huang, H.Q. and Nanson, G.C., 2002. A stability criterion inherent in laws governing alluvial channel flow. Earth Surface Processes and Landforms27 (9), pp. 929-944.
10-Lacey, G., 1958. Flow in alluvial channels with sandy mobile beds, Proceedings of the Institute of Civil Engineers, London, 9, discussion11, pp. 145–164.
11-Mahmoudi, M., Majdzadeh Tabatabai, M.R. and Mousavi Nadoushani, S., 2016. Analytical application of maximum sediment transport capacity to determine hydraulic geometry relationships in gravel bed rivers. Modares Civil Engineering Journal16(3), pp. 177-191. (In Persian).
12-Manning, R., 1891. On the flow of water in open channels and pipes. Transactions of the Institution of Civil Engineers of Ireland20, pp. 161-207.
13-Meyer-Peter, E. and Muller, R., 1948. Formulas for bed load transport. In Proceedings of the 3rd Meeting of IAHR Stockholm.
14-Milhous, R.T., Hogan, S.A., Abt, S.R. and Watson, C.C., 1995. Sampling river-bed material: The barrel Sampler Rivers5 (4), pp. 239-249.
15-Parker, G., 1979. Hydraulic geometry of active gravel rivers. Journal of the Hydraulics Division, ASCE105, pp. 1185–1201.
16-Van Rijn, L.C., 1984. Sediment Transport, Part I-Bed Load Transport. Journal of the Hydraulic Engineering, ASCE110 (10), pp. 1431–1456.
Volume 43, Issue 2
July 2020
Pages 155-170
  • Receive Date: 08 October 2017
  • Revise Date: 01 November 2018
  • Accept Date: 11 November 2018
  • First Publish Date: 21 June 2020