1. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 1 CHAPTER 12: BULK RELATIONS FOR TRANSPORT OF TOTAL BED MATERIAL LOAD Sediment-laden meltwater emanating from a glacier in Iceland. The flow is from top to bottom. The flow to the left is braided, whereas that to the right is meandering. Image courtesy F. Engelund and J. Fredsoe.

2. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 2 QUANTIFICATION OF TOTAL BED MATERIAL LOAD The total bed material load is equal to the sum of the bedload and the bed material part of the suspended load; in terms of volume transport per unit width, q t = q b + q s. Here wash load, i.e. that part of the suspended load that is too fine to be contained in measurable quantities in the river bed, is excluded from q s. Total bed material load is quantified in various ways in addition to q t Flux-based volume concentration C t = q t /(q t + q w ) Flux-based mass concentration X t =  s q t /(  s q t +  q w ) Flux-based mass concentration in parts per million = X t  10 6 Concentration in milligrams per liter =  s q t /(q t + q w )  10 6, where q t and q w are in m 2 /s and  s is in tons/m 3. In the great majority of cases of interest q t /q w << 1, so that the concentration in milligrams per liter is accurately approximated by the mass concentration in parts per million.

3. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 3 RELATION OF ENGELUND AND HANSEN (1967) A variety of relations are available for the prediction of bulk total bed material load. Most of them are based on the regression of large amounts of data. Five such relations are reported here. Although the data bases for some of them include gravel, they are not designed for gravel-bed streams. As such, their use should be restricted to sand-bed streams. Perhaps the simplest of these relations is that due to Engelund and Hansen (1967). It takes the form where The relation is designed to be used in conjunction with the formulation of hydraulic resistance of Engelund and Hansen (1967) presented in Chapter 9. Brownlie (1981) has found the relation to perform very well for field sand-bed streams.

4. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 4 RELATION OF BROWNLIE (1981) The formulation of Brownlie (1981) can be expressed as: In the above relations  g is the geometric standard deviation of the bed sediment and c F takes the value of 1 for laboratory conditions and 1.268 for field conditions. The relation is designed to be used in conjunction with the Brownlie (1981) formulation for hydraulic resistance.

5. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 5 RELATION OF YANG (1973) The formulation of Yang (1973; see also 1996) can be expressed as: In the above relations v s is the fall velocity associated with sediment size D 50.

6. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 6 RELATION OF ACKERS AND WHITE (1973) The formulation of Ackers and White (1973) can be expressed as:

7. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 7 RELATIONS OF KARIM AND KENNEDY (1981) AND KARIM (1998) The formulation of Karim and Kennedy (1981) can be expressed as: where u *c can be evaluated from Brownlie’s (1981) fit to the original Shields curve: The above relation may be used in conjunction with their relation for hydraulic resistance presented in Chapter 9. Karim (1998) also presents a total bed material load equation that is fractionated for mixtures;

8. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 8 REFERENCES FOR CHAPTER 12 Ackers, P. and White, W. R., 1973, Sediment transport: new approach and analysis, Journal of Hydraulic Engineering, 99(11), 2041-2060. Brownlie, W. R., 1981, Prediction of flow depth and sediment discharge in open channels, Report No. KH-R-43A, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, California, USA, 232 p. Engelund, F. and E. Hansen, 1967, A Monograph on Sediment Transport in Alluvial Streams, Technisk Vorlag, Copenhagen, Denmark. Karim, F., 1998, Bed material discharge prediction for nonuniform bed sediments, Journal of Hydraulic Engineering, 124(6): 597-604. Karim, F., and J. F. Kennedy, 1981, Computer-based predictors for sediment discharge and friction factor of alluvial streams, Report No. 242, Iowa Institute of Hydraulic Research, University of Iowa, Iowa City, Iowa. Yang, C. T., 1973, Incipient motion and sediment transport, Journal of Hydraulic Engineering, 99(10), 1679-1704. Yang, C. T., 1996, Sediment Transport Theory and Practice, McGraw-Hill, USA, 396 p.