1. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 1 CHAPTER 11: SAMPLE CALCULATION FOR BEDLOAD, SUSPENDED LOAD AND TOTAL BED MATERIAL LOAD Confluence of the Fly River (upper) and the Ok Tedi (lower), Papua New Guinea. The Ok Tedi is laden with sediment from a copper mine. The flow is from left to right.

2. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 2 SAMPLE CALCULATION The Fly River, Papua New Guinea has been subject to a heavy loading of sediment from the Ok Tedi copper mine. The waste sediment flows 140 km down the Ok Tedi (Ok means “River”) and enters the Fly River at D’Albertis Junction. Mining commenced in 1985. Data for the Fly River at the Kuambit Gaging Station, just downstream of D’Albertis Junction, has been collected since about 1980. Before the commencement of the mine, the total bed material load of the Fly River at Kuambit was estimated (rather crudely) to be in the neighborhood of 4.45 Mt/year (million metric tons per year). Here a full calculation is performed using actual data, pre-mine for the most part. Confluence of the Ok Tedi (lower) and Fly River (upper), Papua New Guinea. The lighter color of the Fly River is due to the disposal of sediment from a mine upstream. Kuambit Gaging Station is about 1 km downstream of the confluence.

3. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 3 SOME INFORMATION River slope S = 5.14 x 10 -5 near Kuambit. Bankfull depth H bf there is 9.45 m, as determined from the cross-section below. The river cross-section is plotted in undistorted form. It is only when the section is viewed in an undistorted plot that it becomes viscerally apparent how wide most natural alluvial streams are.

4. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 4 SOME INFORMATION contd. The relation between B and H was computed from the cross-section of the previous slide.

5. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 5 SOME INFORMATION contd. The pre-mine grain size distribution of the bed of the Fly River at Kuambit is given below; D 50 = D g = 0.211 mm, D 90 = 0.425 mm and  g = 1.63

6. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 6 SOME INFORMATION contd. The flow duration curve at Kuambit for 1994 is given below. The choice is because a) detailed pre-mine discharge measurements are lacking, and b) 1994 was a fairly typical year over the available record.

7. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 7 SUMMARY OF THE CALCULATION The calculation is given in the spreadsheet RTe-bookDepDisTotLoadCalc.xls. The calculation uses a) the Wright-Parker (2004) relation for hydraulic resistance, b) the Ashida-Michiue (1972) relation for bedload transport and c) the Wright-Parker (2004) entrainment relation for the computation of suspended bed material transport. In the Wright-Parker (2004) method, corrections for flow stratification are not implemented for simplicity. The calculation, which uses a single grain size D ( = D 50 here) and the normal flow approximation, proceeds as follows. 1.Assume a range of values of H s, and use the Wright-Parker hydraulic resistance predictor to predict depth H, U, u * etc. for each value of H s up to bankfull. 2.For each value of H s, compute  s * and thus the volume bedload transport rate per unit width q b from Ashida-Michiue. 3.Compute v s from D 50, and then for each value of H s find E from the Wright-Parker entrainment relation and the values of u *s /v s, S and Re p. 4.For each value of H s compute the composite roughness k c from the results of the calculation of hydraulic resistance:

8. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 8 SUMMARY OF THE CALCULATION contd. 5.For each value of H s compute the volume suspended bed material load per unit width q s from the relations 6. Use the geometric relation B = B(H) to determine the width at every depth, and then compute the total volume bed load and suspended bed material loads Q b and Q s as Q b = q b B, Q s = q s B. 7. For the kth value of H s, i.e H s,k, then, compute the values of Q b,k, Q s,k and Q t,k = Q b,k + Q s,k. 8.Determine from the flow duration curve the fraction of time p k for which the flow is in a range characterized by flow discharge Q k corresponding to H s,k. 9.The mean annual loads Q banav (bedload), Q sanav (suspended bed material load) and Q tanav (total bed material load) are then given as

9. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 9 RESULTS FROM CALCULATION OF HYDRAULIC RESISTANCE

10. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 10 RESULTS FROM CALCULATION OF BEDLOAD AND SUSPENDED BED MATERIAL LOAD

11. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 11 WHAT TO DO WHEN THE FLOW GOES OVERBANK? As the flow goes overbank, the channel depth still rises with increasing discharge, albeit much more slowly. This implies a sediment load that increases slowly as stage rises above bankfull. In the case of the Fly River near D’Albertis Junction, the floodplain is over 10 km wide, i.e. so wide that little increase in sediment load is likely realized. On the other hand, as flow goes overbank in a meandering river, the thread of high velocity can leave the channel and cut across the vegetated floodplain, causing the load to decrease as it loses its source from the river bed. In the case of the Fly, the wide floodplain should suppress this as well. So as a first approximation, in this case overbank load = bankfull load

12. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 12 RESULTS FROM CALCULATION OF TOTAL LOAD

13. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 13 SUMMARY OF RESULTS Bankfull discharge Q bf = 3018 m 3 /s Mean annual discharge Q m = 2355 m 3 /s Bankfull discharge is exceeded 29% of the time Note that a) the bankfull discharge is less than double the mean annual discharge, and b) the river is overbank for a significant amount of time. Such numbers are common for large, low-slope tropical streams. In most temperate streams, however, a) Q bf is much larger than Q m, and b) bankfull discharge is exceeded a few percent of the time at best. Mean annual bedload transport rate Q bavan = 0.34 Mt/a Mean annual suspended bed material load Q savan = 2.14 Mt/a Mean annual total bed material load Q tavan = 2.48 Mt/a Percentage of annual bed material load that is bedload = 13.6%

14. 1D SEDIMENT TRANSPORT MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 14 REFERENCES FOR CHAPTER 11 Ashida, K. and M. Michiue, 1972, Study on hydraulic resistance and bedload transport rate in alluvial streams, Transactions, Japan Society of Civil Engineering, 206: 59-69 (in Japanese). Wright, S. and G. Parker, 2004, Flow resistance and suspended load in sand-bed rivers: simplified stratification model, Journal of Hydraulic Engineering, 130(8), 796-805.