SAMPLE CALCULATION FOR BEDLOAD, SUSPENDED LOAD AND TOTAL BED MATERIAL LOAD

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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.
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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 DAlbertis Junction. Mining
commenced in 1985. Data for the Fly River at the
Kuambit Gaging Station, just downstream of
DAlbertis 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.
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SOME INFORMATION
River slope S 5.14 x 10-5 near
Kuambit. Bankfull depth Hbf 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.
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SOME INFORMATION contd.
The relation between B and H was computed from
the cross-section of the previous slide.
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SOME INFORMATION contd.
The pre-mine grain size distribution of the bed
of the Fly River at Kuambit is given below D50
Dg 0.211 mm, D90 0.425 mm and ?g 1.63
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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.
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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 ( D50 here) and the normal flow
  approximation, proceeds as follows.
• Assume a range of values of Hs, and use the
  Wright-Parker hydraulic resistance predictor to
  predict depth H, U, u etc. for each value of Hs
  up to bankfull.
• For each value of Hs, compute ?s and thus the
  volume bedload transport rate per unit width qb
  from Ashida-Michiue.
• Compute vs from D50, and then for each value of
  Hs find E from the Wright-Parker entrainment
  relation and the values of us/vs, S and Rep.
• For each value of Hs compute the composite
  roughness kc from the results of the calculation
  of hydraulic resistance

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SUMMARY OF THE CALCULATION contd.

• For each value of Hs compute the volume suspended
  bed material load per unit width qs 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 Qb and Qs as Qb qbB, Qs
  qsB.
• 7. For the kth value of Hs, i.e Hs,k, then,
  compute the values of Qb,k, Qs,k and Qt,k Qb,k
  Qs,k.
• Determine from the flow duration curve the
  fraction of time pk for which the flow is in a
  range characterized by flow discharge Qk
  corresponding to Hs,k.
• The mean annual loads Qbanav (bedload), Qsanav
  (suspended bed material load) and Qtanav (total
  bed material load) are then given as

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RESULTS FROM CALCULATION OF HYDRAULIC RESISTANCE
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RESULTS FROM CALCULATION OF BEDLOAD AND SUSPENDED
BED MATERIAL LOAD
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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
DAlbertis 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
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RESULTS FROM CALCULATION OF TOTAL LOAD
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SUMMARY OF RESULTS
Bankfull discharge Qbf 3018 m3/s Mean annual
discharge Qm 2355 m3/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) Qbf is
much larger than Qm, and b) bankfull discharge is
exceeded a few percent of the time at best. Mean
annual bedload transport rate Qbavan 0.34
Mt/a Mean annual suspended bed material load
Qsavan 2.14 Mt/a Mean annual total bed material
load Qtavan 2.48 Mt/a Percentage of annual bed
material load that is bedload 13.6
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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.