Calculate Sediment Loads in Papua New Guinea's Fly River

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
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
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.
Fly River at Kuambit October 17, 1982
0
50
0 50 100 150 200 250 300 350 400
Lateral Distance m
Elevation
m
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
SOME INFORMATION contd.
Relation between Water Surface Width and Cross-
sectionally averaged Depth, Kuambit 1982
300
310
320
330
340
350
360
370
0 1 2 3 4 5 6 7 8 9 10
H (m)
B
(m)
The relation between B and H was computed from the cross-section of the
previous slide.

5
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
Bed Grain Size Distribution, Kuambit, Pre-Mine
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10
D mm
Percent
Finer

6
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.
Flow Duration Curve, Kuambit, 1994
0
10
20
30
40
50
60
70
80
90
100
100 1000 10000
Q (m3
/s)
Percent
Time
Exceeded

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 ( = D50 here) and the normal flow approximation, proceeds as follows.
1. 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.
2. For each value of Hs, compute s* and thus the volume bedload transport rate per
unit width qb from Ashida-Michiue.
3. Compute vs from D50, and then for each value of Hs find E from the Wright-Parker
entrainment relation and the values of u*s/vs, S and Rep.
4. For each value of Hs compute the composite roughness kc from the results of the
calculation of hydraulic resistance:
)
Cz
(
c
e
H
11
k 


8
SUMMARY OF THE CALCULATION contd.
5. 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.
8. 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.
9. The mean annual loads Qbanav (bedload), Qsanav (suspended bed material load)
and Qtanav (total bed material load) are then given as


 

 k
k
,
t
av
tan
k
k
,
s
sanav
k
k
,
b
banav p
Q
Q
,
p
Q
Q
,
p
Q
Q































1
c
u
v
b
b
s
b
s
d
k
H
30
n
/
)
1
(
/
)
1
(
,
EH
u
q 

9
RESULTS FROM CALCULATION OF HYDRAULIC RESISTANCE
Fly River at Kuambit
0
5
10
15
20
25
0 2 4 6 8 10
H (m)
Various
Parameters
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
qw (m2/s)
Cz
t*
ts*
Fr
kc (m)
u*s (m/s)
Cz (left axis) * (right axis)
qw (left axis)
s* (right axis)
u*s (right axis)
Fr (right axis)
kc (right axis)

10
RESULTS FROM CALCULATION OF BEDLOAD AND SUSPENDED BED
MATERIAL LOAD
Bedload and Suspended Load Calculations per Unit Width
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
0 2 4 6 8 10
H (m)
Various
parameters
qb (m2/s)
E
I
qs (m2/s)
qt (m2/s)

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
RESULTS FROM CALCULATION OF TOTAL LOAD
Total Volume Loads
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
10 100 1000 10000
Q (m3
/s)
Q
b
(m
3
/s),
Q
s
(m
3
/s),
Q
t
(m
3
/s)
Qb (m3/s)
Qs (m3/s)
Qt (m3/s)

13
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%

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.

Calculate Sediment Loads in Papua New Guinea's Fly River

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