
Not all channels are formed in sediment and not all
rivers transport sediment. Some have been carved into
bedrock, usually in headwater reaches of streams
located high in the mountains. These streams have
channel forms that often are dominated by the nature of
the rock (of varying hardness and resistance to
mechanical breakdown and of varying joint definition,
spacing and pattern) in which the channel has been cut.
Competence :
Competence refers to the largest size (diameter) of sediment
particle or grain that the flow is capable of moving; it is a
hydraulic limitation. If a river is sluggish and moving very
slowly it simply may not have the power to mobilize and
transport sediment of a given size even though such
sediment is available to transport. So a river may be
competent or incompetent with respect to a given grain size.
If it is incompetent it will not transport sediment of the
given size. If it is competent it may transport sediment of
that size if such sediment is available
Capacity refers to the maximum amount of sediment of a
given size that a stream can transport in traction as bedload.
Given a supply of sediment, capacity depends on channel
gradient and discharge. Capacity transport is the
competence-limited sediment transport (mass per unit time)
predicted by all sediment-transport equations. Capacity
transport only occurs when sediment supply is abundant
(non-limiting).
Sediment supply refers to the amount and size of sediment
available for sediment transport. Capacity transport for a
given grain size is only achieved if the supply of that calibre
of sediment is not limiting (that is, the maximum amount of
sediment a stream is capable of transporting is actually
available). Because of these two different potential
constraints (hydraulics and sediment supply) distinction is
often made between supply-limited and capacity-limited
transport. Most rivers probably function in a sedimentsupply limited condition although we often assume that this
is not the case.
The sediment load of a river is transported in various ways
although these distinctions are to some extent arbitrary and
not always very practical in the sense that not all of the
components can be separated in practice:
1. Dissolved load
2. Suspended load
3. Wash load
4. Bed load
Dissolved load is material that has gone into solution and is
part of the fluid moving through the channel. The amount of
material in solution depends on supply of a solute and the
saturation point for the fluid. For example, in limestone
areas, calcium carbonate may be at saturation level in river
water and the dissolved load may be close to the total
sediment load of the river. In contrast, rivers draining
insoluble rocks, such as in granitic terrains, may be well
below saturation levels for most elements and dissolved
load may be relatively small.
Total dissolved-material transport, Qs(d)(kg/s), depends on
the dissolved load concentration Co (kg/m3), and the stream
discharge, Q (m3/s): Qs(d) = CoQ
Suspended-sediment load is the clastic (particulate)
material that moves through the channel in the water
column. These materials, mainly silt and sand, are kept
in suspension by the upward flux of turbulence
generated at the bed of the channel. The upward
currents must equal or exceed the particle fall-velocity
(Figure ) for suspended-sediment load to be sustained.
Suspended-sediment concentration in rivers is measured
with an instrument like the DH48 suspended-sediment
sampler shown in Figure. The sampler consists of a cast
housing with a nozzle at the front that allows water to enter
and fill a sample bottle. Air evacuated from the sample bottle
is bled off through a small valve on the side of the housing.
The sampler can be lowered through the water column on a
cable. the sampler is lowered from the water-surface to the bed
and up to the surface again at a constant rate so that a depthintegrated suspended sediment sample is collected.
The instrument must be lowered at a constant rate such
that the sample bottle will almost but not quite fill by
the time it returns to the surface. The sample bottle is
then removed and capped and returned to the laboratory
where the fluid volume and sediment mass is
determined for the calculation of suspended-sediment
concentration.
Although wash load is part of the suspended-sediment load it
is useful here to make a distinction. Unlike most suspendedsediment load, wash load does not rely on the force of
mechanical turbulence generated by flowing water to keep
it in suspension. It is so fine (in the clay range) that it is
kept in suspension by thermal molecular agitation
(sometimes known as Brownian motion, named for the
early 19th-century botanist who described the random
motion of microscopic pollen spores and dust). Because
these clays are always in suspension, wash load is that
component of the particulate or clastic load that is “washed”
through the river system.

Unlike coarser suspended-sediment, wash load tends to be
uniformly distributed throughout the water column. That is,
unlike the coarser load, it does not vary with height above
the bed.
Bed load is the clastic (particulate) material that moves
through the channel fully supported by the channel bed
itself. These materials, mainly sand and gravel, are kept
in motion (rolling and sliding) by the shear stress acting
at the boundary. Unlike the suspended load, the bedload component is almost always capacity limited (that
is, a function of hydraulics rather than supply). A
distinction is often made between the bed-material load
and the bed load.
Bed-material load is that part of the sediment load
found in appreciable quantities in the bed (generally >
0.062 mm in diameter) and is collected in a bed-load
sampler. That is, the bed material is the source of this
load component and it includes particles that slide and
roll along the bed (in bed-load transport) but also those
near the bed transported in saltation or suspension.
Development of Sediment Transport
Formulae
 Empirical formulae developed for bedload,
suspended load and total sediment transport
rate using laboratory and field data.
 They are based on hydraulic and sediment
conditions – Water depth, velocity, slope and
average sand diameter etc.
 There can be significant differences
between predicted and measured sediment
transport rates, WHY?
19
Development of Sediment Transport
Formulae con’t
 These differences are due to change in:
- Water temperature,
- Effect of fine sediment,
- Bed roughness,
- Armouring, and
- Inherent difficulties in measuring
total sediment discharge.
 Use of most appropriate formula based on
the availability of conditions, experience and
knowledge of the engineer.
21
1. Bedload Formula – Meyer-Peter &
Müller (1948)
Valid for D > 3.0mm
qb*
q sb
D gDs  1
o
gD ( s  1)
Sediment Flow Rate
m3/s/m

8(FS  Fc* )3 / 2
Where D is average
sand diameter
Critical Shields
Parameter = 0.047
qsb  D gDs  1  8( Fs  0.047)
3/ 2
The Shields diagram empirically shows how the dimensionless critical
shear stress required for the initiation of motion is a function of a
particular form of the particle Reynolds number, Rep or Reynolds
22
number related to the particle.
2. Total Sediment Transport Load –
Ackers & White’s Formula (1973)
Dimensionless Grain
Diameter
Mobility Number
Sediment Flow Rate
m3/s/m
 g (  s  )  1 
Dgr  D

2



1/ 3
Flow
velocity
1 n


u*
V


Fgr 
gD(  s  )  1  32 log 10 Dm D  
Hydraulic
m
n
mean
 Fgr
 qD  V 
depth
qs  C 
 1
 
n
 Agr
 Dm  u* 
Flow
discharge
23
3. Total Sediment Transport Load –
Engelund/Hansen’s (1967) Formula
f   0.1
/
Friction factor
qt   s  
  
 s  
Sediment
transport load
5/ 2
2 gSy
f 
V2
 3
 gD 


/
1/ 2
Shields
Parameter

0.1 5 / 2
3
qt 

g
(
s

1
)
D
s
50
f/

( s   ) D
N/s/m
24
𝐷50
𝐶𝑎 = 𝑋1
𝑋2
𝜏−𝜏 𝑐 1.5
[ 𝜏 ]
𝑐
1
− − − (1)
3 0.3
(𝜌 𝑠 −𝜌 𝑤 )𝑔
{𝐷50 [
] }
2
𝜌𝑤 𝜐
Where “Ca is the suspended sediment concentration,
“ X1”and “X2” are the parameters, D50 is the sediment
particle diameter, ρS is the density of sediments (2650
kg/m3), ρW is the density of water(1000kg/m3),υ is
the kinematic viscosity of water (10-6 m2/s) and g is
the gravitational acceleration (9.81 N/m2), τ is the
shear stress and τc is the critical bed shear stress
determined by the following equation (2)

𝜏 = 𝜌𝑤 𝑔𝑦𝐼𝑓 − − − − − − − − − − − − − − − 2

Where ρw is the density of water, “y” is the depth of
flow“g” is the gravitational acceleration and “If” is
the frictional slope If is calculated as follows
(equation (3))
𝑈2
𝐼𝑓 = 2 4/3 − − − − − − − − − − − − − − (3)
𝑀 𝑦

Where “M” is the Stickler’s coefficient “I” is the
longitudnal slope of the canal and “U” is the velocity
which is calculated by equation (4)
2 1
3 2
𝑈 = 𝑀𝑟ℎ 𝐼 − − − − − − − − − − − − − − − (4)

“rh” is the hydraulic depth which is assumed to be
equal to the depth of flow because the width of the
cross-section of the canal is very large. Critial shear
stress is calculated by equation (5)
𝜏𝑐 = 𝐶𝑔 𝜌𝑠 − 𝜌𝑤 𝐷50 − − − − − − − − − − − (5)

Where τc is the critical shear stress, “C” is the
Shield’s parameter determined by Shield’s curve in
which Reynolds number is along abscissa and “C” is
in ordinate. Reynolds number is calculated by
equation (6)
𝑢∗ 𝑑
𝑅=
− − − − − − − − − − − − − − − − (6)
𝜐

Where u* is the shear velocity, “d” is the particle’s
diameter and “υ” is the viscosity of water. Velocity
“U” for logarithmic profile is calculated by equation
(7)
𝑈 1
30𝑦
𝑢∗

=
𝑘
ln
𝑘𝑠
− − − − − − − − − − − − − (7)
Where “u*” is the shear velocity, “k” is constant=0.4,
“y” is the flow depth and “ks” is the bed roughness
height calculated by equation (8)
𝑘𝑠 = (26 ∗ 𝑛)6 − − − − − − − − − − − − − −(8)
“u*” in equation 7 is calculated by equation (9)
Hunter Rouse concentration “Cy”is calculated as

𝑢∗ =

𝜏
− − − − − − − − − − − − − − − − (9)
𝜌𝑤
Where “y” is the water depth, “h” is the depth of each
layer from the bottom and the suspension parameter
“z” is calculated by equation (11)
𝐶𝑦
𝑦−ℎ 𝑎 𝑧
=(
) − − − − − − − − − − − − − (10)
𝐶𝑎
ℎ 𝑦−𝑎
𝑤
𝑧=
− − − − − − − − − − − − − − − (11)
𝑘𝑢∗

Root mean square error is calculated by
𝐸=
1
𝑛
𝑛
𝐶𝑠 𝑖 − 𝐶𝑜 𝑖 2
[
] − − − − − − − − − (12)
𝐶𝑠 𝑖
𝑖=1
Cell no
(1)
Distance
from
bed(m)
(2)
8
7
6
5
4
3
2
1
3.716
3.325
2.934
2.543
2.151
1.760
1.369
0.587
Hunter
Cell flux
Velocity(m/s)
Rouse
Cell
(m3/m3)
3
3
(3)
Conc.(m /m ) height(m)
(6)=(3)*(4)*(5)
(4)
(5)
2.365
2.334
2.300
2.261
2.215
2.160
2.091
1.859
3.22669E-10
2.03269E-08
1.79447E-07
9.272E-07
3.88495E-06
1.53559E-05
6.43409E-05
0.002934879
0.3912
0.3912
0.3912
0.3912
0.3912
0.3912
0.3912
0.5867
2.98448E-10
1.8559E-08
1.61434E-07
8.19922E-07
3.36596E-06
1.29745E-05
5.26315E-05
0.003201703

The values of Manning’s “n” used in optimization
were 0.0143, 0.017, 0.02 and 0.025 where the
optimized value of “n” becomes 0.02 having
minimum error in sediment concentration, bed levels
and the water levels. So the optimized bed roughness
is 0.0197, calculated from equation 8. Different
parameters in Van Rijin’s equation were optimized by
using MATLAB. The values of empirical parameter
“X1” were 0.015, 0.3 and 1.5 while for “X2” 5%,
10% 15% and 20% of depth of flow were used for
optimization process as explained by Olsen (2011)

The optimized value of “X1” was obtained as 0.015
and “X2” was 15% of depth of flow. Optimization
was done for each month (from May 2011 to October
2011). Results of sensitivity analysis are shown in the
graphs in the next slide