Earthen Channel Design
Earthen Channel Design
Earthen Channel Design
Meandering Channel
Follow the sinuous path
Braided Channel
Channels flows in more than one sub-channels, because the
natural topography does not match the hydraulic conditions
of a river.
SINUOSITY
The meander ratio or sinuosity index is the ratio of actual
length, Lm, along a meandering river to the straight
distance, S, between the end points (AB).
Meander
Belt
STRAIGHT CHANNEL
MEANDERING CHANNEL
BRAIDED CHANNEL
BRAIDED CHANNEL
EARTHEN CHANNEL DESIGN
ALLUVIUM
Alluvial soil:
The soil which is formed by continuous deposition of silt is known as alluvial
soil.
The river carries heavy charge of silt in rainy season. When the river
overflows its banks during the flood, the silt particles get deposited on the
adjoining areas. This deposition of silt continues year after year.
This type of soil is found in deltaic region of a river. This soil is permeable
and soft and very fertile.
Non-alluvial soil
The soil which is formed by the disintegration of rock formation is known as
non-alluvial soil.
It is found in the mountains regions of a river. The soil is hard an
impermeable in nature. This is not fertile
INTRODUCTION
The other worse problems whose origin lies in faulty design are;
weed growth infection, heavy seepage losses entitling
development of water-logging alongside the canal.
INTRODUCTION
Canal design practices also depend on the conditions,
particularly the soil formation, sediment transport characteristics,
operational needs and desired standards of maintenance
Sediment Discharge, Qs
Sediment size, d
Slope of canal
and velocity
Secondary factors:
Acceleration due to gravity, g
Shear stress
Viscosity
Temperature
Determining
(1) depth,
(2) bed width,
(3) side slope and
(4) longitudinal slope of the channel so as to produce a non-silting
and non-scouring velocity for the given discharge and sediment
load.
APPROACHES USED FOR DESIGN OF EARTHEN CANALS
Empirical
Semi-empirical
Rational
EMPIRICAL APPROACHES
Empirical Approaches (Regime Theories):
The stable channel is said to be in state of regime if the flow is such that
silting and scouring need no special attention
CONCEPT OF CHANNEL IN REGIME
Channel in Regime (Stable Channel)
Lindley (1919): When an artificial channel is constructed in
alluvium to carry silty water, its bed and banks would silt or scour
until the depth, slope and width attain a state of balance, to
which he designated as channel in regime.
Vc = mKDN
KENNEDY REGIME THEORY
Vc = mKDN
Where
Vc = Critical velocity i.e. non silting and non scouring velocity
It depends on the nature and the charge (Parts/million) of the silt. It has a
greater value for coarser silt (value varies 1.1 – 1.2 for canals having
coarser sediment than UBDC and 0.8 – 0.9 for finer sediments)
Vc = 0.55 D0.64
Design the canal using Kennedy’s method for the following data:
Q = 80 m3/sec
S = 1:5500
Solution:
EXAMPLE PROBLEM
Q = 80 m3/sec
S = 1:5500 = 0.00018 m/m
m=1
Assume D = 2.5 m
1
D
V = 0.55 D0.64 = 0.989 m/sec 1.5
1.803
A = 80.918 m2 B
n = 0.0225
EXAMPLE PROBLEM
A = B D+ 1.5D2
B = 28.617 m
P = 32.223 m
R = A/ P = 2.511 m
C = 52.479
V=0.59B0.355
B=3.8D1.61
V=1.434log10B
S=1/(2log10Qx1000)
DESIGN OF EARTHEN CHANNEL
Lacey’s Regime Theory (1930):
The material may range from very fine sand to gravel, pebbles
and boulders of small size.
According to Lacey, there is only one longitudinal slope at which
the channel will carry a particular discharge with a particular
silt grade.
Perimeter: P 4.75 Q
V 0.63 fR
1/ 2
Velocity:
V 10.8 R 2 / 3 S 1/ 3
LACEY’S REGIME THEORY
Perimeter: P 2.67 Q
Slope:
S 0.0005423 f 5/3
/ Q1/ 6
Velocity:
V 1.154 fR
1/ 2
V 16 R S 2/3 1/ 3
Lacey’s Regime Theory
Drawbacks:
The silt grade and silt charge are not clearly defined.
LACEY’S REGIME THEORY
Steps involved for the design of Earthen
Canals:
Given: Values of discharge Q, sand size d in mm, side slope zH:lV, (if
not given assume 1/2H: 1V, 1H:1V, 1.5H:1V etc)
Estimate:
wetted perimeter as:
P 4.75 Q
From the known sediment size, d50, in mm, find Lacey’s silt factor
f 1.76 d50
LACEY’S REGIME THEORY
5
3
0.0003 f
Find out the slope of the channel by: S 1
6
Q
Solve the equation for velocity and determine the hydraulic
radius, R,
V 0.63 fR
1/ 2
V 10.8 R 2 / 3 S 1/ 3
Find out the area of cross-section (A) and wetted perimeter (P) in
terms of depth of flow (D) and bed width (B)
Solve the equation for Area (A) and (P) simultaneously and
develop a quadratic equation in terms of bed width (B) or depth
of flow (D)
LACEY’S REGIME THEORY
Example Problems:
V 0.63 fR
1/ 2
V 0.63 fR
1/ 2
Hydraulic Radius (R) = 1.63 m
V 10.8 R 2 / 3 S 1/ 3
Velocity (v) = 0.863 m
R A/ P
Depth of flow (D) = 1.76m B 2 1 z D P
2
D
b b 2 4ac
2a
B P 2 1 z2 D
A PD 2 D 2
1 z zD
2 2
B A zD 2 / D
Quadratic equation
z 2 1 z D
2 2
PD A 0
a z 2 1 z 2 , b P, c A
FURTHER DEVELOPMENT IN REGIME THEORY
Further development in regime theory are:
Lacey’s Shock Theory (1940)
Lacey’s Shock Theory (1940)
Lacey’s Shock Theory (1940)
Lacey’s Shock Theory (1940)
Blench’s Method (1951)
Blench’s Method (1951)
3
Simons and Albertson Method (1957)
Simons and Albertson Method (1957)
Simons and Albertson Method (1957)
Simons and Albertson Method (1957)
NUMERICAL
(1 +200 / 233)
NUMERICAL
NUMERICAL
NUMERICAL
v2 / gDS
NUMERICAL
Shahid and Watts (1994)
RATIONAL METHOD
Duboys Formula
Permissible Velocity Method
Tractive Force Method
Above formulae in combination with Manning and other formula are used to
design channel by rational method
qs
1/ 3
d 1/ 4 Ref. Irrigation and hydraulic
V 0.2 1/ 3
y5/9 Structures, Theory, Design and
q S Practice By Dr Iqbal Ali
N 4 / 3 1 c (Chapter 4)
S
EXAMPLE
Design an unlined earthen channel to carry a discharge of 60 cfs with a bed
load 100 PPM. Mean diameter of bed material is 0.25 mm
Solution
qs
100
q
Assume Depth of flow, y D 2.5 ft
S c 0.00025d 0.8 / ym 0.000250.25 0.8 / 2.5 0.0001
Assuming, N 0.0225, and using eq below
qs 0.11 2 Ny1/ 3 S 3 / 2 S c
1
S
3/ 4
q d
0.1162.4 0.02252.5 S 3 / 2 0.0001
2 1/ 3
6
100 10 1
S
3/ 4
0.25
4 0.0001
0.272 10 S 3/ 2
S
S 9.75 10 4
EXAMPLE
Now using eq. below
1/ 3
q d 1/ 4
V 0.2 s 1/ 3
y5/9
q 4/3 Sc
N 1
S
V 0.2 100 10
6 1/ 3 0.251/ 4
1/ 3
2.5 5/9
0.0001
0.0225 1
4/3
4
9.75 10
V 1.75 ft / s
A BD 0.5D 2
D 2.5 ft
A Q / V 60 / 1.75 34.1 ft 2
B 12.4 ft
Assuming 0.5 : 1 side slope and
S 9.75 10 4
PERMISSIBLE VELOCITY METHOD
Permissible Velocity Method
In permissible velocity method, channel size is selected such that mean flow
velocity for design discharge under uniform flow conditions is less than
permissible velocity.
Permissible Velocity
Permissible velocity is defined as the mean velocity at or below which
bottom and sides of channels are not eroded.
Size of particles
Depth of flow
Curvature of channel
PERMISSIBLE VELOCITY METHOD
Maximum permissible velocities for different materials are given in
the table. The values listed in the table are for straight channels having flow
depth of about 3 .50 ft.
0 .75
Reduction Factor for Channel Sides
s yS
Reduction factor (tractive force ratio) for critical tractive force on channel
sides is:
i.e K=Tractive force on side slope/Critical Tractive force
TRACTIVE FORCE METHOD
Critical shear stress for cohesive and non cohesive materials is given
in the figures. These values are for straight channels and should be
reduced for sinuous channels as below:
Side Slope
Side slope of canal should be so selected that they remain stable
under all operating conditions. Side slope ranges from vertical to 1:3
for lined canals to 1:1/2 to 1:3 for unlined canals, depending on site
conditions and angle of repose.
MISCELLANEOUS CONSIDERATIONS
Free Board
Free board is vertical distance between full supply level and top of
canal banks. It depends on full supply depth and discharge of canal
and generally ranges from 1 ft. to 4 ft. for small distributaries and
main canals carrying 3000 cfs discharge. For canals carrying 10000
cfs or more discharge, it is 5.5 ft.