EARTHERN DAM

contents
1. Types of Earth Dam
2. Causes of Failure
3. Criteria for Safe Design
4. Section of an Earth Dam
5. SeepageAnalysis
6. Seepage Control Measures
7. Spillways and its design
8. Energy dissipators
9. Stilling basins
10. USBR gudielines

Types of Earth Dams
a) Homogeneous Embankment Type
b) Zoned Embankment Type
c) Diaphragm Embankment Type
2. Hydraulic Fill Dam
Depending upon method of construction,
1. Rolled Fill Dam
 In this type of dams, successive layers of moistened or damp soils are laid one
over the other.
 They are then thoroughly compacted and bonded with the preceding layer by
means of power-operated rollers of proper design and weight.
In this Hydraulic Fill dams, the construction, excavation, transportation of the earth
is done by hydraulic methods.
Method:
 Outer edges of the embankments are kept slightly higher than the middle portion
of each layer.
During construction, a mixture of excavated materials in slurry condition is
pumped and discharged at the edges. This slurry of excavated materials and water
consists of coarse and fine materials.
 When it is discharged near the outer edges, the coarser materials settle first at
the edges, while the finer materials move to the middle and settle there.
 Fine particles are deposited in central portion to form a water tight central core.
 In this method, compaction is not required.

Homogeneous Embankment Type Dams
 Constructed with uniform and homogeneous materials.
 Suitable for low height dams (up to 10m).
 Usually constructed with soil and grit mixed in proper ratios.
The seepage action of such dams are not favorable,
therefore, for safety in case of rapid drawdown, the upstream
slope is kept relatively flat (3:1)
Homogeneous section is modified by constructing rock toe at
the downstream lower end and providing horizontal filter drain.

Zoned Embankment Type Dams
 Made up of more than one material
 Outer shells are made of pervious, freely draining materials
Central portions called core or hearting made from materials
which are relatively impervious.
The thickness of the core wall is made sufficiently thick to
prevent leakage of water through the body of the dam.
A suitable drainage system, in the form of horizontal drain or
a rock toe is also provided at downstream side.

Diaphragm Embankment Type Dams
Constructed with pervious materials, with a thin impervious
diaphragm in the central part to prevent seepage of water.
Impervious diaphragm may be made of impervious clayey
soil, cement concrete or masonry or any impervious material
The main difference in zoned and diaphragm type of dams
depend on the thickness of the impervious core or diaphragm.
 The thickness of the diaphragm is not more than 10 m.

Causes of Failure
3. Structural Failures  30%
2. Seepage Failures  30%
a) Piping
b) Sloughing
1. Hydraulic Failures  40%
a) Overtopping
b) WaveErosion
c) Toe Erosion
d) Gullying
a) Upstream slope failure due to sudden
drawdown
b) Failure by excessive pore pressure
c) Downstream slope failure by sliding
d) Failure due to settlement of foundation
e) Failure by sliding of foundation
f) Failure by spreading

Failure due to Tree
roots Over
Topping
Gulling
Piping
Foundation
Settlement
Seepage through
Foundation
Sloughing
Toe
Erosion
Downstream
Sliding

Criteria for Safe Design
1. To avoid overtopping failure, spillway of adequate capacity
and sufficient freeboard must be provided
2. The seepage line is well within the downstream face so that
no sloughing of the slope takes place
3. The upstream and downstream slopes are flat enough to
be stable with the materials
4. The shear stress induced in the foundation should be less
than the shear strength of the foundation material. For this
purpose, the embankment slopes should be sufficiently flat.
5. The upstream and downstream faces are properly protected
against wave action
6. There should not be any possibility of free passage of water
through the embankment or through the foundation
7. The foundations, abutments, and embankment must be
stable for all conditions of operation
8. The dam as a whole should be earthquake resistant

Section of an Earth Dam
1.Top Width
2.Free Board
3.Casing or outer shells
4.Central Impervious Core
5.Cut-off Trench
6.Downstream drainage system

Top Width
1. The top width of the dam depends upon:
a) Construction material
b) Height of structure
c) Roadway
2. Empirical Formulae:
a) B = Z/5 +3  for very low
b) B = 0.55 Z1/2 + 0.2 Z for lower dams (<30m)
c) B = 1.65(Z+1.5)1/3  for higher dams (>30m)
Where Z = Height of dam
3. A minimum width of 6m is required for maintenance so that small trucks can
operate on it
4. The berm may be provided for the dam, which are more than 10 m in height.
Minimum berm width may be kept as 3 m.

Free Board
Free board is vertical difference between the horizontal crest of the embankment
and reservoir level.
Normal Free Board  Top of the crest to normal reservoir level
Minimum Free Board  Top of the crest to Maximum Reservoir Level during floods
The USBR suggests:
Minimum of 2 m and maximum of 3 m over maximum flood level

Casing or Outer Shells
1. The function of casing is to impart stability and protect the
core.
2. The relatively pervious materials, which are not subjected to
cracking on direct exposure to atmosphere, are suitable for
casing.
3. IS: 8826 – 1978 provides recommendations for suitability of
soil used for earth dams

Central Impervious Core
1. The core provides impermeable barrier within the body of the dam.
2. Impervious soils are generally suitable for the core (IS 1498 -1970). However
soils having high compressibility & liquid limit, and having organic contents may
be avoided, as they are prone to swelling & formation of cracks.
Following guidelines are recommended for design of core (for Small Dams)
1. The core may be located either centrally or inclined upstream.
2. The minimum top width should be kept 3 m
3. The top level of the core should be fixed at 0.5 m above MWL.
4. The side slopes may be kept 0.5:1 and 1:1.
5. Thickness of core at any section shall not be lesser than 30% (preferably not less
than 50 percent) of maximum head of water acting at that section.

Cutoff Trench
1. To reduce loss of stored water through foundations and abutments
2. To prevent sub-surface erosion by piping.
The following guidelines may be adopted for design of cut off.
1. The cut off shall be located such that its centre line should be within the base of
impervious core and should be upstream of centre line of dam.
2. The positive cut off should be keyed at least to a depth of 0.4 metre into
continuous impervious sub stratum or in erodable rock formation.
3. A minimum bottom width of 4.0 metre is recommended.
4. Side slopes of at least 1:1 or flatter may be provided in case of over burden while
1/2:1 and 1/4:1 may be provided in soft rock and hard rock respectively.
5. The cut off in the flanks on either side should normally extend up to the top of
impervious core.

Downstream Drainage System
To ensure safety of dam, it is very important to handle the seepage water in the dam
so as to maintain the original particles of soils in their place.
The measures commonly adopted for safe disposal of seepage water through
embankment dams are;
1. Toe drain  installed in oldest homogenous dams to prevent softening at d/s
2. Horizontal filter  used in moderate high dams
3. Inclined or vertical filter (chimney filter)  used in higher homogeneous dams
Purpose:
 To reduce pore pressure in the downstream portion of the dame
 To control piping failure
Generally, a multi-layer filter or inverted filter is provided in which subsequent layer
becomes increasing coarser than the previous one.
According to Terzaghi, the filter material should fulfill the following criteria:
1. D15 of filter / D85 base material > 4 and < 20
2. D15 of filter / D15 base material < 5
3. The gradation curve of the filter material should be nearly parallel to the gradation
curve of the base material.
Note:
D15 is permeability protection limit,
D85 is piping predicting limit

Seepage Analysis
Objective:
To estimate the quantity of seepage (rate of leakage) through dam using Flow Net
Assumptions:
1. Soil is homogeneous (Coefficient of permeability is constant everywhere)
2. Soil is isotropic (Coefficient of permeability is same in all directions)
3. Size of pore spaces do not change
4. Darcy’s law is valid (Flow is laminar) Q=kiA
5. Soil is completely saturated (Degree of saturation is 100%)
6. Hydraulic boundary conditions at entry and exit are known
7. During flow, volume of soil and water remains constant

Flow Net
A flow net is a graphical representation of the paths taken by water in passing
through soil.
Characteristics of Flow Net:
1. Flow lines represent flow paths of particles of water
2. Flow lines and equipotential line are orthogonal to each other
3. The area between two flow lines is called a flow channel
4. The rate of flow in a flow channel is constant (∆q)
5. Flow cannot occur across flow lines
6. An equipotential line is a line joining points with the same head
7. The velocity of flow is normal to the equipotential line
8. The difference in head between two equipotential lines is called the potential
drop or head loss (∆h)
9. A flow line cannot intersect another flow line.
10. An equipotential line cannot intersect another equipotential line

Top Flow Line or Phreatic Line
Flow Line
Equipotential Line
Field
Flow Net for an Earth Dam
Phreatic Line is a seepage line separating saturated and unsaturated zones

Where k’ = Equivalent Permeability of the transformed field

Plotting of Phreatic Line
• In order to draw flow net, it is first essential to find the location and
shape of Phreatic
• line or top flow line separating Saturated and Unsaturated Zones.
• Phreatic line can be located by
1. Graphical Method or Casagrande Method
2. Analytic Method
3. Experimental Method

1. Draw Arc taking C as
centre and CF as Radius
Discharge through the body of dam, q = k s
(for Isotropic Soils)
2. Draw Directrix and
Find Focal Distance S
3. Draw Parabola
curve
(y2= 2sx + s2)

Seepage Control Measures
Seepage Control measures are required to prevent adverse effects of water
percolating through embankment and its foundation.
1. Embankment Seepage Control
a) Toe Filter
b) Horizontal Drainage Filter
c) Percolating Filter d/s of toe
d) Embankment Zoning
e) Chimney Drains extending upwards to embankment
2. Foundation Seepage Control
a) Impervious Cutoff
b) Upstream Impervious Blanket
c) D/s Seepage berms
d) Drainage Trenches
e) Relief Wells

0.3H to 0.4H
H
0.25L to L
L
To keep phreatic line well within the section of embankment and also facilitates drainage

 The following are the seepage control measures to prevent the adverse
effects of water percolating through embankments and their foundations.
• Embankment seepage control
• Foundation seepage control
Measures for control of
seepage

Embankment seepage
control
1. Impervious core
a. Central vertical core
b. Upstream inclined core
2. Toe filter
3. Horizontal drain filter
4. Downstream coarse sections
5. Chimney drains extending upwards into
embankments

1. Impervious cutoff
2. Upstream impervious
blanket
3. Downstream seepage
berm
4. Drainage trenches
5. Relief wells

 The impervious core forms barrier for the seeping water.
 The impervious core may be
 central vertical type or
 an upstream inclined type.
 The inclined core has the advantage that the d/s portion of the
dam can be constructed first and core placed later.
 The thickness of the filter can be made thinner than that in vertical
core type.
Inclined core reduces the pore pressure in the d/s portion of
the dam and thereby increases safety of dam.

The central portion provides higher pressure at the contact
of the core and
It reduces the possibility of leakage and piping.
 Minimum top width of core – 3 m
Top of core- 1m above MWL
Thickness of core – 30 to 50 % of head at any level.

Embankment seepage
control
2. Horizontal Drainage Filter
 Horizontal drainage filter – 25 - 100 % of the distance from c/l of
dam to the toe.
 Keeps phreatic line well within the embankment
 Provides drainage from dam foundation
 Accelerates consolidation

Horizontal Drainage
Filter
Drainage
Filter

Rock toe – height 30 to 40
% of head
 Provided with graded layers
Keeps the seepage well
within section

Embankment seepage
control
4. Downstream coarse
section
 Intercepts the flow through the embankment
 Avoids piping

Embankment seepage
control
 With high degreeof embankmentstratification, a vertical drain
is also called as Chimney drain
 Brings down the phreatic line

Foundation Seepage
1.Impervious cutoff
• Reduces seepage
• May be a cutoff trench or grout curtain sheet pile
cutoff.

Foundation
Seepage
2. u/s impervious blanket
• U/s blankets of 0.6 m to 2 m thick reduces
seepage.

Foundation
Seepage
3. d/s seepage berm
• Used where the d/s top strata is relatively thin and
uniform
• Provides additional weight to resist uplift
• Offers protection against possible sloughing

Foundation
Seepage
4. Drainage trench
• Used where there exists a thin pervious top
stratum

Foundation
Seepage
4. Relief wells
• Provision of relief well along the toe line
intercepts the seepage and reduces uplift
pressures d/s of dam.

Problem-1
An earth dam of homogeneous and isotropic soil with a horizontal filter is
made up of soil having k = 10-4 cm/s. Indicate the magnitude of seepage flow
for the section shown in fig. Find the coordinates of the phreatic line at
distances of 10, 20, 30 , 40 and 50 m from the focus.

Sol :
Horizontal projection of u/s face L = 30 X 3 = 90m
BC = 0.3 X L = 0.3 X 90 = 27 m
D = 27 + 24 = 51 m
From the fig:
D2
Base width = 6 + 33 X  3  + 33 X  3  = 204 m
 1   1 
   
s = + H2
- D
 s = 512
+ 302
- 51
= 8.17 m

Seepage flow / day = k.s
10-4
= X 8.17 X 60 X 60 X 24
100
m3
= 0.71 day
m
Equation of the phreatic line with origin focus is given by
x2
+ y2
= x + s
 x2
+ y2
= x2
+ s2
+ 2.x.s
 y2
= s s + 2x
 y = 8.17 8.17 + 2. x
Hence for different values of x & y

Calculate the seepage through an earth dam resulting on an
impervious foundation with the following data:
Height of dam = 60 m
u / s slope = 2.75 : 1
d / s slope = 2.5 : 1
Free board = 2.50 m
Crest width = 8. 00 m
Length of drainage = 120 m
Coefficient of permeability in the x – direction = kx = 3.5 X 10-
3 m/s Coefficient of permeability in the y – direction = ky = 1.5
X 10-7 m/s

Sol :
L = 57.5 X 2.75 = 158.125 m
BC = 0.3 L = 158.125 X 0.3 = 47.44m
D = 47.44 + 2.5 X 2.75 + 8+ 30 = 92.315m
With respect to the transformed sections:

Dt = 0.65 X92.315 = 60 m
H = 60 - 2.5 = 57.5 m
k' = k . k = 3.5 X 10-3
X 1.5 X 10-7
x y
Transformed section:
Vertical diemensions - Remains unchanged
Horizontal diemensions to be multiplied by
ky
kx
= 2.29 X 10-7 m
s

s = D 2
+ H 2
- D
t t t
602
+ 57.52
- 60
23.10 m
q = k'.s
= 2.29 X 10-7
= 52.90 X 10-7
From fig:


Now
X 23.10
m3
s
m

• Functions of a spillway
• Types of spillways
• Study of the ogee shaped spillway and
• Design procedure for obtaining ogee profile
SPILLWAYS

Definition of a spillway
• A spillway is a structure constructed at a dam site, for effectively
disposing of the surplus water from upstream to downstream.
• The spillway starts functioning when the water level rises above the
maximum water level in the reservoir.
• Hence, a spillway is a safety valve for a dam.

Definition of a spillway
flood without
• It is designed for the maximum estimated flood.
• It must have the capacity to discharge the design
causing damage to the dam.
• It is observed that most of the dams have failed due to provision of
inadequate spillways.
• Therefore, a spillway with adequate capacity, is a must for any
storage dam.
• A spillway can be located
– either in the body of the dam or
– at one end of it or
– entirely away from it independently in a saddle depending upon the site
conditions.

Types of Spillways
The spillways are classified as follows:
• Main spillway and
• Subsidiary or emergency spillway.
• The main spillway is the one which is called upon to work under the
design floods.
• An emergency spillway is provided for additional safety when a flood
greater than design flood occurs or when the main spillway gates fail.
• Under normal operation, emergency spillways are not required to
function.
• Emergency spillways are provided for earth and rock-fill dams to avoid
over topping.

Controlled and uncontrolled spillways:
• The flow of water over a spillway may be controlled by installing gates
over the spillway crest. Such a spillway is known as a controlled spillway.
• When gates are not provided over the crest of a spillway; it is known as
uncontrolled spillway.
• A controlled spillway has got more flexibility of operation and thus gives
better control and increased usefulness of the reservoir.

• Depending upon the type of the structure constructed for
disposing of the surplus water, the spillways are classified as:
• Straight drop spillway
• Ogee or overflow spillway
• Chute or open channel or trough spillway
• Side channel spillway
• Shaft spillway and
• Siphon spillway.

1.Straight Drop spillway:
• This is the simplest type of spillway and may be constructed on
small bunds or on thin arch dams.
• It is a low weir having d/s face either vertical or nearly vertical.
• Directs the small discharges away from the face of the overfall
section as shown in Fig.

2. Ogee shaped spillway:
• This is the most common type of spillway provided on gravity dams, arch
and buttress dams.
• It can be used on valleys where the width of the river is sufficient to
provide the required crest length.
• Ogee spillway is an improvement upon the straight drop spillway.
• The profile is also known as S-curve or parabolic curve since the falling
nappe takes the form of a parabola.
• This maximum head is called the design head.
• The negative pressures cause cavitation and hence they should not exceed
4.5m.
• On the other hand if the head on the spillway is less than the design head,
the lower nappe adheres to the crest creating positive pressures and
thereby reducing the coefficient of discharge.

Chute or Trough spillway
• Simplest type of spillway
• Easily provided independently at low costs
• It is lighter and adaptable to any type of foundations.
• It is easily provided on earth and rock-fill dams.
• It has the following parts:
i) Entrance channel
ii) Control structure (low ogee weir)
iii) Chute channel and
iv) Energy dissipation arrangement at the bottom.
Entrance channel: An approach channel trapezoidal in shape with side slopes 1:1
may be constructed so as to lead the reservoir water upto the control structure.

Chute or Trough spillway:
• Chute spillways carry supercritical flow through the steep slope of an open
channel.
• In order to avoid a hydraulic jump, the slope of the spillway must be steep
enough for the flow to remain supercritical.
• Proper spillways help with flood control, prevent erosion at the ends of
terraces, outlets & waterways and are simple to construct.
• However, they can only be constructed at sites with natural drainage and
moderate temperature variation and have a shorter life expectancy than
other types of spillways.

Side channel spillway:
• The side channel spillway differs from the chute spillway in the
direction of flow of water after leaving the crest.
• In a chute spillway the water flows at right angles to the weir
crest after spilling over it, where as in a side channel spillway the
flow runs parallel to the crest .
• This type of spillway is provided in narrow valleys where no side
flanks of sufficient width to accommodate a chute spillway are
available.

Shaft spillway:
• In a shaft spillway, the water from the reservoir enters into a
vertical shaft which conveys this water into a horizontal tunnel
which finally discharges the water into the river d/s.
• Sometimes the vertical shaft may be excavated through some
natural rocky island existing on the u/s of the river near the
dam.
• Vertical artificial shafts may also be constructed sometimes.

Siphon spillway
• Siphon spillway utilizes the siphonic action to discharge the surplus
water.
• Consists of a closed conduit system formed in the shape of an Inverted
U.
• The level of the air-vent may be kept at normal pool level, while the
entry point of the siphon pipe may be kept still lower so as to prevent
the entry of debris etc into the siphon
• Siphons are two types
1) Saddle siphon spillways 2) Volute siphon spillways.

Siphon spillway- Saddle
siphon
Saddle siphons are two types
(i) Hooded type and (ii) Tilted outlet type
A small deprimer hood is kept above the main hood and both the
hoods are connected through the air-vent.
• The inlet of the deprimer hood is kept just at the reservoir
level.

Siphon spillway Saddle
siphon
Siphon
Water shooting from baby
siphon closing the outlet

Siphon spillway Saddle
siphon
• Depriming is the reverse process of priming.
• It is the action of the siphon from the time air starts entering
the siphon through the vents until the siphonic action is
stopped.
• Without air-vent, siphonic action continues till the reservoir
level is brought down to the level at inlet which is much below
the FRL.

Siphon spillway- Tilted Outlet Type
• It is a saddle type of siphon in which the vertical shaft has a
tilted outlet which maintains a water level.
• The maximum negative pressures occur at the crown or the
throat of the siphon.
• To avoid cavitation, this negative pressure should not exceed
7.5m of water.
• The vertical distance from the crown of the siphon to the
discharge end should not exceed the value of about 7.5m.

Siphon spillway Tilted Outlet Type
fig. 14.7.

Siphon spillway Tilted Outlet Type
Discharge formula:
The discharge through the siphon
Q = CA √(𝟐𝒈𝑯)
where
where
A = Area of cross section at crown = L x b
L = length and b = height of the throat
H = operating head
= Reservoir level - centre of outlet (if siphon is discharging freely)
= Reservoir level - Downstream tail water level
(if outlet end is submerged)
C = coefficient of discharge which may be taken as 0.65 .

Siphon spillway- Volute Siphon:
• It is a special type of spillway designed in India.
• It consists of a dome supported on pillars with a funnel placed
underneath.
• A vertical pipe taken down the funnel to pass the discharge
through the dam.
• It is bent at the discharge end.
• The top or lip of the funnel is kept at reservoir level and a
number of volutes are fixed in the funnel to induce a spiral
motion to the water passing along them

Siphon spillway - Volute Siphon:

Siphon spillway
The discharge through the volute siphon is given by
Q = A 2g (H – HL) = CA 2gH
where A = area of cross - section of pipe
C = coefficient of discharge
H = maximum operating head
HL = Head loss through the siphon
Volute Siphon:

PROBLEM:
A saddle siphon has the following data:
Full reservoir level = 135.00 m
Level of centre of siphon outlet: 129.60 m
High flood level : 135.85m
maximum flood discharge: 1200 m3 /s
The dimensions of the throat of the siphon are, width:8m, Height : 4m.
Determine the number of siphons required to pass the flood safely.
The siphon discharges freely in air. Assume coefficient C=0.65.

Solution:
• Operating head, H
• H = H.F.L - R.L of outlet centre H =
135.85 - 129.60 = 6.25m.
• Assuming C = 0.65, A = 8 x 4 = 32m 2
Discharge through each siphon Q = CA 2gH
Q = 0.65 x 32 x 2x 9.81 x 6.25 = 231.2 m3/s.
1200
Number of siphons required = 231.2 = 5.2 or say 6

PROBLEM: A siphon spillway whose cross section is 2m high and 4m wide is provided on the dam.
The tail water at design flow is 7m below the summit of the siphon and the water level on the u/s
side is 2m above the summit. Calculate the siphon discharge. What length of an ogee spillway is
required to pass the same flood with the same head water elevation. Assume coefficient for siphon
spillway as 0.60 and for ogee spillway as 2.25.
Solution:
(i) Siphon spillway
Net operative head: 7+2 = 9m
Q = CA 2gH
= 0.6 x 4 x 2 2 x 9.81 x 9 =63.5 cumecs.
(C = 0.6 assumed)
(ii) Ogee spillway for ogee spillway head H= 2m
Q = CL H3/2
C = 2.25 (assumed)
H = 2m
63.5 = 2.25 x L x 23/2
L = 63.5
2.25 x 2 x 2
= 10m

Summary on types of spillways :
• Chute, shaft, side channel and siphon spillways are adopted when
there is no adequate space to provide an ogee spillway.
• Chute spillway Is provided on earth and rockfill dams.
• In side channel spillway, the water flows parallel to the crest.
• It Is provided in narrow valleys where side flanks of sufficient width
are not available to accommodate the chute spillway.
• Shaft spillway is used if the topography prevents the use of a chute /
side channel spillway.
• Siphon spillway may be saddle type or volute type. It discharges water
with a greater head by syphonic action.

Design of the shape of Crest of Spillway:
• Theoretically, the profile should correspond to the lower nappe of a free
falling jet.
• Such a profile should cause no negative pressures on the crest under
design head.
• In practice, due to friction on the surface of the spillway, negative
pressures occur.
• In order to avoid these negative pressures consistent with practicability,
various modified profiles have been proposed.

Design of the shape of Crest of Spillway:
Creager’s profile:
• Creager has proposed a practical profile for ogee spillway with
vertical u/s face and u/s face sloping at 45°.
• A table of coordinates with u/s face vertical connecting x and y for
unit head of overflow is furnished.
• The coordinates for any head ‘H' can be obtained by multiplying the
x and y values by H.

Co-ordinates
for
head
Lower Nappe Upper Nappe
0 0.41 -2.72
0.33 0.12 -2.63
0.66 0.02 -2.53
0.98 0 -2.43
1.31 0.02 -2.30
1.91 0.21 -2.03
2.62 0.50 -1.68
3.28 0.88 -1.25
3.94 1.85 -0.72
4.59 1.94 -0.10
5.58 3.02 1.00
6.56 4.30 0.21
8.20 6.89 4.92
9.84 10.20 8.20
11.48 12.00 12.00
13.12 18.40 16.40
14.76 23.50 21.45
Multiply co-
CREAGER’S PROFILE

Waterways Experimental station (W.E.S) Profile:
• Several standard ogee shapes have been developed by U.S.
Army Corps of Engineers at their Waterways Experimental
Station (W.E.S).
• Such shapes are known as 'WES standard spillway shapes' they
adopt curves whose equations contain fractional powers
connecting x and y for the d/s profile. The equation is
• 𝑑
xn = K𝐻𝑛−1𝑦

Waterways Experimental station (W.E.S) Profile:
• where x and y are coordinates of the points with the origin at
the highest point 'C' of the crest.
• Hd is the designed head including the velocity head.
• K and n are constants depending upon the slope of the u/s
face. The values of K and n are tabulated.

• Different profiles are shown In Fig.
Slope of the u/s face of the
spillway K n
(a)Vertical
(b)1:3 (IH :
3V)
(c)1: 1½ (1H :
1.5V)
2.0
1.936
1.939
1.85
1.836
1.810

Different profiles are shown In Fig.
D/s curve
HO.13.1
D/s curve
EQ.13.1
ver
sss
According to the latest studies of U.S. Army Corps the u/s curve of the
ogee spillway has the following equation
y =
𝟎.𝟕𝟐𝟒 𝒙+𝟎.𝟐𝟕 𝑯𝒅 𝟏.𝟖𝟓
𝑯𝒅
.
𝟎 𝟖𝟓 d
+ 0.126 H = 0.4315 H 0.375
d d
(x * 0.27H ) 0.625
The u/s profile extends up to x = -0.27 Hd

• The following table of coordinates can also be used for obtaining
the WES profile with vertical u/s face.
X
Hd
y/Hd
Lower Nappe Upper Nappe
0 0.125 -0.831
0.10 0.033 -0.807
0.25 0.000 -0.763
0.50 0.034 -0.668
0.75 0.129. -0.539
1.00 0.283 -0.373
1.50 0.783 0.088
2.0 1.393 0.743
3.0 3.303 2.653
4.0 6.013 5.363
5.0 9.523 8.873
Dr GK ViswanadhJNTUH
8/23/2019 25

• The lower nappe and upper nappe can be plotted with the help of the co-
ordinates. A smooth gradual reverse curvature is provided at the bottom of the
d/s face as shown in the Fig.

Discharge equation:
• The discharge over an ogee shaped spillway is given by
• 𝑸 = C Le He
3/2
• where Q = discharge,
• C = coefficient of discharge varies from 2.10 to 2.50
• Le = Effective length of the spillway crest
• He = total head over the crest Including the velocity head.

Discharge equation:
• The effective length is given by
• Le = L - 2[ KPN - Ka] He
• L = net clear length of the spillway
• KP = pier contraction coefficientP
• Ka= abutment contraction coefficient a
• N = Number of piers

The values of KP and Ka depend mainly upon the shape of the piers and that of
abutment and are given below
S. No Pier condition KP
1.
2.
3.
Square Nosed piers with corners rounded on a
radius equal to 0.1 of pier thickness.
Round -
Nosed
piers
Pointed
Nose
0.02
0.01
0.00
Table (Values of KP )

Table: (value of Ka)
S.No Abutment condition Ka
1.
2
Square abutment with head wall at 90°
to the direction of flow
Rounded abutment with head wall at
90° to the direction of flow
0.20
0.10

PROBLEM : Design a suitable section for the overflow portion of a
concrete gravity dam having the d/s face sloping at 0.7H to 1V. The design
discharge for the spillway is 8000 m3/s. The height of the spillway above
the bed level is 104.0m. The spillway consists of 6 spans of 10m width. The
thickness of each pier is 2.5m.Assume coefficient of spillway as 2.2 with
suitable values of kp and ka.

Solution:
Q = C Le
He
3/2
Taking Kp = 0 and Ka = 0.1, Le ≈L.
L = 6 x 10 = 60m.
Assuming C = 2.2 8000 = 2.2 x 60 x He
3/2
He =
8000
60 x 2.2
/
2 3
= 15.5m

Height of spillway = 104m
𝐻 104
𝐻𝑑 15.5
= > 1.33
• Velocity of approach can be neglected. effective
length, Le = L - 2(N. Kp - Ka ) 𝐻𝑒
• = 60 - 2 x 0.1 x 15.5
• = 56.9m.

• The new value of He
e
H 3/2 =
8000
2.2 x 56.9
= 63.90
•
• He = 15.99m or 16m.
• with this new value of the He , Le =56.8m.
• Hence the profile can be designed for 𝐻𝑑 = 16m.

Downstream profile: The W.E.S
profile for a vertical u/s face is
given by
𝑑
xn = K𝐻𝑛−1y for vertical u/s face k=2 n=1.85 from the table
x1.85 2 ( 160.85 )y
y =
2
=
x1.85
16 0.85 =
x1.85
2 ( 10.55)
=
x1.85
21.10
dy 1.85 x0.85
dx = 21.10
=
1
0. 7
since d/s slope of the dam =
1
0. 7
x 0.85 = 16.30 x = 26.68m
y =
( 26.70 )1.85
21.10
y = 20.60m.

X in m Y(m)
1
2
4
.
.
.
2
6
.
7
0
0.047
0.168
0.602
.
.
.
20.60

• U/s profile: The u/s profile is designed using Hd = 16m and the profile extends
upto x = -0.27 x 16 = -4.32m.

• An ogee spillway is mostly suitable for gravity dams specially
when the spillway is located within the dam body in the
same valley.
• For earthen and rockfill dams, a separate, spillway is
generally built in a flank or a saddle away from the main
valley.
• This separate, spillway may be a shaft, side channel, chute or
a siphon spillway.

Stilling
Basin
• A stilling basin may be defined as a structure in which the
energy dissipation action is confined.
• If the phenomenon of hydraulic jump is basically used for
dissipating the energy, it may be called a hydraulic Jump
type of stilling basin.
• The auxiliary devices such as chute blocks, baffles and
end sills may be used as additional measures for
controlling the Jump.

Types of stilling basins - U.S.B.R and B.I.S stilling
basins.
• Various types of stilling basins have been generalized for use in
different types of works by various agencies.
• The designs of these basins have been developed on the basis of
long experience and on model studies, keeping in view the
protection obtained consistent with economy.
• These basins are not simple concrete aprons but are generally
provided with auxiliary devices like baffles, chute blocks and end
sills.

Types of stilling basins - U.S.B.R and I.S.S stilling
basins.
• The U.S.B.R has standardized stilling basins
for different ranges of Froude numbers.
• Similarly B.I.S. (Bureau of Indian Standard Institution) has
also standardized certain stilling basins for use under
different conditions.
• Stilling basins I and II with horizontal aprons and III and IV with
sloping aprons have been standardized.

F1 Length
of the basin
F
1
Length of basin
4
6
3.
6
y2
4
8
≥ 10
2. y2
3. y2
U.S.B.R
Basins:
U.S.B.R has standardised stilling basins for different ranges of Froude numbers. The
important of these basins are:
(i) U.S.B.R stilling Basin II: This is recommended for use on large structures such as dam
spillways, large canal structures when the Froude number (F) > 4.5. The stilling basin
is shown in Fig.
The length of the basin depends upon the Froude number as shown in Table

(ii) U.S.B.R Stilling Basin IV:
• It is used for Froude number lining between 2.5 and 4.5.
• This basin is applicable only to rectangular cross sections.
• Large chute blocks are used to control the oscillating waves.
• The floor of the basin may be set as to provide 5 to 10% more
water depth than y2.
• The length of the basin is kept equal to 5 (y2 – y1)

Fig. U.S.B.R Stilling Basin
IV:

B.I.S. Stilling
Basins:
The B.I.S.laid down the criteria for the designof hydraulic jump
type stilling basins of rectangular cross sections.
Chute blocks, baffles and end sill are also provided in the
basin. The different types of stilling basins are discussed.

• Hydraulic jump type stilling Basin with Horizontal
Apron:(Type I and Type II)
• when the tail water rating curve approximately follows
the jump height curve, the hydraulic jump type stilling
basin with horizontal apron provides the best solution
for energy dissipation.
• There are two types of stilling basins with horizontal
apron.
– (a) Stilling basin in which F1 < 4.5, generally encountered for
weirs and barrages and
– (b) stilling basin in which F1 > 4.5 generally occurs in dams

(i) Stilling Basin Type
I:
The basin floor level, basin length and basin appurtenances are designed as
follows:
Elevation of floor: let HL the head loss in the hydraulic jump and q be the
discharge per unit width. HL is obtained from the u/s and d/s total energy lines.
Knowing HL and q, the values of yC, y1 and y2 can be calculated from the
following formulae
𝑦 −𝑦
HL = 2 1
3
4𝑦1𝑦2
𝑦
2
𝑦2= 1
+ 1
𝑦2
4
+
2𝑞2
𝑔𝑦1
3 𝑞2
yC = Τ𝑔
The elevation of basin floor is given by
Ele. of floor = u/s total energy - u/s specific
energy.

Basin length and depth of Stilling Basin Type I :
• Generallythe floor should not be raised above the
level required from y2 consideration.
• If it becomes necessaryto raise the floor due to
site conditions, the same should not exceed 15% of
y2.
• The basin for this case should be provided with chute
blocks and baffles.

The dimensions of chute blocks, baffles and end sills are
shown
Fig
.

(ii) Stilling Basin Type
II:
• The elevation of the basin floor is fixed as in the case of
Type-I. The length of the basin is determined from Fig.
• The basin floor level is fixed as in the case of type I.
The dimensions of the appurtenances are shown in Fig.

Stilling Basin Type III:
• This type of stilling basin is adopted where tail water
curve is higher than y2 curve at all discharges.
• It is not possibleto standardise design criteria
for sloping aprons as in the case of horizontal aprons.
• Theslopeand over all shapeof the apron are
determined from economic considerations.
• The length is judged by the type and soundness of river
bed d/s.

• The design criteria serves only as a guide in proportioning the
sloping apron designs.
Much depends upon the individual judgement.
The basin should be supplemented by an end sill of height
equal to
0.05 to 0.2 y2 with an u/s slope of 2:1 to 3:1 as shown in fig.

Stilling Basin Type
IV:
• It is suitable for the case where the tail water depth at maximum
discharge exceeds y2 considerably but is equal to or slightly
greater than y2 at lower discharges.
• Like in type III it is not possible to standardise design criteria.
The design criteria laid down by I.S.I serves only as a guide in
arriving at apron dimensions which depend mainly upon
practical considerations.
Fig.
16.8

Spillway crest gates:
• By installing gates over spillways,additional storage can
be made available, specially during low water flow.
• Duringflood times, these gatesare raisedso that full use of
spillway capacity can be made.
• The following are some of the gates used for spillways.

• (i) Dropping Shutters or
permanent Flash
Boards:
• They consist of wooden
panels usually 1.0 to
1.25m high.
• They are hinged at the
bottom and supported
against the water
pressure by struts.

• The shutters fall flat on the crest when the supporting struts are tripped.
• These shutters can be raised or lowered from an overhead cable way.
• Various types of automatic shutters which drop and raise
themselves automatically have been in use nowadays.
• Sometimes flash boards may be used as temporary gates on
spillways of minor importance.
• These fresh boards are supported by pins on the edges.
• They may be braced or hinged.
• Automatic flash boards are designed in such a way that they
fall automatically at a certain head.

DroppinqShutters or permanent Flash
Boards:

• (ii) Stop Logs:
Stop logs consist of wooden beams or planks placed one
upon the other and spanning in the grooves between the
spillway piers as shown in Fig.
They can be placed and removed either by hand or with
hoisting mechanism. They are useful for minor works.

• (iii) Vertical lift gates:
• Thesegatesspan horizontallybetween the groovesmade in
the piers.
• The groovesare lined with steel channelsectionsto provide
a smooth bearing surface and are known as groove guides.
• The gates move between the groove guides. The gates are
usually made of steel.
• Because of the hydrostatic pressure,large
frictional forces are developed in the
guides.

Pla
n
Section
AA
• (iii) Vertical lift
gates:
3
2

(iv) Radial
Gates:
• A radial gate has a curved water supporting face made
of steel.
• The curved water face which is in the shape of a sector
of a circle is properly braced by steel frame work which
is pivoted on horizontal shafts called pins.
• The pins are anchored in the down stream portion of
the spillway piers.
• The gate rotates about the fixed horizontal axis.

Radial
Gates
• Counter weights are used to reduce the lifting force.
Radial, gates can be used with smaller lifting force
for all heads than vertical lift gates.
• The gate can be lifted by means of ropes and chains
acting simultaneously at both ends or with the help
of power driven winches.

v. Drum Gates:
• Drum gates are useful for longer spans of the
order of 40m or so and medium heights say
10m.
• The drum gate consists of a segment of a
cylinder which may be raised above the crest or
may be lowered into the recess made into the
top of spillway.
• The drum gates require large recess and hence
are not suitable for smaller spillways.

Summary:
• U.S.B.R has standardised stilling basins for different
ranges of Froude numbers. Stilling basin type II is
adopted in situations where Froude number is greater
than 4.5.
• Type IV is adopted for Froude numbers less than 4.5. In
both types chute blocks, baffles and end sills are used to
reduce the length of the stilling basin I.S.I has classified
stilling basins into four different types.

• Types I and II are used with horizontal aprons and III and
IV are used with sloping aprons. Spillway crest gates are
divided into various types
• (1) Dropping shutters used for minor works
• (2) Stop logs also used for minor works
• (3) Vertical lift gates
• (4) Radial gates and
• (5) Drum gates.
• The last three are used for large structures.

Principles of energy dissipation
• The water reaching the toe of a spillway, has the energy content
corresponding to the u/s reservoir level, neglecting frictional losses.

• Therefore, the excess energy over that corresponding to the rear M.F.L
has to be suitably dissipated.
• If no energy dissipation arrangements are provided, the surplus energy
dissipates itself by forming scour craters in rear of the dam which may
endanger the stability of the structure.
• These energy dissipation arrangements are known as energy dissipators.

• In planning the energy dissipators, the nature of device to be employed as well
as character of the river bed should be considered.
Basic Principles:
The following are some of the principles employed in the design of energy
dissipation arrangements.
i) Hydraulic jump formation

Hydraulic Jump
• When a stream of water moving with a high velocity and low
depth (super critical flow) strikes another stream of water
moving with a low velocity and high depth (subcritical flow) a
sudden rise in the surface of the former takes place.
• Change of state from supercritical to subcritical.
• This phenomenon is called Hydraulic jump.
• The formation of the Hydraulic jump is always accompanied by
a large scale turbulence and dissipation of most of the kinetic
energy.

Hydraulic Jump
• If the jump is low, the change in depth is small, the water will not
rise abruptly but passes through a number of undulations.
• This jump is called undular jump and energy dissipation is small.
• If the jump is high, change in depth is large and the water surface
rises abruptly.
• It is called a direct jump and energy dissipation is more.

Types of Jump:
Depending upon the incoming flow and the Froude number (F1), the
jump on a horizontal floor can be classified as follows
• Fr1 = 1, no jump can form
• Fr1 = 1 to 1.7 undular jump forms
• Fr1 = 1.7 to 2.5 a weak jump. Energy loss is low. d/s water surface
remains smooth. The velocity distribution is fairly uniform.
• Fr1 = 2.5 to 4.5. Oscillating jump forms. The energy dissipators
andstilling basins are to be designed carefully making use of this
jump.
Fr
1
• = 4.5 to 9.0. A steady jump forms. It is well balanced.The
energy

Jump
Formula:
q =discharge per unit width
V1 and y1 = velocity and depth of flow before the jump.
V2 and y2 = velocity and depth of flow after the jump
F1 = Froude number of super critical flow
F2 = Froude number of subcritical flow.
For a given Y1, Y2 is given by
2
• y =
−y1
𝟐
+
2
y1
𝟒
𝟐
𝒒
𝟐
+
𝒈
𝒚 𝟏
(or)
2
• y =
−y1
𝟐
−
𝟏+ 𝟏+𝟖
𝑭 𝟐
𝟏

Jump
Formula:
The energy loss In the jump is
given by 𝑽 𝟐
2g
∆E= (y1 + 𝟏
) - (y2 + 2
v 2
𝟐
𝒈
) (or)
∆E
=
𝒚 −𝒚
𝟐 𝟏
𝟑
𝟒
𝒚
𝟏
𝒚
𝟐
Height of the jump = 𝑦
2 − 𝑦
1
Length of the jump = 5 to 7 𝑦
2 − 𝑦
1
The depths y1 and y2 are known as initial and sequent depths of
thejump.

Use of Hydraulic jump in energy
dissipation
• For a given value of y1 at the toe of the dam, tail water depth
equal to y2 is required for the formation of the jump.
• If y2 is available, jump forms and part of the energy is dissipated.
• A suitable type of energy dissipator is to be designed so that the
jump forms on the solid apron for all discharges over the spillway.
• Though there is energy dissipation due to the formation of the
jump, the velocity distribution is not however restored to that
pattern obtaining in a natural stream.

• High velocities still persist near the bed and hence scouring may occur.
• Therefore besides creating hydraulic jump, other devices such as end-
sills, buffles etc. are also employed.
• For various discharges over spillway, the tail water depth available in the
stream and the depth of flow y are known from Tail Water Curve (T.W.C)
and the Jump Height Curve (J.H.C).
• JHC – it is a curve representing post jump depth(y2) with discharge q
• TWC – it is a curve representing tail water depth with discharge q
• Depending upon the relative positions of T.W.Cand J.H.C, a suitable
type of energy dissipator making use of hydraulic jump is designed.

Classification of Energy
Dissipators:
It is convenient to study the various energy dissipators employing the principle
of the hydraulic jump according to the following classification:
I. T.W.Ccoinciding with jump height curve for all discharges
II. T.W.Clying above y2 curve for all discharges
III. T.W.Clying below y2 curve for all discharges
IV. T.W.Clying above the y2 curve at smaller discharges and below the y2 curve
at large
discharges.
V. T.W.Clying below the y2 curve at smaller discharges and above the y2 curve
for large discharges.
The tail water rating curve is plotted from the hydraulic data of the rear Channel.
The y2 curve is plotted for different calculated values of y2 knowing q and y1.

Dissipators:
T
.W.C coinciding with jump
height curve for all
discharges
10/21/2020 194

Dissipators:
T
.W.C lying above y2 curve for
all discharges
T
.W.C lying below y2 curve for
all discharges
10/21/2020 195

Dissipators:
2
T
.W.C lying above the y curve at
smaller discharges and below
the y2 curve at large discharges.
T.W.C lying below the y2 curve at
smaller discharges and above the y2
curve for large discharges.

Case 1 : T.W.C tallying with y2
curve:
This is the ideal condition for Jump formation.
The hydraulic jump forms at the toe of the spillway at
all discharges.
A simple concrete apron length 5 (y2 – y1) is enough to
provide protection in the region of the jump
Sometimes chute blocks, baffle piers and end sills are
provided in the stilling basin to reduce the length of the
apron.

Case 2 : T.W.C above y2
curve:
• In this case, when y2 is always below the tail water, the jump
forming at toe is drowned by tail water and no energy is dissipated.
• The high velocity water travels along the channelbottom for a
longer length before getting dissipated.
• This is obviated by constructinga sloping apron above the river
bed level.
• The jump forms on the slopingapron where the depth equalsto y2
is available.
• The slope of the apron must be such that jump forms at some point
on the sloping apron for all discharges.

SKI Jump bucket Fig.
(a) Fig. (a) Slopping
apron
Fig. (b) Roller
bucket
Fig. (c) Slotted
bucket

• In this case the shooting flow continues for considerable
distance d/s before the jump is formed.
• The remedy is to provide a sky-jump bucket type of
energy dissipator

Case 3 : T.W.C Below y2
curve
• It can also be solved by providing a sloping apron below the river
bed as shown in Fig.
• The required depth y2 is obtained on this sloping apron to form
the jump. A sunk basin is formed to increase the depth

Case 4 : T.W.Clying above the y2 curve at smaller
dischargesand
below the y2 curve at large discharges
• Tail water curve lies above y2-curve at small discharges
and below y2-curve for high discharges.
• In this case at low discharges the jump will be drowned
and at high discharges, tail water depth is inadequate.
• The solution to the problem lies in providing a sloping
apron partly above and partly below the riverbed as
shown in Fig.
• For low discharges, the jump forms on the apron above
the bed and for high discharges, the jump forms below
the river bed.

Case 4 : Tail water curve lies above y2- curve at small discharges and below
y2 - curve
for high discharges.

Fig. Slopping apron partly above and
below

Case 5 : Tail water depth Is inadequate at low
discharges and is greater at high discharges.
• The case is just the reverse of the case 4. The same
solution is valid for this condition also.

Jump type stilling
Basin
• A stilling basin may be defined as a structure in which the
energy dissipation action is confined.
• If the phenomenon of hydraulic jump is basically used for
dissipating the energy, it may be called a hydraulic Jump
type of stilling basin.
• The auxiliary devices such as chute blocks, baffles and
end sills may be used as additional measures for
controlling the Jump.

Hydraulic jump type stilling basin with horizontal apron
• In this case the requisite depth for formation of hydraulic
jump can be obtained on an apron near or at the ground
level.
• Hydraulic jump type stilling basins are useful for spillways
on weak bed rock conditions, weirs and barrages on sand
or loose gravel.

• This type of stilling basin can be classified into two
categories:
• (a) Stilling basins in which the value of the Froude number
of the incoming flow is less than 4.5. This case is
generally encountered on weirs and barrages.
• (b) Stilling basins in which the Froude number of the
incoming flow is greater than 4.5. This case is a general
feature for medium and high dams.

Chute blocks, baffles and end
sills

A) Chute
Blocks:
• Chute blocks are placed at the entrance of the basin to
split the jet and lifting a portion it off the floor and thereby
providing a shorter length of the basin than would be
possible without them.
• These blocks also tend to improve the action of the jump.

B) Baffle
Piers:
• These are the blocks placed within the basin.
• They increase turbulence in the basin and help to
stabilise the formation of the hydraulic jump.
• For high velocities, they may be damaged due to
cavitation.
• Hence suitable for small works such as low
spillways.

C) End
sills:
• End sills are used primarily for scour control.
• They deflect the high velocity filaments to the top and
encourage the formation of a ground roller which shifts the
deepest scour further off from the edge of the apron.

Types of stilling basins - U.S.B.R and B.I.S stilling
basins.
• The U.S.B.R has standardized stilling basins
for different ranges of Froude numbers.
• Similarly B.I.S. (Bureau of Indian Standard Institution) has
also standardized certain stilling basins for use under
different conditions.
• Stilling basins I and II with horizontal aprons and III and IV with
sloping aprons have been standardized.

F1 Length
of the
basin
F1
Length of
basin
4
6
3
.
6
8
≥ 10
4.2y2
4.3Y2
U.S.B.R
Basins:
U.S.B.R has standardised stilling basins for different ranges of Froude numbers. The
important of these basins are:
(i) U.S.B.R stilling Basin II: This is recommended for use on large structures such as dam
spillways, large canal structures when the Froude number (F) > 4.5. The stilling basin
is shown in Fig.
The length of the basin depends upon the Froude number as shown in Table

(i) Stilling Basin Type
I:
The basin floor level, basin length and basin appurtenances are designed as
follows:
Elevation of floor: let HL the head loss in the hydraulic jump and q be the
discharge per unit width. HL is obtained from the u/s and d/s total energy lines.
Knowing HL and q, the values of yC, y1 and y2 can be calculated from the
following formulae
𝑦 −𝑦
HL = 2 1
3
4𝑦1𝑦2
𝑦
2
𝑦2= 1
+ 1
𝑦2
4
+
2𝑞2
𝑔𝑦1
3 𝑞2
yC = /𝑔
The elevation of basin floor is given by
Ele. of floor = u/s total energy - u/s specific
energy.

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