lecturenote_1219301080Chapter 2 Embankment Dam-1 (2).pdf

Chapter Two Embankment Dam 2012
Hydraulic structure I Page 1
2.2 Embankment Dam
2.2.1 Introduction
Embankment dam is a water impounding structure constructed from fragmental natural
materials excavated or obtained close to the dam site. The natural fill materials are placed
and compacted without the addition of any binding agent, using high capacity mechanical
plant. They rely on their weight to resist the flow of water, just like concrete gravity
dams.
Embankment dam derive its strength from position, internal friction and mutual attraction
of particles. Relative to concrete dams, embankment dams offer more flexibility; and
hence can deform slightly to conform to deflection of the foundation without failure.
Broadly, depending upon the material used during construction, embankment dams are
classified in to two:
1) Earth fill Embankments: if compacted soils, i.e. clays/silts & sands, account
for over 50% of the placed volume of material
2) Rock fill Embankment: if compacted rock particles larger than a man can
easily lift, i.e. coarse grained frictional material, accounts for over 50% of the
placed volume of materials.
Embankment dam possesses many outstanding merits which could be summarized as
follows:
A. Suitability of the type to different site conditions such as wide valleys, steep sided
gorges, etc.
B. Adaptability to a broad range of foundation condition such as rock and pervious soil
formation,
C. use of natural materials,
D. Extreme flexibility to accommodate different fill materials,
E. Highly mechanized and effectively continuous construction process,
F. Appreciable accommodation of settlement-deformation without risk of serious
cracking and possible failure.
The relative disadvantages of the embankment dam are
A. Inherently susceptible to damage or destruction by overtopping
B. Necessity of separate spillway structure
C. Vulnerability to concealed leakage and internal erosion in dam or foundation
a. Key elements and appurtenances of Embankment dam
Every embankment dam consists of three basic components plus a number of
appurtenances which enable the basic components to function efficiently shown in Figure
2-1.
Foundation:

The foundation of embankment dam could either be earth or rock material. The
foundation provides support resisting both vertical and horizontal loads. It may also resist
seepage beneath the embankment
Figure 2-1 Basic components and appurtenances of Embankment dam
Core or membrane
The primary purpose of the core or membrane is to hold back free water. Depending on
the structural requirements of the dam, the core may be placed at the center or upstream
from the center, or on the upstream face (in the case of certain rock fill dams)
When the foundation is incapable of resisting under seepage the core is extended down
into the foundation to impervious layer. Such an extension of the core is termed cut-off.
Core material:
Earth, concrete or masonry, steel sheeting, etc. are used as core material. Lack of
flexibility of concrete and masonry make them undesirable. An earth core (when suitable
material is available) is usually cheaper and more water tight than any other type.
Suitability of earth core depends on the character of the available soil.
Table 2-1: Permeability of different soil types
Permeability coefficient Typical soil Value as core
2 – 0.002 Sand Considerable leakage
0.002 – 0.0002 Silty clay Usable with good control if some
leakage is tolerable
0.0002 – 0.000006 Silts Little leakage if well compacted
≤ 0.000006 Silty clay, clay Impervious

A core should not be composed of silt which tends to swell upon saturation. To avoid
swelling tendencies, the elasticity index should not exceed 30.
Typical requirements for core compaction are
90 – 97% of standard proctor maximum, or
87 – 95% of modified proctor maximum.
Water content: - as high as possible consistent with the above requirements.
Core thickness: - to control erosion and provide good compaction a minimum core
thickness in meters is given by
b = 6 + 0.1h (clay)
b = 6 + 0.3h (silt)
Where: h = head difference at that point;
b = core width at that point.
Shell
The purpose of shell is to provide structural support for the core and to distribute the
loads over the foundation. The shell also acts as foundation for most of the
appurtenances. Sometimes the core and shell of a dam are constructed of the same
material (homogenous dam).
Shell (embankment) materials
Availability and strength are the requirements for selection.
Strength: - the strength for the upstream side should be that at the inundated condition.
The same strength should be used for the downstream face which is below the
maximum phreatic line.
Permeability: - high permeability is desirable from the standpoint of pressure buildup
during construction and stability during sudden drawdown.
Typical compaction requirements:
95 – 100% of standard proctor maximum;
92 – 97% of modified proctor maximum.
Slopes: - shell slopes are based on stability analysis. When the stability is insufficient,
improvements are possible by adopting
a. Flatter slopes;
b. Increasing strength through high density;
c. Treatment for weak foundation;
d. Drainage of the foundation and embankment.
Table 2-2: Tentative slopes of shoulder for different embankment materials
Soil type Upstream Downstream
Gravel, sandy gravel with core 2.5H : 1V 2.0H : 1V
Clean sand with core 3.0H : 1V 2.5H : 1V
Low density silt, micaceous silt 3.5H : 1V 3.0H : 1V
Low plasticity clay 3.0H : 1V 2.5H : 1V
Composite slopes: - are used for large dams. They can be found in two ways: a series of
straight slopes or a constant slope with berms.

Figure 2-2 composite slopes for shell of embankment dam
A berm is a level surface on the slope that can serve the following purposes
1. Increases slope stability by increasing dam width;
2. Breaks the continuous downstream slope to reduce surface erosion
3. Provides level surface for maintenance operations, roads, etc.
Berm is also used at the bottom of a zone of riprap to provide supporting shoulder.
Height of dam:
Required height of an embankment dam is the vertical distance from the foundation to the
water surface in the reservoir, when the spillway is discharging at design capacity, plus a
free board allowance.
Free Board = maximum wave run-up height + allowance for settlement +
allowance for splash
Maximum wave run-up height = 4hw/3
Where: hw = effective wave height (with expectancy of 1%)
Table 2-3: Wave run-up to maximum wave height ratio on slopes
Slope Ratio of run-up to maximum wave height
Smooth Surface Riprap surface
1.5H : 1V 2.5 1.6
1H : 1V 2.0 1.3
Maximum vertical height of run-up = Expected wave height * appropriate factor from
Table 2-3
Settlement allowance: the following may be used as guide.
For foundation: 1% of height of dam
For embankment: 1-2% of height of embankment
Splash allowance could be taken 0.30 – 0.50m.
Top Width:
 Should be sufficient to keep the phreatic line with in the dam when the reservoir
is full
 Should be sufficient to withstand wave action and earthquake shock

 Has to satisfy secondary requirements such as minimum roadway width.
Appurtenances
Transition filter: - it is provided between core and shell to prevent migration of the core
material into the pores of the shell material. It is particularly needed between
clay cores and rock and gravel shells.
The objective of transition filter is to carry away seepage that has passed
through the core and cut-off and to prevent stratum of the upper part of the
downstream shell.
Toe drain: - it helps to prevent sloughing of the downstream face as a result of rain water
or seepage saturation. In small dams, the toe drain serves also as internal drain.
In large dams with pervious foundation, the toe drain and the internal drain are
sometimes combined. Drains need protective filter (inverted filter) to prevent
clogging of the drain.
Riprap: - required to cover the upstream/downstream face.
Normally riprap extended from above the maximum water level to just below
the minimum.
Sod: - required on the downstream face to prevent rain wash.
For economic reasons, the material available at the particular site has to be
employed as much as possible for the construction of the earth dam and the
quantity of imported material should be minimized.
Internal drains: - they are essential in large dams where the d/s shell is not so pervious.

2.2.2 Types of Embankment dam
The materials available locally control the size and configuration of the dam. Many small
embankment dams are built entirely of a single type of material such as stream alluvium,
weathered bedrock, or glacial till. These are homogeneous dams, constructed more or less
of uniform natural material as shown in Figure .
Figure 2.3 Principal variants of earth fill embankment dams (Values of m are examples)
The central core earth fill profile, shown in Figure (c) and (d), is the most common for
larger embankments dams. Larger embankment dams are also zoned and constructed of a
variety of materials Figure (f), either extracted from different local sources or prepared
by mechanical or hydraulic separation of source material into fractions with different
properties.
An important element in a zoned dam is an impermeable blanket or core which usually
consists of clayey materials obtained locally. In locations where naturally impermeable
materials are unavailable the dams are built of rock or earth-rock aggregates as shown in
Figure 2-, and the impermeable layers of reinforced concrete, asphalt concrete, or riveted
sheet steel are placed on the upstream face of the dam.

Figure 2-4 Principal variants of rock fill embankments dams (values of m are examples)
Selection of the optimum type of embankments for a specific location is determined
largely by the nature and availability of different fill materials in sufficient quantity.
The primary loads acting on an embankment do not differ in principle from those
applicable to gravity dams. There are, however, the conceptual differences there referred
to with regard to the water load which is exerted inside the upstream shoulder fill. Self
weight load, similarly a distributed internal body load, is significant with respect to
stability and internal stress for the embankment and for a compressible soil foundation.
Because of such differences, embankments dam analysis is less formalized and is carried
out quite differently from concrete dam analysis.
2.2.3 Causes of Failure of Embankment dams
Embankment dams, like any other engineering structure, may fail due to improper design,
faulty constructions, lack of maintenance, etc. Generally, causes of failure are grouped
into three classes: Hydraulic failure, Seepage failure and Structural failure.
Hydraulic failures: About 40% of earth dam failures have been attributed to these causes
due to;
1. Overtopping. Occurs when the design flood is less than the coming flood.
Spillway and outlet capacity must be sufficient to prevent overtopping.
Freeboard should also be sufficient to prevent overtopping by wave action.
2. Erosion of upstream faces. Wind waves of water developed due to wind near the
top water try to notch-out the soil from u/s face and may even sometimes
cause the slip of the u/s slope.(upstream slope pitching or rip rap should be
applied.)
3. Erosion of downstream face by gully formation. Heavy rains falling directly over
d/s face and the erosive action of the moving water may lead to the formation
of gullies on the d/s face, ultimately leading to the dam failure.
4. Cracking due to frost action. Frost in the upper portion of dam may cause
heaving of soil with dangerous seepage. Consequently failure. Provide an
additional free board allowance up to a maximum of say 1.5m may be
provided.

Seepage failure: controlled seepage or limited uniform seepage is inevitable in all
embankments and it does not produce any harm. However, uncontrolled or concentrated
seepage through the dam or the foundation may lead to piping*
or sloughing†
and the
subsequent failure of the dam.
Structural failure: about 25% of the dam failures have been attributed to structural
failures. Structural failures are generally caused by shear failures, causing slides.
Causes of failure as categorized based on time of occurrence
During construction
 Unstable slop
 Heavy rainfall that washes the d/s face
 Weak foundation
After construction
 Failure of u/s face due to sudden drawdown
 Failure of d/s when the reservoir is full
 Overtopping
 Seepage failure.
2.2.4 Design features
Some of the more important features that should be considered in the design of
embankment dams are:
1. Zoning of shoulder-fills: the permeability of successive zones should increase
toward the outer slopes, materials with a high degree of inherent stability being
used to enclose and support the less stable impervious core and filter.
2. Spillway location: geotechnical and hydraulic design considerations require that
to minimize the risk of damage to the dam under flood conditions the spillway
and discharge channel are kept clear of the embankment.
3. Freeboard: is the difference between maximum reservoir level and minimum
crest level of the dam. The provision necessary for long-term settlement within
the overall minimum freeboard is determined by the height of dam and the depth
of compressible foundation at any section.
The overall minimum freeboard from spillway sill to dam crest should be at least
1.5m on the smallest reservoir embankment, and it will be very much greater for
larger embankments and/or reservoir.
The minimum height of freeboard for wave action is, generally, 1.5hw
4
271
.
0
763
.
0
.
032
.
0 F
F
v
hw 

 For km
F 32

F
v
hw .
032
.
0
 For km
F 32

Where; v is wind velocity (km/hr)
*
The progressive erosion and subsequent removal of soil grains from within the body of the dam or the
foundation of the dam
†
The progressive removal of soil from the wet d/s face.

F is fetch or straight length of water expansion in km
4. Foundation seepage control: seepage flows and pressure within the foundation
are controlled by cut-offs and by drainage. Cut-offs is impervious barriers which
function as extensions of the embankments core into foundation. The cut-offs are
generally two types:
a) Fully penetrating cut-off: penetrate to impervious strata
b) Partially penetrating cut-off: terminate where the head loss across the cut-
off is sufficient to effect the required degree of control

Figure 2-5 Cut-offs and control of under seepage
5. Outlet works (tunnels and culverts): outlet works should where practicable be
constructed as a tunnel driven through the natural ground of the dam abutments.
Where this is difficult or uneconomical a concrete culvert founded on rock is a
satisfactory alternative.
6. Upstream face protection: several options are available for protection of the
upstream face against wave erosion, ranging from traditional stone pitching with
grouted joints through concrete facing slabs to the use of concrete block work,
rock armoring and riprap.
7. Embankments crest: the top width of larger earthen dam should be sufficient to
keep the seepage line well within the dam, when reservoir is full. The crest should
have a width of not less than 5m, and should carry a surfaced and well-drained
access road. The top width (W) of the earth dam can be selected as per the
following recommendation:
3
5


H
W , For very low dams 4.1
H
H
W 2
.
0
55
.
0 
 , For dams lower than 30m 4.2
 3
1
5
.
1
65
.
1 
 H
W , For dams higher than 30m 4.3
Where: H is the height of the dam.
2.2.5 Criteria for Safe Design of Earth Dam
An earth dam must be safe and stable during phases of construction and operation of
the reservoir. The practical criteria for the design of earth dams may be stated briefly
as follows.

1. No overtopping during occurrence of the inflow design flood.
a.appropriate design flood
b.Adequate spillway
c.Sufficient outlet works
d. Sufficient free board
2. No seepage failure
a.Phreatic (seepage) line should exit the dam body safely without sloughing
downstream face.
b. Seepage through the body of the dam, foundation and abutments should be
controlled by adapting suitable measures.
c. The dam and foundation should be safe against piping failure.
d.There should be no opportunity for free passage of water from U/S to D/S
both through the dam and foundation.
3. No Structural failure
a) Safe U/S & D/S slope during construction
b) Safe U/S slope during sudden draw down condition.
c) Safe D/S slope during steady seepage condition
d) Foundation shear stress within the safe limits.
e) Earth quake resistant dam
4. Proper slope protection against wind & rain drop erosion.
5. Proper drainage
6. Economic section
2.2.6 Seepage analysis
Seepage occurs through the body of all earthen dams and also through their pervious
foundation. The phreatic surface of the seepage regime, i.e. line within the dam section
below which there is positive hydrostatic pressures in the dam, must be kept well clear of
the downstream face to avoid high pore water pressures which may promote slope
instability.
The amount of seepage can be easily computed from the flow net, which consists of two
sets of curves, known as ‘Equipotential line’ and ‘stream lines’, mutually perpendicular
to each other. For homogeneous embankments dam, discharge per unit width (q) of the
dam passing through a flow net is described as:
d
f
N
N
kH
q 
Where: H is the head differential.
Nf is number of stream lines.
Nd id number of equipotential lines.
Determination of Phreatic Lines
It is absolutely essential to determine the position of the phreatic line, as its position will
enable to determine the following:
i. The divide line between the dry (or moist) and submerged soil.

ii. The top stream line and hence, helps us in drawing the flow net.
iii. To ensure that the phreatic line doesn’t cut the downstream face of the dam,
which is extremely necessary for preventing softening of the dam.
A. Homogeneous dam section with horizontal filter
It has been found that the seepage line is pushed down by the filter and it is very nearly
parabolic except near its junction with u/s face. Since the u/s face of the dam (i.e. GB in
Figure 2-7) becomes an equipotential line when fully covered with water, the seepage
line shall be perpendicular to the face near its junction point B.
Figure 2-6 Seepage through homogenous dam section with horizontal filter
Equation of the base parabola
Let a base parabola with focus at F is drawn and produced so as to intersect the water
surface at a point A as shown in fig2.7. Taking the focus (F) as the origin, equation of the
parabola p(x, y) can be written as
FD
x
y
x 

 2
2
Where; FD is the distance of the focus from the directrix, called focal
distance and is represented by S.
Hence the equation of the parabola of the seepage line becomes:
S
x
y
x 

 2
2
Location of A is approximately 0.3HB horizontal distance upstream from point B
according to Cassagrande. Where, H is the projection of the point G on the water surface.
If the horizontal distance between the already determined point A and the focus (F) is
taken as say b, then (b, H) represents the coordinates of the point A on the parabola. And
hence;
S
b
H
b 

 2
2
b
H
b
S 

 2
2
The center point (C) of FD will then be the vertex of the parabola. When x = 0, y= S.
Hence the vertical ordinate FJ at F will be equal to S. Knowing the points A, C, and J and

working out a few more points from the equation, the parabola can be easily drawn and
corrected for the curve BI, so as to get the seepage line BIJC.
The amount of seepage can also be calculated easily from the equation of the seepage line
as derived below.
Darcy’s law is defined as, q = KiA. When steady conditions have reached, the discharge
crossing any vertical plane across the dam section (unit width) will be the same. Hence,
the value i and A can be taken for any point on the seepage line
dx
dy
i 
1
*
y
A 
y
dx
dy
K
q 
But from the equation of the parabola,
xS
S
y 2
2


   
xs
S
S
xs
S
K
q 2
.
2
.
2
.
2
1 2
1
2
1
2










KS
q 

Example:
An earth dam made of a homogeneous material has a horizontal filter and other
parameters as shown in the figure. Determine the phreatic line and the seepage quantity
through the body of the dam.
20
25
25 25 5 15 60
130
A
F
5
2:1
3:1
8
Ø = 25°
c = 24 kN/sq.m
dry = 18.0 kN/cu.m
sub = 12.0 kN/cu.m
Ø = 12°
c = 54 kN/sq.m
dry = 18.3 kN/cu.m
sub = 18.3 kN/cu.m
k = 5*10^-6 m/sec
Fig. Section of the homogeneous earth dam.
Horizontal Filter
Figure 2-7a Section of a homogenous earth dam
For the origin of the Cartesian co-ordinate system at the face of the filter (point F), the
equation of the parabola of the seepage line can be expressed as:
S
x
y
x 

 2
2
At point A, x = 65m, and y = 20m. Inserting into the parabola equation, S = 3.07m.
Working out a few more points from the equation, the parabola can be easily drawn and
corrected for the curve at the upstream face of the dam, so as to get the seepage line.
x -1.51 0 10 15 25 30 40 45 55 65
y2
0 9.06 69.26 99.36 159.56 189.66 249.86 279.96 340.16 400.36
y 0 3.01 8.32 9.97 12.63 13.77 15.81 16.73 18.44 20.01
25
25 25 5 15 60
130
20
Phreatic line
The amount of seepage flow is
Q = kS
= 5 * 10-6
* 3.07
= 15.35 * 10-6
m3
/sec per meter width of dam

B. Homogeneous dam section without horizontal filter
The focus (F) of the parabola will be the lowest point of the downstream slope as shown
in Figure . The base parabola BIJC will cut the downstream slope at J and extend beyond
the dam toe up to the point C i.e. the vertex of the parabola.
Figure 2.7B Homogeneous dam section without filter
The seepage line will, however, emerge out at K, meeting the downstream face
tangentially there. The portion KF is known as discharge face and always saturated. The
correction JK (say ∆a) by which the parabola is to be shifted downward can be
determined as follows:
α‡
in degrees
a
a
a



30o
0.36
60o
0.32
90o
0.26
120o
0.18
135o
0.14
150o
0.10
180o
0.0
Where α is the angle which the discharge face makes with the horizontal. a and ∆a can
be connected by the general equation;
  




 



 o
o
a
a
a
400
180 
Example
An earth dam made of a homogeneous material has the coefficient of permeability K=
5*10-4
cm/ sec and the other parameters are as shown in the Figure 2-. Determine the
phreatic line and the seepage quantity through the body of the dam.
‡
α will be equal to 180o
for a horizontal filter case and it will be less than 90o
when no drainage is
provided.

Figure 2-7C Body of homogeneous earth dam
4.5m
2:1
3:1
RL = 197.5m
RL = 178.0m
RL = 200.0m
H = 19.5m
66m 44m

2.8 Characteristics of Phreatic line (Seepage line)
Based on the above discussions, the characteristics of the phreatic line may be
summarized below:
1. At the entry point, the phreatic line must be normal to the upstream face
since the upstream face is a 100% equipotential line. For other entry
condition (Fig.2.8), the phreatic line starts tangentially with the water
surface.

Fig 2.8: Entry conditions of phreatic line
2. The pressure along the phreatic line is atmospheric. Hence the only change
in the head along it is due to drop in the elevation of various points on it.
Due to this, the successive equipotential lines will meet it at equal vertical
intervals.
3. The focus of the base parabola lies at the break out point of the bottom
flow line, where the flow emerges out from relatively impervious medium
to a highly pervious medium.
4. When horizontal filter or drainage toe is provided, the phreatic line would
tend to emerge vertically.
5. In the absence of any filter, the seepage line will cut the downstream slope
at some point above the base. The location of this point, and the phreatic
line itself, is not dependent on the permeability or any other property, so
long as the dam is homogeneous. The geometry of the dam alone decides
these.
6. The presence of pervious foundation below the dam does not influence the
position of phreatic line.
7. In the case of a zoned dam with central impervious core, the effect of
outer shells can be neglected altogether. The focus of the base parabola
will be located at the downstream. Toe of the core (Fig. 2.8)
2.2.7 Stability analysis
Three considerations govern the design of an earth embankment.
i. Side slopes must be stable;
ii. Dimensions must be sufficient to control seepage;
iii. Base width must be long enough to distribute weight of dam over sufficient area
to prevent overstress in the foundation.
An earthen embankment usually fails because of the sliding of a large soil mass along a
curved surface.
Stability of side slopes of earth dam
Forms of side slope failure:

Toe failure: - most likely to occur when the slopes are relatively steep or when the soil
below the toe of the slope is strong.
Base failure: - occurs when the slopes are flat or when the soil below the toe is relatively
weak.
Face or slope failure: - occurs only when there is a relatively weak zone in the upper
part of the slope or when there is a very strong stratum above the toe level.
The method used for examining the stability of slopes of earthen embankments is called
the Swedish Slip Circle Method or the Slices Method. It assumes the condition of plane
strain with failure along a cylindrical arc. The location of the Centre of the possible
failure arc is assumed. The earth mass is divided into a number of vertical segments
called slices as shown in figure2.6. O is the center and r is the radius of the possible
failure.
Figure 2-9.1 possible slip surface in Earth fill dam
The side slopes of earth dam will be stable if the soil mass is not dislodged from the
slopes. However, the soil mass in an earthen dam is subjected to forces which tend to
cause movement or sliding of the soil mass. These forces are known as actuating, driving
or disturbing forces which mainly consists of gravity forces. The movement or sliding of
the soil mass in an earthen dam is resisted by the resisting or stability forces which are
provided mainly by the shearing strength of the soil.
The stability of the side slope of an earthen dam is thus analyzed by assuming a surface
slippage within the soil mass and by determining the resisting and the disturbing forces
acting on this surface and the moments of these forces about the center of rotation n, and
then factor of safety against sliding is calculated.
The forces acting on the slices are:
1. The self-weight W of the slice acting vertically downward through the center of
gravity.
2. The cohesive forces acting tangentially opposite to the direction of probable
slippage

3. The soil reaction across the arc. When the soil mass is about to slide, the soil
reaction will act at an angle ф (the angle of internal friction of the soil) to the
normal i.e. radial direction
4. The soil reaction on the two vertical sides of the slice exercised by the adjacent
slices on the right and left respectively.
5. Pore pressures at the base of the arc, and left and right side of the slice.
Usually it is assumed that the soil reactions on the two vertical sides of the slice cancel
each other and so also the pore pressures on the two sides balance each other
The disturbing force is the component of weight of slice in tangential direction i.e.,

sin
W
T  ,
Where: α is the angle which the slope makes with the horizontal.
The total disturbing forces will be summation of disturbing forces for all slices;
....
3
2
1 



 T
T
T
T
The total disturbing moments over the sliding surface will be equal to
 

 i
i
i
d T
r
r
T
M
The magnitude of shear strength developed in each slice will depend upon the normal
components of that slice. Its magnitude will be:

tan
N
L
c 


Where; c is the unit cohesion of the soil
∆L is curved length of the slice
Ф is the angle of internal friction
N is equal to Wcosα
The total resisting force will be summation of resisting forces for all slices;
 


 
tan
N
L
c
  
tan

 

 N
L
c
The total resisting moment over the entire sliding surface will be equal to
 
 
 


 
tan
N
L
c
r
Mr
Hence the factor of safety against sliding

 




T
N
L
c
M
M
FS
d
r

tan
For determining the stability of the proposed side slope of an earth dam it is necessary to
find the least factor of safety which may occur on any of the possible surfaces of slippage
or slip circles. Slip circle which yields the least factor of safety is the most critical and
hence it is known as critical surface slippage or critical slip circle. For locating the critical
surface of slippage, it is necessary to try several different surfaces of slippage as one trial
gives the value of factor of safety for that arc only.

W4
V42
V41
h4
α
4
N4
Phreatic line
b
τ4
For preliminary analysis 4 to 5 slices may be sufficient; however, 10 to 15 slices are
considered in general. It is not necessary for the analysis to make all the slices of equal
width, but for the sake of convenience it is customary to have slices of equal width.
In order to reduce the number of trials, Fellenius has suggested a method of drawing a
line, representing the locus of the critical slip circle. The determination of this line PQ is
shown in Figure . The point P is obtained with the help of directional angles α1 and α2 as
shown in Error! Reference source not found.
Table 2-4 Slope and respective directional angle
Slope
Directional angles
α1 in degrees α2 in degrees
1:1 27.5 37
2:1 25 35
3:1 25 35
4:1 25 35
5:1 25 35
a. downstream slope b. upstream slope
Figure 2.9.2 locus of critical circle
Design parameters to be employed in stability analysis may be summarized as follows:
a. Stability of downstream slope during steady seepage (reservoir full)
The most critical condition for the d/s slope occurs when the reservoir is full and the
seepage is taking place at full rate.
The seepage water below the phreatic line exerts a pore pressure on the soil mass which
lies below the phreatic line, see Figure 2.9.3.

Figure 2.9.3 stability of downstream slope during steady seepage
Consider slice number 4 in Figure , the weight of the slice is defined as;
42
41
4 *
* V
V
W sat
dry 
 

α4 read from the scaled drawing of the earth fill dam. And tangential component of W4 is
defined as, whish is shear stress developed at failure plane,
4
4
4 sin
W
T 
The pore pressure for slice 4 is represented by the piezometric head h4. Hence pore water
pressure is
4
4 h
U w
w 

Shear strength developed for the slice is quantified from two soil parameters, apparent
cohesion c and angle of shearing resistance ф. Shear strength at failure plane is defined as
  


 tan
cos 4
4
4
4
4
4 L
h
W
cL w



Where; L4 is
4
cos
b
The factor of safety of slide 4 is
 
4
4
4
4
4
4
4
4
4
sin
tan
cos




 W
L
h
W
cL
T
FS w




The factor of safety for the entire circle is then given by the equation
 

  


i
i
i
i
w
i
i
i
i
W
L
h
W
L
c
FS




sin
tan
cos
b. Stability of Upstream Slope during sudden drawdown
For the u/s slope, the critical condition can occur, when the reservoir is suddenly emptied.
In such case, the water level within the soil will remain as it was when the soil pores were
full of water. The weight of this water within the soil now tends to slide the u/s slope
along a circular arc.
The tangential components of the saturated soil lying over the arc will create a disturbing
force; while the normal component minus the pore pressure shall supply the shear
strength of the soil.

Table 2-5: General format of computation
Slice# W T N U l Ul N’=N-ul tanΦ N’tanΦ Cl N’tanΦ+cl
1
…
n
Σ T Σ
(N’tanΦ+cl)
The factor of safety is finally obtained from the equation

 

 '
'
tan
T
N
L
c
FS
i
i 
Where: N’
represents normal components on submerged density
T’
represents tangential components on saturated unit weight of the soil
2.9.1 Stability of earth dam against horizontal shear developed at the base of the
dam
Approximate method for checking the stability of u/s and d/s slopes under steady
seepage from consideration of horizontal shear at base
1. Stability of u/s slope during sudden drawdown
It is based on the simple principle that a horizontal shear force Pu is exerted by the
saturated soil. The resistance to this force Ru is provided by the shear resistance
developed at the base of the soil mass, contained within the u/s triangular shoulder GMN
of Fig.
Considering unit length of the dam, the horizontal force Pu is















2
2
45
tan
2
2
1
2
2
1 h
h
P w
u 


Where;
 
h
h
h
h dry
sub 1
1
1






Shear resistance Ru of u/s slope portion of the dam developed at base GN is given by


 tan
2
1
tan 








 h
B
cB
W
cB
R u
sub
u
u
u
Where; W is the weight of the u/s triangular shoulder of the dam
The factor of safety against can be easily calculated, using
u
u
P
R
FS 
It should be more than 1.5.
2. Stability of d/s slope under steady seepage

It is based on the consideration of horizontal shear at base under the d/s slope of the dam.
The horizontal shear force Pd is given by, referring Fig;















2
2
45
tan
2
2
2
2
2
2 h
h
P w
u 


Where;
 
h
h
h
h dry
sub 2
2
2






Shear resistance Rd of d/s slope portion of the dam is given by;
  


 tan
tan 2
1 A
A
cB
W
cB
R sub
dry
u
d
d 




The downstream profile RTS of the downstream slope portion of the dam has an area A1
and of dry soil above seepage line and the area of submerged soil say A2 below the
seepage line.
The entire weight W may be calculated on the basis of submerged soil as it will be on a
still safer side. In that case,
h
B
W d
sub


The factor of safety against shear can be easily determined as;
d
d
P
R
FS 
2.10 Foundation analysis
Foundation stress in earth dams are not usually critical except when the foundation
material consists of unconsolidated clay or silt with low shearing strength.
Consider a dam on homogeneous, unconsolidated earth foundation of thickness t
Figure 2.9.4 Homogenous embankment dam with pervious foundation of thickness t
The downward force exerted on the foundation at the center of the dam tends to squeeze
the foundation material from under the dam. But shear stress develops in the foundation
resisting this action. Assuming the foundation loading to vary as indicated above, Leo
Jugenson suggested the following maximum stresses:
If t > L, τmax= 0.256γf Hs ; Where γf = specific weight of fill
Usually t < L

If t < L/10, τmax = γf Hs t/L
Shear strength = Ss = c + σ tanΦ
The factor of safety against overstress is
FS = Ss/ τmax
A minimum value of FS = 1.5 is recommended.
Example:
Design the embankment dam shown in Figure 2- used as an example for analysis of
seepage flow. Detail all the necessary procedures and important consideration in the
process.
Design Solution
The stability design process starts by determining the phreatic line profile which is done
before. The critical slipage circle is then drawn by following the suggestion made by
Fellinus. Here a single slipage circle is considered for illustration and four slices were
considered for both upstream and downstream slope failure. The geometric information’s
were then determined as shown below.
13.8
12.5
A1
A2
A3
A4
A3
A4
A2
A1
20
25
25 25 5 15 60
130
Phreatic line
5
1
2
0
.2
7
1
.
3
Fig. Sample of failure circle, slices and related measurments of the earth dam section
Geometric properties of slices
Upstream Downstream
Slice
Area(m2
)  (deg) hw (m)
L (m)
Area (m2
)

(deg)
L (m)
A1 25.97 32 0 14.5 68.58 40 18
A2 111.68 24 6.1 22 111.48 28 15.4
A3 120.83 15 6.2 20.7 96.1 17 14.2
A4 55.52 4 3.6 20.1 40.11 7 13.7
Area in relation with phreatic line.
Area (m2
) Dam U/s shoulder D/s shoulder
Under seepage line 1102.08 838.1 221

(saturated)
Dry portion 584.92 99.4 404
Total 1687 937.5 625
To assess the overall stability of the dam considering 1m length,
Item
Dam U/s shoulder D/s shoulder
Area(m2
) Weight(kN) Area(m2
) Weight(kN) Area(m2
) Weight(kN)
Under seepage
line 1102.08 13224.96 838.1 10057.2 221 2652
Dry portion 584.92 10528.56 99.4 1789.2 404 7272
Total 1687 23753.52 937.5 11846.4 625 9924
The stability design then proceeds by first considering the entire embankment and its
interaction with the foundation.
Shear resistance of the dam at the base(R)
R = C + W tanΦ
Where: C = total cohesive resistance of the soil at the base
= c*B*1 = 24 * 130 * 1
= 3120 kN
Wtan = 23753 * tan250
= 11076 kN
R = 3120 + 11076
= 14196 kN
Horizontal force due to hydrostatic pressure of water
P = ½ w h2
= ½ * 10 * 202
= 2000kN
Factor of safety against failure due to horizontal shear at the base
FS = R/P = 7.1 > 1.5 Safe!
Check stresses in the foundation
t = 8m < L/10 = 130/10 =13,
Hence,
τmax= γf Hs t/L
= 18.3 * 20* 8/130
= 22.52kN/m2
Shear strength = Ss = c + σ tanΦ
= c + W/L tan
= 54 + 23754/130 * tan 120
= 92.8 kN/m2
The factor of safety against overstress is
FS = Ss/ τmax = 92.8/22.52 = 4.12 > 1.5 Safe!
Stability of u/s and d/s slopes against sliding shear.
Upstream slope (under sudden drawdown):
Considering unit length of the dam, the horizontal force Pu is

 
 
7
.
14
25
8
.
13
25
18
8
.
13
*
12
1
1
1







h
h
h
h dry
sub 


6
.
2816
2
8
.
13
10
2
25
45
tan
2
25
*
7
.
14
2
2
45
tan
2
2
2
2
2
1
2
2
1































h
h
P w
u 


Shear resistance Ru of upstream slope portion of the dam developed at base GN is given
by,
1
.
9574
47
.
0
*
4
.
11846
75
*
54
tan 



 
W
cB
R u
u
Where; W is the weight of the upstream triangular shoulder of the
dam.
The factor of safety against shear can be easily calculated,
5
.
1
4
.
3
6
.
2816
1
.
9574




u
u
P
R
FS Safe!
It has been known that the maximum intensity of shear stress occurs at a distance 0.6Bu
(where Bu is the base length of the upstream shoulder) from the heel and is equal to 1.4
times the average shear intensity.
Hence, maximum shear stress induced (τmax) = 1.4(Pu/Bu)
= 1.4 (2816.6/75)
= 52.6
The unit shear resistance developed at the same point is
τf = c + 0.6hsubtan
= 24 + 0.6 * 25 * 12 * tan 250
= 107.9
FS at the point of maximum shear should be greater than unity.
FS = τf / τmax = 107.9 / 52.6 = 2.0 > 1 Safe!
For the downstream shoulder, similarly,
  15
25
5
.
12
25
18
5
.
12
*
12
1 




7
.
2683
2
5
.
12
10
2
25
45
tan
2
25
*
15 2
2
2
















u
P
3
.
7904
47
.
0
*
9924
60
*
54
tan 



 
W
cB
R u
u

5
.
1
9
.
2
7
.
2683
3
.
7904




u
u
P
R
FS Safe!
Maximum shear stress induced (τmax) = 1.4(Pu/Bd)
= 1.4 (2683.7/50)
= 75.1
The unit shear resistance developed at the same point is
τf = c + 0.6hsubtan
= 24 + 0.6 * 25 * 12 * tan 250
= 107.9
FS at the point of maximum shear should be greater than unity.
FS = τf / τmax = 107.9 / 75.1 = 1.44 > 1 Safe!

Analysis of upstream and downstream slopes by Swedish Circle method:
Upstream slope
Slice
Area
W T N U L UL N’=N-
ul
tanΦ N’tanΦ Cl N’tanΦ+cl
A1 25.97 32 467.46 247.72 396.43 0 14.5 0 396.43 0.47 186.32 348 534.32
A2 111.68 24 1340.16 545.09 1224.3 61 22 1342 -117.7 0.47 -55.32 528 472.68
A3 120.83 15 1449.96 375.28 1400.55 62 20.7 1283.4 117.15 0.47 55.06 496.8 551.861
A4 55.52 4 666.24 46.47 664.62 36 20.1 723.6 -58.98 0.47 -27.72 482.4 454.68
Σ T 1214.56 Σ (N’tanΦ+cl) 2013.54
5
.
1
66
.
1
56
.
1214
54
.
2013
tan
'
'






 
T
N
L
c
FS
i
i 
Safe!
Downstream slope
Slice
Area
W T N l N’=N-
ul
tanΦ N’tanΦ Cl N’tanΦ+cl
A1 68.58 40 1234.44 793.48 945.64 18 945.64 0.47 444.45 432 876.45
A2 111.48 28 2006.64 942.06 1771.76 15.4 1771.76 0.47 832.73 369.6 1202.33
A3 96.1 17 1729.8 505.74 1654.22 14.2 1654.22 0.47 777.48 340.8 1118.28
A4 40.11 7 721.98 87.99 716.6 13.7 716.6 0.47 336.8 328.8 665.6
2329.27 Σ (N’tanΦ+cl) 3862.66
5
.
1
66
.
1
27
.
2329
66
.
3862



FS Safe!

2.11 Internal drainage system
General
Purpose of drainage:
1. To reduce the pore pressure thereby increasing the stability of the dam
2. To prevent piping so that soil particles are not carried away from the embankment.
A drainage system consists of two components.
a. the protective filter
b. the conduit which collects and disposes of the seepage.
Protective filter: - serves to allow free drainage and to prevent erosion.
It is provided between
Riprap and embankment
Core and embankment
Embankment and drains
Experiments by Terzaghi, Bertram and others have shown that a filter need only hold the coarse
15% of the grain size. These coarse particles D85 and over, will collect over the filter opening
bridging over it and trapping finer particles.
Size of filter holes, Df  D85 ( of the soil being filtered)
From tests, the following criteria are established.
D15 (filter)  4 to 5 D85 (soil); to satisfy prevention of migration of soil particles.
D15 (filter)  4 to 5 D15 (soil); for free drainage.
Filter gradation curve should be smooth and parallel to the soil being filtered. When the soil is
gap graded recompute and re-plot the grain size distribution using only the fraction finer than the
break as representing the entire soil; apply the filter criteria to this distribution
Filter thickness:
Thin filter is desirable to minimize flow resistance. Practical considerations, however, put
minimum sizes as shown in Table-2.6.
Table-2.6: Representative mean filter thickness
Filter Thickness for given head, cm
0 – 25 m 25 – 50 m 50 – 100 m
Fine sand 15 30 45
Coarse sand 25.5 45 60
Gravel 30 60 75
For every fine grained soil a multiple layered filter is necessary. Each successive layer is
designed to fit the D15 and D85 of the finer layer it must filter. The last layer must fit the openings
of the drain conduit which carries the water away.

Example:
Determine the size of the bed material for the embankment dam with the grain size shown below.
Grain size Riprap Dam
D15 70 mm 0.3 mm
D85 130 mm 2.0 mm
Drain Conduit:
Function: to collect water from the filter and carry it away with as little head as possible.
Quantity of Flow: Estimated from the seepage analysis. A factor of safety of 5 is not uncommon.
Simplest conduit: uniform coarse fragmental material (coarse sand, gravel, crushed rock, etc.)
A properly designed filter must surround the drain. For high discharges or when suitable crushed
rock is not available, pipe conduits wig perforated and flexible joints are employed.
Types of drain
Trench drain:
Trench drain is used for intercepting seepage through homogeneous foundations and those
containing horizontal pervious strata or seams
Figure2-11.1 Trench Drain
Mound drain: used when the need for embankement drainage exceeds that of the foundation.
Figure 2.11.2 Mound drain

Position- when there is cut-off, the drain is placed immediately downstream from the cut-off to
relieve any pressure build up.
When there is no cut-off, the position depends on the seepage analysis of dam and foundation.
Upstream location
Increases stability at the cost of increased seepage and cost of conduit.
Minimum distance from downstream toe to provide substantial increase in stability is 1/3 of the
base width. Maximum distance is 2/3 of base width, from downstream toe.
Blanket drain:
This is horizontal drain placed on top of foundation.
To intercept water from vertical fissures in the foundation;
To lower the seepage line in the embankment
Figure 2.11.3 Blanket drain
Riprap:
Riprap is required on the upstream slope and the downstream slope below the tail water level. An
estimation of the required weight of rock pieces required for riprap is given by Hudson as
W  (H2 ρst tan α) / (3.2Δ2)
Where: the factor 3.2 is for smooth quarry stone
ρst = density of rock
α = angle of slope
Δ = (ρst – ρw)/ ρw
ρw = density of water
Types of riprap
Dumped riprap: consists of angular broken rock dumped from truck and spread.
Hand-placed riprap: consists of more or less prismatic stone placed on end to form rough
pavements.

Figure 2.11.4 Types of riprap
2.3. River Diversion
River diversion is a technique of diverting river water away from downstream part into the canal
or tunnel or to particular confined side.
River diversion takes place for two purposes:
 For construction purpose
 For water use purpose
River Diversion construction purpose
During construction of gravity or embankment dam, concreting of dam or placing of earthen
material cannot be done in water. Therefore, before starting construction of major dam, the river
water has to be diverted away from the dam site so that the construction can be done in dry
condition.
Coffer Dam: usually earthen embankment (for economic purpose) is constructed on the U/S and
D/S of the dam site to isolate the construction area which is to be kept dry.
 The diversion tunnel or canal takes off U/S of the coffer dam on the U/S and then
joins on the D/S of the coffer dam in the D/S side.
 Some water usually seeps into the construction area, which has to be pumped out
to keep the area dry.
The diversion of river water can be accomplished in either of the following ways:
I. Provision of diversion tunnel or Channel

D/S coffer dam
U/S
Diversion tunnel or
diversion channel
Costruction zone
U/S coffer dam
D/S
Used during construction of both concrete & embankment dams
II. Two stage construction
Instead of diverting the river into a tunnel or channel, it is some times more
economical to have two stage construction of gravity dam. In such a case, the flow is,
first of all, diverted and confined to one side of the channel by constructing semi
circular coffer dam. Then construction progresses in free water zone. On the next
stage the diverted water is allowed to overtop or to pass through outlet on the side of
already constructed portion of the dam.
This method is suitable only during construction of concrete dam.
U/S
Co
ns
tru
cti
on
ar
ea
i. 1st stage diversion
D/S
diverted
flow
Coffer
dam
U/S
ii.2nd stage diversion
overtopped
flow
Completed
portion of
the dam
D/S
Construction
zone on the
2nd stage
III. River diversion through the construction site (through culverts in the body of
the dam) Example: Gilgel Gibe Hydroelectric project

Construction zone
of main dam
U/S coffer dam
Culverts
Culverts
Culverts
Construction
zone
of
main
dam
D/S Coffer dam
Choice of design flood
Flood occurs when the flow depth h is larger than the limit depth hL and the
corresponding limit discharge QL can be predicted. If the limit discharge QL
has a return period of n years, the probability of flooding within one year is
P1 = n-1
And for m years of construction
Pm = 1 – (1- n-1
)m
This probability is also referred to as the hydrologic risk of the construction site. For n
>> m, Pm = m/n. For instance if the risk of flooding is limited say to 10%, the design
flood has a return period of n = 10m. Accordingly, the design discharge QD = QL = Qn
where n = 10m.
Generally for different construction period and hydrologic risk of 5% & 10% the value
of return period for the design discharge is determined from the following graph.

Diversion by culvert/tunnel and coffer dam
Tunnels are usually confined to steep side rock valleys. They have the advantage of not
interfering with foundation excavation and dam construction work. Culvert under embankment
dams may be preferred in flat valleys or where the rock is too poor for efficient tunneling, but
tunneling appears to be the most frequent choice.
River diversion through tunnels is the commonest practice in the construction of high head dams.
An economic and engineering study of coffer dam height versus tunnel size may be done to
establish the most economic combination for the maximum diversion discharge. It is also
possible to plot a chart to see the tunnel –to-coffer dam cost alternative and to select the most
economical combination.
Graph for determination of return period for design discharge for different
construction period and hydrologic risk.
0
100
200
300
400
500
600
700
0 5 10 15 20 25 30 35
Construction period (years)
Return
period
(years)
10% hydrologic risk
5% hydrlolgic risk

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