4th Grade of Civil Engineering Department
Academic Year 2021-2022
Prepared BY
Assoc. Prof Dr.Thamir M. Ahmed
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*EARTH
DAMS
DESIGN
π«πππππ ππ π―ππ ππππππ πΊπππππππππPart 2
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Earth Dams:β’ They are trapezoidal in shape
β’ Earth dams are constructed where the foundation or the underlying
material or rocks are weak to support the masonry dam or where the
suitable competent rocks are at greater depth.
β’ Earthen dams are relatively smaller in height and broad at the base
β’ They are mainly built with clay, sand and gravel, hence they are also
known as Earth fill dam or Rock fill dam
Earth Dams: are the most simple and economic (oldest dams)
Types of earth dams:
1. Homogeneous embankment type
2. Zoned embankment type
3. Diaphragm type
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yx kk
2 β Rolled fill method:
- Soil is prepared at certain moisture content.
- Put into layers (15 β 30) cm .
- Pressed by rollers having adequate weights .
Methods of construction of Earth Dams:
1 β Hydraulic fill method
- Pumping of (earth + water through pipes ).
- Liable to considerable settlement due to drying and
consolidation.
- During rest, grains of earth are graded, thus ,this should be
considered by filter design.
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Causes of failure of earth dams:1. Hydraulic failure causes 40%
2. Seepage failure causes 30%
3. Structural failure causes 25%
4. External causes 5%
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Hydraulic Failure is due to:
1. Overtopping (design level is underestimated)
2. Erosion of US face (wave action β height)
3. Cracking in upper portion of dam due to frost action (additional
freeboard allowance up to 1.5 m)
4. Erosion of DS face due to rain action (maintenance β berms -
grass)Seepage failure is due to:
1. Uncontrolled seepage (causes scour through DS wet zone β needs
adequate filters)
2. Piping (through dam foundation β either prevention or control of
percolationβ¦may cause dam subsidence)
Structural failure is due to:
1. Foundation slide by soft soil (fine silt β soft clay, β¦all dam body
slides on foundation)
2. Slide of slopes (US or DS slopes)
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SECTION OF AN EARTH DAMThe preliminary design of an earth dam is done on the basis of past experience
and on the basis of the performance of the dams.
preliminary selection
The preliminary section include the following terms
:
(1) Top width.
(2) Free board.
(3) Casing or outer shells.
(4) Central impervious core.
(5) Cut-off trench.
(6) Downstream drainage system.
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Top Width:The crest width of an earth dam depends on the following
considerations :(i) Nature of the embankment materials and minimum allowable
percolation distance through the embankment at the normal
reservoir level.
(ii) Height of the structure.
(iii) Importance of the structure.
(iv) Width of highway on the top of the dam.
(v) Practicability of construction.
(vi) Protection against earthquake forces.
b = H / 5 + 3
b = 0.55 H1/2 + 0.2
b = 1.65 (H + 1.5)1/3
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Nature of spillway Height of Dam Free Board
Free Any Minimum 2 m and maximum
3 m over the maximum flood
level
Controlled Less than 60 m 2.5 m above the top of gates
Controlled Over 60 m 3 m above the top of the
gates
2- FREE BOARDThe U.S.B.R. suggests the following free boards:
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Type of material Upstream
slope
Downstream slope
(i) Homogeneous well graded
material
2 : 1 2 : 1
(ii) Homogeneous coarse silt 3 : 1 2 .5: 1
(iii) Homogeneous silty clay, or clay
H less than 15 m
H more than 15 m
2 .5 : 1
3 : 1
2 : 1
2 .5 :1
(iv) Sand or sand and gravel with
clay core
3 : 1 2 .5 : 1
(v) Sand or sand and gravel with
R.C. core wall
2 .5 :1 2 : 1
SIDE SLOPES FOR EARTH DAMS ACCORDING TO TERZAGHI
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Height of
dam above
foundation
level (m)
Height of
dam above
H.F.I. (m)
Top width
(m)
U/S
slope
D/S
slope
Up to 4.5 1.2 to 1.5 1.8 1 : 1 1 .5 : 1
4.5 to 7.5 1.5 to 1.8 1.85 2 .5 : 1 1 .75 : 1
7.5 to 15 1.85 2.5 3 : 1 2 : 1
15 to 22.5 2.1 3.0 3 : 1 2 : 1
PRELIMINARY DIMENSIONS OF EARTH DAMS ACCORDING TO STRANGE
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Cutoff Trench. Cutoff is required to:(a) reduce loss of stored water through foundation and abutments,
(b) prevent sub-surface erosion by piping.
Notes:
(i) The alignment of the cutoff trench should be fixed in such a
way that its central line should be within the u/s base of the
impervious core and it should be keyed into rock or continuous
impervious strata.
(ii ) The bottom width of cutoff trench may be fixed taking
following factors into consideration :
(a) Provide sufficient working space for compaction equipment,
(b) Provide sufficient working space to carry out curtain grouting,
(c) Provide safety against piping.
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A minimum width of 4 m is recommended. A bottom width of 10 % of hydraulic
head may be provided for safety requirements of piping. This may be suitably
increased to satisfy other requirements of mechanical equipments and curtain
grouting. The side slopes depend upon sub-strata. Side slopes of at least 1 : 1
or flatter may be provided in case of overburden, while 1/2 and 1/4 : 1 may be
provided in soft rock and hard rock respectively.
(iii) The positive cutoff should be taken at least one meter into continuous
impervious substratum.
(iv) The partial cutoff is specially suited for horizontally stratified foundations
with relatively more pervious layer near lop. The depth of the partial cutoff in
deep pervious alluvium will be
governed by :
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(a) Permeability of substrata, and
(b) relative economics of depth of excavation governed
usually by cost of dewatering versus length of u/s impervious
blanket.
(v) The backfill material for cutoff trench shall have same
properties as those prescribed for impervious core.
(vi) The cutoff in the flanks on either side should normally
extend up to the top of the impervious core, particularly in
case of steep abutments.
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SEEPAGE ANALYSIS:(PHREATIC UNE IN EARTH DAM)
Casagrande assumed the phreatic line to be a base parabola with its focus at
F, the starting point of the filter FE. The following is the procedure for locating
the phreatic line graphically by using CASAGRANDEβS METHOD OF
DETERMINING PHREATIC LINE IN A DAM WITH HORIZONTAL DRAINAGE
FILTER:
1. AB is the upstream face. Let its horizontal projection be L. On the water
surface, measure the distance BC=0 3 L. Then the point C is the starting point
of the base parabola.
2. To locate the position of the directrix of the parabola, we utilize the principle
that any point on the parabola is equidistant from the focus as well as directrix.
Hence with the point C as the centre, and CF as the radius, draw an arc to cut
the horizontal line through CB in D. Draw a vertical tangent to the curve FD at
D. Evidently, CD=CF. Hence the vertical line DH is the directrix.
3. The last point G on the parabola will evidently lie midway between F and H.
4. In order to locate the intermediate points on the parabola we use the
principle that its distances from focus and directrix must be equal. For
example, to locate any point P, draw vertical line QP at any distance x from F.
Measure the distance QH. With F as the center and QH as the radius, draw an
arc to cut the vertical line through Q in point P.
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as the centre and QH as the radius, draw an arc to cut the vertical line
through Q in point P.
5. Join all these points to get the base parabola. However, correction is to
be made at the entry point. The phreatic line must start from B, and not
from C. Also the phreatic line is a flow line, and must start perpendicularly
to the u/s face AB which is a 100 % equipotential line. Hence the portion of
the phreatic line at B is sketched free hand in such a way that it starts
perpendicularly to AB, and meets the rest of the parabola tangentially
without any link. The base parabola should also meet the d/s filter
perpendicularly (vertically) at G.
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q = k Γ i Γ A
π =ππ¦
ππ₯(y= saturated depth), A = y = 1m
For q:
π = π Γππ¦
ππ₯Γ π¦
= π Γd S2 + 2SX 0.5
dx
= π Γ 0.5 Γ π2 + 2ππ Γ 0.5 Γ 2π Γ (π2 + 2ππ) Γ 0.5
= π Γ π Ξ€π2 π ππ almost for horizontal filters
π = π Γ π Γ πΏ
CRITERIA FOR SAFE DESIGN OF EARTH DAMAn 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) The embankment must be safe against overtopping during occurrence
of the inflow design flood by the provision of sufficient spillway and outlet
works capacity.
(2) The dam must have sufficient free board so that it is not overtopped by
wave action.
(3) The seepage line should be well within the d/s face so that no sloughing
of the slope takes place.
(4) Seepage flow through the embankment, foundation and abutments must
be controlled by suitable design provisions so that no internal erosion takes
place. The amount of water lost through seepage must be controlled so that
it does not interfere with planned project functions.
(5) There should be no opportunity for the free passage of water from
upstream to the downstream either through the dam or through the
foundation.
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(6) The portion of the downstream of the impervious core should be properly
drained.
(7) The upstream and downstream slopes should be so designed that they
are safe during and immediately after the construction.
(8) The downstream slope should be so designed that it is safe during steady
seepage case under full reservoir condition.
(9) The upstream slope should be stable during rapid drawdown condition.
(10) The upstream and downstream slopes of the dam should be flat enough
so that shear stress induced in the foundation is enough less than the shear
strength of the material in the foundation to ensure a suitable factor of safety.
(11) The dam as a whole should be earthquake resistant.
(12) The upstream slope must be protected against erosion by wave action,
and the crest and down stream slope must be protected against erosion due
to wind and rain. The above criteria of design have been covered at length in
the subsequent articles.
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DOWNSTREAM DRAINAGE SYSTEM
(1) It reduces the pore water pressure in the downstream portion
of the dam, and hence increases its stability.
(2) It checks the piping by checking the migration of the particles.
(i) Toe drains Fig. (a)
(ii) Horizontal blanket drains Fig. (b)
(iii) Chimney drains Fig. (c)
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Toe drain
Horizontal blanket drain
Chimney drain
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Graphical general solution:Cassagrande has given a general solution to
evaluate ππ for various inclinations of discharge face. Let a be the angle
which the discharge face makes with the horizontal. The various values
ofπ«π
π+π«πhave been given by cassagrande, as shown in table .
πΆ in degrees βπ
π + βπ
Remarks
πππ
πππ
πππ
ππππ
ππππ
ππππ
ππππ
0.36
0.32
0.26
0.18
0.14
0.10
0.0
Note: Intermediate
values can be
interpolated, or read out
from a graph between Ξ±
andβπ
π+βπplotted with the
values given here.
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(π + βπ)is the distance FJ (i.e. the distance of the focus from the point where the
parabola cuts the d/s face) and is known.(βπ)can then be evaluated. (π) and (βa)
can be connected by general equation.
βπ = (π + βπ)180π β πΌ
400π
B) Analytical solutions for determining the position of point k, i.e. the point at
which the seepage line intersects the d/s slope.
Case (a) when Ξ± <πππ
Schaffernak and van Iterson have derived an equation for determining the value
of βaβ (and thus fixing the position of point K) in terms of H, bβ and Ξ±. Their final
equation is
π =πβ²
cos πΌβ
πβ²2
πππ 2πΌβ
π»2
π ππ2πΌ
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Case (b) when Ξ± lies between πππ and πππ
Cassagrande has derived an equation for determining the value of βaβ in term of b, H and Ξ±.
His final equation is:
π = π2 β π»2 β π2 β π»2πππ‘2πΌ
Where b is defined in figure.
H is the head causing flow and Ξ± is the angle which the d/s face makeswith the horizontal
(clockwise) as defined earlier
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Since PF = QH
β΄ x2 + y2 = QF + FH = X + S β¦(i)
Where: S = FH = focal distance
From (i): π2 + π2 = π2 + π2 + 2ππ
X =Y2β S2
2S
Or π2 = 2ππ + π2
This is the equation of the base parabola.
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In order to get an expression for the discharge q through the body of the dam for
the present case of horizontal filter, we observe that, through the vertical section
PQ:
π = π Γ π Γ π΄ = π Γππ¦
ππ₯Γ (π¦ Γ 1) β¦(ii)
But from equation (ii),
π¦ = (2ππ + π2) Ξ€1 2β¦(iii)
β΄πy
πx=
π
(2xs+s2)1/2
Substituting in (iii), we get:
q = k π = π Γπ
(2π₯π +π 2)1/2Γ (2ππ + π2) Ξ€1 2
π = π Γ π
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This is very simple expression for discharge q in terms of focal distance S. The
distance S can either be determined graphically , or can be calculated analytically
by considering coordinates of point C, as follows:
From (i) π = ππ + ππ β π
At C, X=D and y = H
β΄ πΊ = π«π +π―π β π«
Hence π = π Γ π = π Γ π«π +π―π β π«
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From the drawing, it can be found that the line will
cut the D/S face of the dam at the point (J)
coordinates (8.39m, 4.195m) J and away from the
point F on the face amount of the backside distance
a + Ξa = 9.38m
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Y = β0.98 + 1.98X(m)X (m)No. of point
0.9901
3.3052
4.56103
5.54154
6.37205
7.24266
7.77307
8.02328
8.38359
9.074110
9.494511
10.005012
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This distance must be adjusted in fact, a distance of Ξa to face down the
backside as we mentioned previously, from the following equation: -
400βa = (a+βa) (180 β Ξ±)
Ξ± = tan-1 (Β½) = 26.565ΒΊ
To find the co-ordinates of the point of the new (K) can follow the following
method: -
Given the shape use theory of a right-angled triangle: -
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