𝑫 𝒊 𝑯 𝒂 𝒊 𝑺 part 2 earth dams design

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

𝑫𝒆𝒔𝒊𝒈𝒏 𝒐𝒇 𝑯𝒚𝒅𝒓𝒂𝒖𝒍𝒊𝒄 𝑺𝒕𝒓𝒖𝒄𝒕𝒖𝒓𝒆𝒔Part 2

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Earth Dams:• They are trapezoidal in shape

• 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.

• Earthen dams are relatively smaller in height and broad at the base

• 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 – Rolled fill method:

- Soil is prepared at certain moisture content.

- Put into layers (15 – 30) cm .

- Pressed by rollers having adequate weights .

Methods of construction of Earth Dams:

1 – 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 – 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 – berms -

grass)Seepage failure is due to:

1. Uncontrolled seepage (causes scour through DS wet zone – needs

adequate filters)

2. Piping (through dam foundation – either prevention or control of

percolation…may cause dam subsidence)

Structural failure is due to:

1. Foundation slide by soft soil (fine silt – soft clay, …all dam body

slides on foundation)

2. Slide of slopes (US or DS slopes)

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 CASAGRANDE’S 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 × i × A

𝑖 =𝑑𝑦

𝑑𝑥(y= saturated depth), A = y = 1m

For q:

𝑞 = 𝑘 ×𝑑𝑦

𝑑𝑥× 𝑦

= 𝑘 ×d S2 + 2SX 0.5

dx

= 𝑘 × 0.5 × 𝑆2 + 2𝑆𝑋 × 0.5 × 2𝑆 × (𝑆2 + 2𝑆𝑋) × 0.5

= 𝑘 × 𝑆 Τ𝑚2 𝑠𝑒𝑐 almost for horizontal filters

𝑄 = 𝑘 × 𝑆 × 𝐿

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 𝜟𝒂 for various inclinations of discharge face. Let a be the angle

which the discharge face makes with the horizontal. The various values

of𝚫𝐚

𝐚+𝚫𝐚have been given by cassagrande, as shown in table .

𝜶 in degrees ∆𝒂

𝒂 + ∆𝒂

Remarks

𝟑𝟎𝒐

𝟔𝟎𝒐

𝟗𝟎𝒐

𝟏𝟐𝟎𝒐

𝟏𝟑𝟓𝒐

𝟏𝟓𝟎𝒐

𝟏𝟖𝟎𝒐

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 α

and∆𝑎

𝑎+∆𝑎plotted with the

values given here.

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(𝑎 + ∆𝑎)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.(∆𝑎)can then be evaluated. (𝑎) and (∆a)

can be connected by general equation.

∆𝑎 = (𝑎 + ∆𝑎)180𝑜 − 𝛼

400𝑜

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 α <𝟑𝟎𝒐

Schaffernak and van Iterson have derived an equation for determining the value

of ‘a’ (and thus fixing the position of point K) in terms of H, b’ and α. Their final

equation is

𝑎 =𝑏′

cos 𝛼−

𝑏′2

𝑐𝑜𝑠2𝛼−

𝐻2

𝑠𝑖𝑛2𝛼

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Case (b) when α lies between 𝟑𝟎𝒐 and 𝟔𝟎𝒐

Cassagrande has derived an equation for determining the value of ‘a’ in term of b, H and α.

His final equation is:

𝑎 = 𝑏2 − 𝐻2 − 𝑏2 − 𝐻2𝑐𝑜𝑡2𝛼

Where b is defined in figure.

H is the head causing flow and α is the angle which the d/s face makeswith the horizontal

(clockwise) as defined earlier

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Since PF = QH

∴ x2 + y2 = QF + FH = X + S …(i)

Where: S = FH = focal distance

From (i): 𝑋2 + 𝑌2 = 𝑋2 + 𝑆2 + 2𝑋𝑆

X =Y2− S2

2S

Or 𝑌2 = 2𝑋𝑆 + 𝑆2

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:

𝑞 = 𝑘 × 𝑖 × 𝐴 = 𝑘 ×𝜕𝑦

𝜕𝑥× (𝑦 × 1) …(ii)

But from equation (ii),

𝑦 = (2𝑋𝑆 + 𝑆2) Τ1 2…(iii)

∴𝜕y

𝜕x=

𝑠

(2xs+s2)1/2

Substituting in (iii), we get:

q = k 𝑞 = 𝑘 ×𝑠

(2𝑥𝑠+𝑠2)1/2× (2𝑋𝑆 + 𝑆2) Τ1 2

𝒒 = 𝒌 × 𝒔

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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) 𝒔 = 𝒙𝟐 + 𝒚𝟐 − 𝒙

At C, X=D and y = H

∴ 𝑺 = 𝑫𝟐 +𝑯𝟐 − 𝑫

Hence 𝒒 = 𝒌 × 𝒔 = 𝒌 × 𝑫𝟐 +𝑯𝟐 − 𝑫

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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 + Δa = 9.38m

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Y = √0.98 + 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 Δa to face down the

backside as we mentioned previously, from the following equation: -

400∆a = (a+∆a) (180 – α)

α = tan-1 (½) = 26.565º

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: -

𝑫 𝒊 𝑯 𝒂 𝒊 𝑺 part 2 earth dams design

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