EMBANKMENT DAMS

(Nurek earth and Rockfill dam, Tajikistan)

Contents

1) Introduction

2) Types of embankments dams

3) Causes of Failure

4) Design considerations

5) Seepage analysis and control

6) Stability analysis

7) Construction techniques

1) INTRODUCTION

• Most ancient type of embankments

• Can easily be constructed on earth foundations

• More susceptible to failure as compared to gravity dams

Hirakund dam (Composite structure of earth, concrete and masonry.)

4.8 Km long 60.0 m River Mahanadi Orrisa

Beas Dam or Pong Dam 133 m on the river Beas

Ramganga Dam (1962) 125.5 m Near Kalagarh, earth and rockfill

Tehri Dam 260.0 m, Earth and Rockfill

Narek Dam 300.0 m Earth dam built in late 1970s on the Vaksh river

Narek, Tajiskistan

SOME OF THE EMBANKMENT DAMS

2a) TYPES OF EARTHEN EMBANKMENT DAMS

1. Homogeneous dam

• constructed of a single material

• slope pitching is provided

• Such dams are of moderate and low heights

• Drainage filter is provided to arrest the phreatic line

(a) Homogenous earthen dam

with toe drain

(b) Homogenous earthen dam

with horizontal blanket

(c) Homogenous earthen dam

with inclined chimney connected

to horizontal blanket

2. Zoned embankment type

• Provided with a central impervious core which control the seepage

• Filter controls the piping action

• Outer zone gives stability to the central zone

• Pure clay is not suitable for core due to shrinkage and swelling

properties of pure clay. However, clay mixed with fine sand or fine gravel

are suitable.

• Silts or silty clays used as the satisfactorily central core material

• Freely draining materials such as coarse sands and gravels are used in

outer shell

(a) Zoned dam with central vertical clay

core and toe drain

(b) Clay core zoned dam with central

vertical core and chimney filter with

horizontal blanket

(c) Inclined clay core zoned dam with

chimney filter with horizontal blanket

3. Diaphragm type embankments

• Have a thin impervious core, which is surrounded by earth or rock fill

• Diaphragm made of impervious soil, cement, steel, timber etc. – control

seepage and tied to the bed rock or to a very impervious foundation

• If the thickness of the diaphragm at any elevation is less 10 m or less

than the height of the embankment above the corresponding elevation,

the dam is called diaphragm type.

2b) TYPES OF ROCKFILL EMBANKMENT DAMS

1. Central vertical clay core

2. Inclined clay core with drains

3. Decked with asphalt or concrete membrane on upstream face with drains

(a) Rock-fill dam with vertical clay core,

chimney filter and horizontal blanket

(b) Rock-fill dam with inclined clay core,

chimney drain and horizontal blanket

(c) Decked rock-fill dam with upstream

asphaltic or concrete membrane with

chimney drain and horizontal blanket.

The phreatic line is for the small

amount of water that leaks through

the cracks of the upstream membrane

3) CAUSES OF FAILURE OF EARTH DAMS

1. Hydraulic failures

2. Seepage failures, and

3. Structural failures

(i) Hydraulic Failures

(a) Overtopping of dam resulting in washout

- sufficient free board is required

(b) Erosion of upstream face by waves

breaking on the surface

- Stone pitching or riprap should be provided

(c) Cracking due to frost action

- frost in the upper portion of dam cause heaving and cracking of soil

- additional free board of the order of 1.5 m be provided

(e) Erosion of downstream toe

-Erosion due to cross-currents from

spillway-controlled by side walls of

spillway

- erosion due to tail water – controlled

by providing stone pitching or riprap

upto the height of tail water depth

(d) Erosion of downstream face by

impact of rain and resulting sheet flow –

gully erosion

- Controlled by filling the cuts, grassing

the slopes, providing proper berms

(ii) Seepage Failures

(a) Piping through foundations

due to highly permeable cavities or

fissures or strata of coarse sand or

gravel

(b) Piping through dam

flow channels develop due to faulty construction, insufficient

compaction, cracks developed in embankment due to

foundation settlement, shrinkage cracks, animal burrows etc.

(c) Seepage by the outer surface

of conduit, may lead to

progressive piping

(d) Sloughing of downstream toe

due to saturation of soil (pore

water pressure)

(iii) Structural Failures

(a) Foundation slide

due to weak foundation like soft soil

such as fine silt, soft clay etc.

Failure of upstream slope caused by

failure of foundation

Failure of downstream slope caused by

failure of foundation

(b) Failure of upstream face due to

sudden drawdown

(c) Failure of downstream face during

full reservoir operation also being

steep

(c) Excessive settlement of dam

foundation

4) DESIGN CONSIDERATIONS

(A) Free Board

(B) Top Width

(C) Upstream and Downstream Slopes

(D) Suitability of Soils for Construction of Earth Dams

(E) Design of Filters

(F) Slope Protection

(G) Seepage Control

(A) FREE BOARD

(distance between max. Reservoir level and top of he dam)

(i) Wave height by Moliter equation

Free board = 1.5 hw

(km/hr) velocity Wind (km); Fetch(m);

km 32 for F 032.0

km 32 for F 271.0763.0032.0 4/1

VFh

VFh

FVFh

w

w

w

(ii) US BUREAU OF RECLAMATION (USBR) Recommendations

Spillway type dam height Min. free board above MWL

Uncontrolled Any height 2-3 m

Controlled < 60 m 2.5 m above top of gate

Controlled > 60 m 3.0 m above top of gate

Additional 1.5 m for frost action.

(iii) Saville method (IS 10635: 1993)

Normal free board = Free board above the FRL

Minimum free board = Free board above the MWL

Procedure for Computation of Normal Free Board

(1) Effective Fetch

Draw a line AB with A on dam axis and B on FRL so as to cover the maximum

reservoir water spread area within 450 on either side of line AB

Draw 7 radials at 60 interval on each side of AB

Effective Fetch

cos

cosXFe

(2) Compute wind velocity on water

Read wind velocity on land from IS 875 for 50 year return period for the region

Wind velocity on water = αv × wind velocity on land

Fe (km) αv

1 1.1

2 1.16

4 1.24

6 1.27

8 1.30

>10 1.31

(3) Compute wave height

(m) (s); (m/s); (m); (m);

56.1

length wave

45.0

period waveand

0026.0

2

0.25

2

0.47

22

LTVFeh

TL

V

gF

V

gT

T

V

gF

V

gh

w

e

ew

Design wave height, hd = 1.67 hw

(4) Compute wave run up R on smooth surface from the following chart

correspond to L

R/h

d

Type of Pitching Roughness coefficient

Cement concrete surface 1.0

Flexible brick pitching 0.8

Hand place riprap

Laid flat 0.75

Laid with projection 0.60

Dumped riprap 0.50

Run up on rough surface = Run up on smooth surface × roughness coefficient

If corrected R < hd; adopt R = hd

Wave run up on the rough surface

(5) Wind set up computation

Wind set-up is the result of piling up of the water on one end of the reservoir on account

of the horizontal driving force of the blowing wind.

D

FSWind

62000

V upset

2

S (m); V (km/h); F(km); D(m)=Average depth of water along fetch length F

Free board = R+S

If free board < 2 m; adopt 2m

Top of dam = FRL+ Normal free board

Minimum Free Board at MWL

• Calculate effective fetch at MWL

• Consider ½ to 2/3 wind velocity on land for computation of hw

• Take hd = 1.27 hw

• Minimum free board => 1.5 m

(B) TOP WIDTH

Top width, A > 3 m

A =H/3+3 for low dams 15-20 m height (USBR)

)();(

36.3

Code Japanese

H3.6 A

m 150 for H USBR

3/1

1/3

mHmA

HA

unit SI Use 1.5H1.65 A

m 30 For H

2.0 H0.55 A

m 30 For H

1/3

1/2

H

H = height of dam (m) above stream bed

(C) UPSTREAM AND D/S SLOPES (Terzaghi’s Side slopes)

Types of material U/s (H:V) D/s (H:V)

Homogeneous well graded 2.5:1 2:1

Homogeneous coarse silt 3:1 2.5:1

Homogeneous silt clay

(a) H < 15 m 2.5:1 2:1

(b) H > 15 m 3:1 2.5:1

Sand or sand and gravel with a central clay core 3:1 2.5:1

Sand or sand and gravel with a RC diaphragm 2.5:1 2:1

G = Gravel; W = well graded; P = Poorly graded; C = clay; S = Sand

M = silt; O = Organic; Pt = highly organic soil; H = high compressibility;

I = Medium Compressibility; L= low compressibility

(D) SUITABILITY OF SOILS FOR CONSTRUCTION OF EARTH DAMS

(E) DESIGN OF FILTERS (IS Code 9429-1999)

The filter material used for drainage system shall satisfy the following criteria:

• Filter materials shall be more pervious than the base materials;

• Filter materials shall be of such gradation that particles of base material

do not totally migrate through to clog the voids in filter material; and

• Filter material should help in formation of natural graded layers in the

zone of base soil adjacent to the filter by readjustment of the particles

Determination of Gradation of base material

Category Percentage finer than 75 micron

1 > 85%

2 40-85%

3 15-39%

4 < 15%

Note: Wherever the base soil in categories 1, 2 and 3 contains particles larger than 4.75

mm, the percentage of particles passing 4.75 mm shall be adjusted to 100 percent.

(a) Minimum D15 (f)

D15 (f) 5D15 (b) 0.1mm

(b) Maximum D15 (f)

D15 (f) should not be less than 0.2mm

Base soil category Criteria

1 D15 (f) ≤ 9D85 (b)

≥ 0.2mm

2 D15 (f) ≤ 0.7 mm

3 D15 (f) ≤ (40-A)/(40-15)*(4D85 (b)-0.7 mm)+0.7 mm

4 D15 (f) ≤ 4D85 (b)

A is the percent passing the 75 micron sieve after re-grading

(c) To minimize segregation, filters should have relatively uniform grading. D90

(f) should be less than 20 mm- to minimize segregation. Limit of D10(f) and

D90(f) are given below

D10 (f) (min) mm D90 (f) max (mm)

< 0.5 20

0.5-1.0 25

1.0-2.0 30

2.0-5.0 40

5.0-10 50

10-50 60

Filters should have a maximum particle size of 75 mm. Material passing the

75 micron sieve shall not exceed 5 percent.

Example (Two layer of filters)

FINE FILTER

Particle size gradation of base material is given below:

As size of material is more than 4.75 mm, it is re-graded by a factor 100/88)

From the particle size distribution graph

D15(b) = 0.0022 mm;

D85(b) = 1.5 mm

Fine Filter

Percentage finer than 75 micron is 33%, thus the category of base material is III

Minimum D15 (f)

D15 (f) 5D15 (b)=5*0.0022=0.011 which is less than 0.1mm

Adopt D15 (f) = 0.1 mm

Maximum D15 (f)

A = 33%

D15 (f) ≤ (40-33)/(40-15)*(4*1.5-0.7+0.7

= 2.2 mm which is greater than 0.2 mm OK

Adopt maximum particle size of 75 mm and material passing the 75 micron

sieve =5 %

From the graph

Lower limit D10(f) = 0.09 mm correspondingly D90(f) = 20 mm

Upper limit D10(f) = 0.5 mm correspondingly D90(f) = 25 mm

However, the available material is in the range of curve 5 & 6, as shown in the graph.

Percentage finer than 75 micron is less than 15%, thus the category of base

material is IV

Minimum D15 (f) – based on upper limit of fine filter (Curve 6)

D15 (f) 5D15 (b)=5*1=5 mm which in more than 0.1 mm

Adopt D15 (f) = 5 mm

Maximum D15 (f) - based on lower limit of fine filter (Curve 5)

D15 (f) ≤4D85(b)=4*3=12 mm which is greater than 0.2 mm OK

Adopt maximum particle size of 75 mm and material passing the 75 micron

sieve =5 %

From the graph

Lower limit D10(f) = 1 mm correspondingly D90(f) = 30 mm

Upper limit D10(f) = 1 mm correspondingly D90(f) = 30 mm

COARSE FILTER

Coarse Filter

DESIGN OF FILTER

IS Code 9429-1980

(i) D15 of filter/D85 of base < 5

(ii) 4 < D15 of filter/D15 of base < 20

(iii) D50 of filter/D50 of base < 25

(iv) Gradation curve of filter should be nearly parallel to the gradation curve of

base material

0

10

20

30

40

50

60

70

80

90

0.01 0.1 1 10 100 1000

Perc

enta

ge f

iner

Grain size (mm)

Base material F1 F2

Sand layer filter (F1)

d15 = 0.78 mm

d50 = 1.90 mm

d85 = 3.91 mm

Gravel layer filter (F2)

d15 = 8.75 mm

d50 = 21.24 mm

d85 = 43.74 mm

Base material (B)

d15 = 0.07 mm

d50 = 0.17 mm

d85 = 0.35 mm

Example

(F) SLOPE PROTECTION

(a) PROTECTION OF UPSTREAM SLOPE

Upstream protection is required against the wave action. The dumped rock

riprap is preferred type of protection.

DUMPED STONE RIPRAP (Singh & Varhney 2004)

Design of the dumped stone riprap is related to the criteria for the selection of

rock size and thickness of the rip rap layer directly to the design wave height.

(a) For embankment slopes 2:1 to 4:1 dumped riprap shall meet the following

criteria:

Placing riprap with hydraulic excavators

(Hand-placed riprap)

(b) Riprap shall be well graded from a maximum size at least 1.5 times the

average rock size to 2.5 cm spalls suitable to fill voids.

(c) Rip rap blanket shall extend to at least 2.4 m below the lowest low water.

(d) Filter shall be provided between the riprap and embankment to meet the

following criteria:

No filter is required if embankment material meets the above requirements for

the D85 size.

Thickness of riprap layer should be at least 1.5 times the size of the average

(D50) rock of weight W50.

HAND PLACED RIPRAP – labor cost high, now rarely being used

SOIL-CEMENT SLOPE PROTECTION

• Provided, if suitable rock for riprap is unavailable at the site.

• Consisted of a series of approximately horizontal layers of soil-cement

compacted in stair-step fashion up the embankment slope. The layer is

usually 2 to 3 m wide, compacted 15 cm vertical thickness.

• The most efficient construction 100 % of the soil should pass the 50 mm

sieve, at least 55% should pass the 4.75 mm sieve and between 5 and 35 %

should pass the 75 micron sieve.

• The cement content varies from about 7 to 15 % by volume of soil-cement.

2 to 3 m

Thickness 15 cm

U/s face of dam

(b) PROTECTION OF DOWNSTREAM SLOPE

Needed against erosion by rain-water and sometimes by wind also. If d/s

slope is rock – no protection required.

Turfing is provided.

Horizontal drain be provided at suitable interval and be joined with vertical

drain

5a) SEEPAGE THEORY

EquationLaplace--- 0

; 0 equation Continuity

;

Kh soil isotropicfor

;

2

2

2

2

y

h

x

h

y

v

x

u

y

hKv

x

hKu

yv

xu

x

y

y

y

yx

Ky

h

x

h

K

y

h

x

h

K

y

hK

x

h

y

v

x

u

y

hKv

x

hKu

y

2

2

2

2

x

2

2

2

2

x

2

2

2

2

x

Kxx' ----- 0

'

yieldsK

x'x of nSubsitutio

(1) 0 K

0 K

; 0 equation Continuity

;

soil isentropicfor

(a) Seepage through isotropic soil

f

d

yx

y

f

d

f

d

d

N N

HKKq

Kxx' x'-y with scale on dam draw the -

soil isentropicFor

N N

HK

qqflow seepage Total

channelsflow ofNumber N

drop ofNumber N

N

HK

y) (asH Kyx

HKKiAq AB, acrossflow

xK

x

(b) Seepage through isentropic soil

(2) Eq.from discharge seeepage thecompute andflownet draw the then

Kxx' x'-y with scale on dam draw the soil, isentropicfor Thus

(2) N N

HKKq

H

y)' (asy K

x'

H

Kxx' asy

x

Hq AB, acrossflow

y

f

d

yx

x

y

x

d

yx

y

x

x

x

K

NKK

x

K

K

KK

Phreatic lines in earth dams

Determination of phreatic line is required for

(a) Drawing flow net

(b) Estimating pore pressure

(c) Determination of saturation of downstream slope etc.

(a) For homogeneous dam with a horizontal filter

Shape of phreatic line is parabolic except near its junction with the upstream face

Casagrande AB=0.3HB

y

bHbS

SbHb

Sxyx

SFD

FDxyx

dx

dy K

KiAq

flow Seepage

Apoint At

directrix tofocus from distance length focal ,

22

22

22

22

KSq

SxSSxS

SKq

SxS

SS

SxS

SxSxSxy

2

2

22

222

22

22

2

1

2

1

dx

dy

2 as

(b) For homogeneous dam without filter

• Focal point F is located at the lowest point of downstream slope

• Portion KF is discharge face and shall be fully saturated

Casagrande general graphical solution

Angle of discharge face

(degree)

30 0.36

60 0.32

90 0.26

120 0.18

135 0.14

150 0.10

180 0

aa

a

400

180 aaaMay also be calculated by

known thusequation,parabola from known is aaa

(a) > 900

(b) = 1800

a =0

a

C

Directrix

a+a =S-(a+a)cos(180-)

a+a=S/(1-cos )

D

Directrix

(c) = 900

5b) SEEPAGE CONTROL MEASURES IN EMBANKMENT

DAM AND FOUNDATION

Basic requirements for the design of an earth or rockfill dam is to ensure safety

against internal erosion, piping and excessive pore pressure in the dam.

The seepage of reservoir water through the body of the dam or at the

interfaces of the dam with the foundation or abutment creates two main

problems, apart from causing excessive water loss and thereby reducing

usable storage of reservoir:

1. Seepage force causing excessive water loss

2. Piping

Seepage control and drainage features - adopted for the embankment

dam

Impervious core

Inclined/vertical filter with horizontal filter

Network of inner longitudinal drain and cross drains

Horizontal filter

Transition zones/transition filters

Intermediate filters

Rock toe

Toe drain

Relief wells

Upstream Impervious Blanket

Section of homogenous dam showing seepage control features

Section of zoned dam showing seepage control features

Inclined/Vertical Filter

Inclined or vertical filter abutting downstream face of either impervious core or

downstream transition zone is provided to collect seepage emerging out of

core/transition zone and thereby keeping the downstream shell relatively dry.

Horizontal Filter

It collects the seepage from the inclined/vertical filter or from the body of the dam,

in the absence of inclined/vertical filter, and carries it to toe drain.

The horizontal filter may extend from 25 to 100% of the distance from d/s toe to

the centre line of the dam. From practical considerations, a minimum

thickness of 1.0 m is desirable.

Graded filter be provided.

Inner Longitudinal and Inner Cross Drains

When the filter material is not available in the required quantity at reasonable cost,

a network of inner longitudinal and inner cross drains is preferred to

inclined/vertical filters and horizontal filters. This type of drainage feature is

generally adopted for small dams, where the quantity of seepage to be drained

away is comparatively small.

Transition Zones and Transition Filters

Transition zones/filters in earth and rockfill dams in the upstream and

downstream shells are necessary, when the specified gradation criterion is not

satisfied between two adjacent zones. They help to minimize failure by internal

piping, cracking, etc, that may develop in the core or by migration of fines from

the core material.

The filter material used for drainage system shall satisfy the following criteria:

a) Filter materials shall be more pervious than the base materials;

b) Filter materials shall be of such gradation that particles of base material do

not totally migrate through to clog the voids in filter material; and

c) Filter material should help in formation of natural graded layers in the zone

of base soil adjacent to the filter by readjustment of particles.

Horizontal Filters at Intermediate Levels

Horizontal filter layers at intermediate levels are sometimes provided in

upstream and downstream shells, to reduce pore pressures during

construction and sudden drawdown condition and also after prolonged

rainfall.

These filter layers should not be connected with inclined or vertical filters. A

minimum space of 2.0 m or more, should be kept between the face of

inclined/vertical filter and downstream intermediate filter

Horizontal intermediate filters

Rock Toe

The principal function of the rock toe is to provide drainage. It also protects the

lower part of the downstream slope of an earth dam from tail water erosion.

The top level of the rock toe/pitching should be kept above the maximum tail

water level (TWL). In the reach where the ground level at the dam toe is above

the maximum tail water level, only conventional pitching should be adopted.

The top of such pitching should be kept 1.0 m above the top of horizontal filter,

or stripped level, whichever is higher.

Details of rock toe/pitching protection and toe drains are illustrated for various

combination of Tail Water Level (TWL) and stripped Ground Level (SGL).

1. Rock toe when TWL is higher than SGL

2. Pitching when TWL is higher than SGL

3. Rock toe + pitching when TWL is higher than rock toe

4. Pitching when SGL is above TWL

5. Pitching and lined toe drain

Height of rock toe is generally 30 to 40% of the reservoir head and gradation

of material should satisfy the filter criteria.

Toe Drain

Toe drain is provided at the downstream toe of the earth/rockfill dam to collect

seepage from the horizontal filter or inner cross drains, through the foundation as

well as the rain water falling on the face of the dam.

Closed toe drain

TWL

Relief Wells

To reduce the sub-stratum

uplift pressure d/s of the dam

to avoid boiling of sand and

piping

Generally spacing of well is

15 m c/c.

The well screen consists of

GI pipe of 10-15 cm dia.

Slotted with 5 mm to 50 mm

opening and covering about

10% circumference area of

the pipe.

Filter should meet the filter

criteria discussed earlier.

D85 filter > hole diameter

A typical relief well (all dimensions are in mm)

Positive Cut-off Trench

The positive cut-off trench consists of an impervious fill placed in a trench formed

by open excavation into an impervious stratum. Grouting of the contact zone of

the fill and the underlying strata constitutes an integral part of the positive cut-off.

Concrete Diaphragm

A single diaphragm or a double diaphragm may also be used for seepage

control.

Complete Partial

Grout Curtain

• Grouted cut-offs are produced by injection, within the zone assigned to the

cut-off, of the voids of the sediments with cement, clay, chemicals, or a

combination of these materials.

• Reduce permeability

• Approximate range of grain sizes that can be normally be grouted by different

types of grout material and mixture.

Types of grout Dia. of the material (mm) that can be grouted

Cement 0.5 - 1.4

Clay, cement, bentonite 0.3 – 0.5

Clay-chemical, bentonite chemical 0.2 - 0.4

Chemical 0.1 – 0.2

• Blanket grouting is done to a depth of 5-10 m through holes at spacing 3-5 m

• Curtain grouting is done to higher depth

Sheet Pile Cut-offs

Used in silty, sandy and fine gravel foundation, difficult to drive pile in boulders

Grout curtain

Upstream Impervious Blanket

Upstream impervious blanket is provided when a positive cut-off is too expensive.

Thickness 0.6 to 3 m. Effective control of exit gradients can generally be achieved

by a blanket length of about 5 times the head, combined with relief wells and

drainage trenches.

(A) Completely impervious blanket

f

d

f Zx

Hkq

Without blanket

f

d

f ZxL

Hkpq

With blanket

Substituting first Eq. into the second yield

dxp

pL

1

(B) Blanket for finite permeability (Bennet’s solution)

Total discharge qf at distance x from downstream end of blanket

dxZ

hkqdqqq

x

L b

bof

xL

Lboff

dxZ

hkdq

b

bb

Discharge through blanket of thickness Zb in elemental distance dx

x

hadx

hd

ZZk

kha

Z

h

Zk

k

dx

hd

Z

hk

dx

hdZk

dx

dq

Zdx

dhkqfoundationthefor

Z

hk

dx

dq

dx

dqAs

dxZ

hk

dx

d

dx

dq

dx

dq

bff

b

bff

b

b

bff

f

fff

b

b

f

fo

b

x

Lb

fof

2

2

2

22

2

2

2

2

a where

0

Bennet’s basic differential equation for a blanket of

finite permeability and constant thickness

o

ax

0

hh ;0t

ehh

blanket of length Infinite

xA ( x=0 at downstream of blanket) 0h ;t xA

(i)

b

bff

r

ax

r

f

r

ffff

k

ZZk

ax

aheahx

h

dx

dhAs

Zx

hkZ

dx

dhkq

1

i.e, blanket, infinite theas

discharge same thepasses which,x is imperviouscompletly equivalent of length Let the

0

r

Discharge Reduction (1-p)

Without blanket

With blanket

f

d

f Zx

Hkq

f

rd

f Zxx

Hkpq

rd

d

xx

xp

1e

1e

dx

dh

as

eehdx

dh

constant h eehh

blanket of length Finite

2ax

2ax

ax-ax

n

n

ax-ax

n

ax

x

h

a

r

r

f

d

f Zx

Hkq

f

rd

f Zxx

Hkpq

rd

d

xx

xp

Discharge Reduction (1-p)

Without blanket

With blanket

(ii)

1e

1efactor by reduces x length effective length, finitefor Thus

length infinite as same 1

length finitefor 1e

1e

2ax

2ax

r

2ax

2ax

axxas

ax

r

r

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300

facto

r

x

This factor increase with increase of x, but rate of increase becomes

very slow after , therefore for design optimum value of 2 ax 2 ax

m 176 x optimum

0.008 a

cm/s 10

cm/s 105

5.1

20

5

3

b

f

b

f

k

k

mZ

mZ

cosWN sinWT

TRTRMd

6) STABILITY OF SLOPES

The slices method (Swedish slip circle method)

1. Locate the centre of the possible failure arc

2. Divide earth mass into 6 – 12 slices (vertical) of equal thickness

3. Numbered the slices

4. Compute the weight of slice taking into consideration dry and saturated weight of

soil

Total disturbing moment (R=radius of failure surface)

Resisting moment

RNLcMR

)tanˆ(

NRLc tanˆ

RNcL )tan(

R

d

R

M

MSF ..

T

NcL

tan

T

UNcLSF

tan)(..

Factor of safety against sliding

Under pore pressure

byW )0(2

111

byyW )(2

1212

byyWNNN)(

2

11

by

yyyWW NN )

2....( 121

N= No. of slices

Various materials, namely riprap, internal filters, rock toes etc. falling within the

sliding mass shall be considered to have the same properties as those of the

respective zones within which they are located.

Location of the centre of the critical slip circle (Fellenius, 1936)

P is obtained by knowing 21&

Slope 1 2

1:1 28 37

2:1 25 35

3:1 25 35

4:1 25 35

5:1 25 37

Few points

The most critical circle passes through the toe/heel of the slope when > 30, or

slope angle > 530, irrespective of .

The most critical circle intersects the slope in front of the toe or heel if < 30,

and slope angle < 530

Location of critical

circle for d/s slope

Location of critical

circle for u/s slope

1. For very small value of (<3o) and < 53o, the centre of the critical arc

likely to fall on a vertical line drawn through the centre of the slope.

2. Critical arc cannot penetrate the hard strata and will be tangent to it.

Stability of embankment dams should be checked for the

following conditions

1. Stability during and at the end of construction

2. Stability of d/s slope during steady seepage

3. U/s slope under sudden drawdown

4. Steady seepage with sustained rainfall for d/s slope

5. Stability of u/s and d/s slopes under earthquake condition

1. Stability during and at the end of construction

Embankment dam is normally compacted at 80 to 90% saturation that is

80 to 90 % of the pore space is filled by water and the rest by air bubble.

The compression of this water-air pore fluid under increasing load of

embankment causes build up of pore pressure.

For stability check, pore pressure is required

Hilf (1948) method: the induced pore pressure

w

wa

V

pu

p

VV

pu

02.0

and,V saturated becomes soil theand solution into goesair When

percent) (in soil embankment of eunit volum inpresent water pore of volumeV

percent) (in ionconsolidat ofstart before

embankment of eunit volum in pores soil inair free of volumeV

volumeembankment original of portiona as ncompressio embankment

pressure catmospheri Absolute

02.0

0

a

w

a

0

0

2. Stability of d/s slope during steady seepage

- Dam is fully saturated below phreatic line

- Can be solved using Effective stress method

T

UNcLSF

tan)(..

N = Wcos W use saturated unit weight for soil below phreatic line

U Estimated by drawing flow-net T = W sin

T

NcLSF

tan'..

5.1.. SF

Total stress method (IS 7894)

N’ = W cos W = based on submerged unit weight of soil

T = W sin W = based on saturated unit weight of soil

All zones of the dam and foundation lying below the tail water level, if any shall

be considered as buoyant (submerged) for both N’ & T.

])1([ hnhhh rcww

3.1.. SF

3.0 U/s slope under sudden drawdown

Effective stress method

Pore pressure is computed using Bishop formula

hw = pore water pressure at a point

w = unit weight of water

hc = height of core material at the point

hr = height of shell material at the point

n = porosity of shell

h = drop in head under steady seepage condition at the point

h

Measured pore pressure in Alcova dam (USBR, Design of small dams)

Total stress method

Zones above phreatic line: All materials shall be considered as moist

Zones in drawdown range: For computing driving forces the core material and

non-free-draining material shall be considered as saturated and freely draining

material shall be considered as moist. For computing resisting forces, consider

submerged unit weight of soil.

Zones below drawdown level: All zones including foundation zone below the

drawdown level shall be considered as submerged for computing both the

driving and resisting forces.

4.0 Steady seepage with sustained rainfall for d/s slope (IS7894)

Shell and other material lying above the phreatic line shall be considered as

moist for calculating driving forces and buoyant for resisting forces.

Saturation of shell material shall be assumed as

• 50% if K < 10-4 cm/s

• 0% if K > 10-2 cm/s (in between assume linear variation)

F.S. > 1.3 (Use total shear stress method)

5.0 Stability of u/s and d/s slopes under earthquake condition

- follow the same procedure, however, increase T by Te = W cos .h

and decrease N by Nc = W sin .h

Thus T = (1+h) W cos

N = (1-h) W sin

F.S. > 1

h = horizontal earthquake coefficient.

7) CONSTRUCTION TECHNIQUES

Hydraulic Fill Dams

In this type of dams, the construction, excavation, transportation of the earth is

done by hydraulic methods. 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 the central portion to form a water tight central core. In this

method, compaction is not required.

A pool is created between the 'beaches'. The core level is always below the beach

level because the rate of sedimentation there is much slower.

The width of the core is controlled by the percentage of fines in the borrow soil and

the level of water in the core pool. At the start of each 1-2m lift, the level in the

core pool is raised to provide a width somewhat greater than the maximum limit of

core in the shell. A core zone with jagged edges is shown above.

Rolled fill method:

All fill material for the embankment should be placed in layers (or lifts) not

greater than 150mm thick.

The largest size particle should not be greater than 1/3rd the height of the lift,

that is, 50mm. Each layer should be thoroughly compacted before the next

layer is placed. A minimum of 6 passes to achieve the required compaction

effort is generally required by a suitable compaction machine

The compaction effort achieved should be on average 98% Standard

maximum Dry Density (MDD).

The minimum compaction effort should be 95% Standard MDD. If the range

of compaction effort varies throughout the dam, then it can lead to the dam

embankment settling to different degrees (differential settlement) causing the

embankment of the dam to crack. This may ultimately lead to leakage and

dam failure.

Rolled fill method (continued)

The material forming the embankment should be placed with sufficient

moisture to ensure proper compaction. The moisture content should be in the

range of –1% to + 3% of optimum moisture content (OMC). If the material is

too dry, water should be added. If the material is too wet it should be spread

and mixed.

Before each additional 150mm lift is added to the embankment, the

preceding lift should be scarified to ensure that the two lifts are properly

joined so that no natural paths for seepage are present that may result in

dam failure.

The construction operations fall into four principal groups of activities, relating

to

(1) Material source development: Activities involve the opening out of borrow

areas or quarries, including the installation of fixed plant, e.g. crushers,

conveyors, etc. Access and haulage roads are also constructed between the

various borrow areas and the embankment site, and excavation

and haulage plant is mobilized.

(2) Foundation preparation and construction: Activities, including river

diversion, can proceed concurrently with the development of the fill sources.

Topsoil and weathered surface drift deposits etc. are removed. In the case of

a soft, compressible foundation, strength can be enhanced.

(3) Fill construction and control: Control of placing is centred upon

supervision of water content, layer thickness and compaction procedure.

(4) Ancillary works construction: embraces the construction of spillway and

stilling basins, culverts or tunnels for outlet works etc.