EMBANKMENT DAMS
(Nurek earth and Rockfill dam, Tajikistan) Tajikistan)
Contents 1)
Introduction
2)
Types Ty pes 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 SOME OF THE EMBANKMENT 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
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
(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
(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
(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
h w 0.032 VF 0.763 0.271 F 1 / 4
for F 32 km
h w 0.032 VF
for F 32 km
hw (m); Fetch F (km); Wind velocityV (km/hr) Free board = 1.5 h w (ii) US BUREAU OF RECLAMATION (USBR) Recommendations Spillway type
dam height
Min. free board above MWL
Uncontrolled Controlled Controlled
Any height < 60 m > 60 m
2-3 m 2.5 m above top of gate 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 45 0 on either side of line AB Draw 7 radials at 60 interval on each side of AB Effective Fetch
X cos Fe cos
(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
gF e 0 . 0026 2 2 V V
gh w
0.47
and wave period T
gF e 0.45 2 V V
gT
0.25
wave length L 1.56T
2
hw (m); Fe(m); V (m/s); T (s); L(m) Design wave height, hd = 1.67 hw
(4) Compute wave run up R on smooth surface from the following chart correspond to L
d
h / R
Wave run up on the rough surface 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
(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.
Wind set up S
V2 F 62000 D
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 h w • 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)
USBR for H 150 m A 3.6 H
1/3
Japanese Code A 3.6 H 1 / 3 3 A( m); H ( m)
For H 30 m A 0.55 H
1/2
0.2 H
For H 30 m A 1.65H 1.5
1/3
Use SI unit
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
(a) H < 15 m
2.5:1
2:1
(b) H > 15 m
3:1
2.5:1
Homogeneous silt clay
Sand or sand and gravel with a central clay core 3:1
2.5:1
Sand or sand and gravel with a RC diaphragm
2:1
2.5:1
(D) SUITABILITY OF SOILS FOR CONSTRUCTION OF EARTH DAMS
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
(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 1
Criteria 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
Filters should have a maximum particle size of 75 mm. Material passing the 75 micron sieve shall not exceed 5 percent. (c) To minimize segregation, filters should have relatively uniform grading. D 90 (f) should be less than 20 mm- to minimize segregation. Limit of D 10(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
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;
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 Upper limit D (f) 0.5
correspondingly D90(f) = 20 mm correspondingly D (f) = 25 mm
However, the available material is in the range of curve 5 & 6, as shown in the graph. COARSE FILTER 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
Coarse Filter
DESIGN OF FIL FILTER TER IS Code 9429-1980 (i)
D15 of filter/D85 of base
(ii)
4
<5
< D15 of filter/D15 of base
(iii) D50 of filter/D50 of base
< 20
< 25
(iv) Gradation curve of filter should should be nearly parallel parallel to the gradation gradation curve curve of base material
Example Base material (B)
Sand layer filter (F1)
Gravel layer filter (F2)
d15 = 0.07 mm
d15 = 0.78 mm
d15 = 8.75 mm
d50 = 0.17 mm
d50 = 1.90 mm
d50 = 21.24 mm
d85 = 0.35 mm
d85 = 3.91 mm
d85 = 43.74 mm
90 80 70 r e n i f e g a t n e c r e P
60 50 40 30 20 10 0 0.01
0.1
1
10 Grain size (mm)
100
1000
(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 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 t he design wave height. (a) For embankment slopes 2:1 to 4:1 dumped riprap shall meet the following criteria:
(Hand-placed riprap)
Placing riprap with hydraulic excavators
(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 W 50. 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.
U/s face of dam
Thickness 15 cm 2 to 3 m
(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
u x
v y
;
for isotropic soil Kh
h u K x
;
Continuity equation
2h 2h 2 0 2 x y
h v K y u v 0; x y
- -- Laplace Equation
for isentropic soil
h u K x x
;
Continuity equation
h v K y y u v 0; x y
2h 2h K y 2 0 K x 2 x y K x 2 h
2h 2 0 2 K y x y Subsitution of x x'
2h 2h 2 0 2 x' y
(1) K x K y
- - - --
yields
x' x
K y K x
(a) Seepage through isotropic soil
flow across AB, q KiA K
K
H y K H x
H
N d
N d Number of drop N f Number of flow channels Total seepage flow q q
K
H
N d
N f
For isentropic soil - draw the dam on scale x'-y with x' x q
K x K y
H N d
N f
K y K x
(as x y)
(b) Seepage through isentropic soil
H flow across AB, q K x y x K x
H x'
K x K y q
K x K y
H N d
N f
K x
as
y
x' x
K y K x
(as x' y)
K y H N d (2)
Thus for isentropic soil, draw the dam on scale x'-y with x' x
K y K x
then draw the flownet and compute the seeepage discharge from Eq. (2)
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
x 2
FD
x
2
y 2
x FD
S , focal length distance from focus to directrix y
2
x S
At point A b
2
2
H
S b 2
b S
H 2
Seepage flow q KiA dy y K dx
b
x S 2 x 2
as y
dy
1
1
2
2 xS S 2 S
dx
q K q KS
2 xS S 2
2 S
2 xS S 2 S 2 xS S 2
2 xS S 2
(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)
a a a
30
0.36
60
0.32
90
0.26
120
0.18
135
0.14
150
0.10
180
0
May also be calculated by
a a a
180 400
a a is known from parabola equation, thus a known
(a)
> 900
a+a =S-(a+a)cos(180-) a+a=S/(1-cos )
Directrix
(b) = 1800 a =0
Directrix
C
a
D
(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
Inclin ed/Vertic al 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. Horizon tal 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. In n e r L o n g i t u d i n a l a n d In n e r Cr o s s D r a i n s
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
T r an s i t i o n Z o n e s a n d Tr a n s i t i o n F i lt e r s
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.
Horizon tal Filters at Interm ediate 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
Roc k 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.
TWL 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
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
P o s i t i v e C u t - o f f T r en c h
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.
C o n c r e t e D i ap h r a g m
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
Grout curtain Sheet Pile Cut-offs
Used in silty, sandy and fine gravel foundation, difficult to drive pile in boulders
U p s t r e a m Im p e r v i o u s B l an k e t
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 Without blanket
q k f
H xd
Z f
With blanket
pq k f
H L x d
Z f
Substituting first Eq. into the second yield
L
1 p p
xd
(B) Blanket for finite permeability (Bennet’s solution) Discharge through blanket of thickness Z b in elemental distance dx
dqb k b
h Z b
dx
Total discharge qf at distance x from downstream end of blanket L x
x
q f q f o dqb q f o k b L
L
h Z b
dx
x
dq f dx As dq f dx
dq fo dx
dq fo
h
dx L
Z b
k b
dx d 2 h
Z b
dx 2 d 2 h dx 2
k f Z f
h
for the foundation q f k f dq f
dx
0
dx
k b
d x
k b
d 2 h dx 2 h
k f Z f Z b
a 2h
k b
dx
Z f
h Z b
a 2h
where a 2
k b k f Z f Z b
Bennet’s basic differential equation for a blanket of finite permeability and constant thickness
(i) Infinite length of blanket
h h 0 e ax
dh
Let the length of equivalent completly impervious is x r , which passes the same discharge as the infinite blanket, i.e, q f k f As xr
dh dx
dh dx 1 a
Z f k f
h xr
h xr
Z f
ah0eax ah
k f Z f Z b k b
Discharge Reduction (1-p) Without blanket q k f
H xd
Z f
With blanket pq k f
p
H xd x r
xd x x
Z f
(ii) Finite length of blanket
h h n eax e-ax dh dx as dh dx
h n constant
ah n eax e-ax
h x r
e a e
1 2ax 1
2ax
xr
Discharge Reduction (1-p) Without blanket q k f
H xd
Z f
With blanket
pq k f
H xd x r
Z f
p
xd xd xr
e a e
1 2ax 1
2ax
x r
as x
for finite length
x r
1 a
same as infinite length
Thus for finite length, effective length x r
e reduces by factor e
2ax 2ax
1 1
This factor increase with increase of x, but rate of increase becomes
very slow after x 2 a
, therefore for design optimum value of x 2 a 1.2 1
Z f 20m Z b 1.5m
0.8 r o t c a f
0.6
k f 5 10 3 cm/s
0.4
k b 10 5 cm/s
0.2
a 0.008 optimum x 176 m
0 0
50
100
150 x
200
250
300
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 N W cos T W sin Total disturbing moment (R=radius of failure surface)
M d TR R T Resisting moment
M R
(cL ˆ
N tan )R
c L R tan N ˆ
(cL N tan ) R
R
Factor of safety against sliding F .S .
M R M d
cL N tan
T
Under pore pressure F .S . W 1
W 2
W N
1
(0
2
1 2
(y 1
(y N 1
(N U )tan T
y 1) b
2 1
cL
y 2) b
N= No. of slices
y N ) b
W W ( y1 y2 .... y N 1
y N 2
)b
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
1 & 2
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
u
p0 V a 0.02V w
p0 Absolute atmospheric pressure
embankment compression as a portion of original embankment volume Va volume of free air in soil pores in unit volume of embankment before start of consolidat ion (in percent) Vw volume of pore water present in unit volume of embankment soil (in percent) When air goes into solution and the soil becomes saturated Va , and u
p0 0 02V
2. Stability of d/s slope during steady seepage - Dam is fully saturated below phreatic line - Can be solved using Effective stress method F .S .
N = Wcos T = W sin
cL
(N U )tan T
W use saturated unit weight for soil below phreatic line U Estimated by drawing flow-net
Total stress method (IS 7894) F .S .
cL
N ' tan T
N’ = W cos T = W sin
W = based on submerged unit weight of soil 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
5
3.0 U/s slope under sudden drawdown Effective stress method Pore pressure is computed using Bishop formula
hw w [hc hr (1 n) h ]
h
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
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 N c = W sin .h Thus
T = (1+h) W cos
N = (1-h) W sin F.S. > 1
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 – of –1% 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.
