HS CH 2

Design Principles of Dam 2016
Chapter Two
2. Design Principles of Dam
2.1 Concrete Dams

Concrete dams are constructed of mass concrete. Slopes of these dams are not
similar, generally steep downstream & nearly vertical upstream slopes and
relatively slender profile dependent on the type.
2.1.1 Forces Acting on Concrete dams

Loads can be classified in terms of applicability or relative importance as primary
loads, secondary loads, & Exceptional loads.
Primary loads: are identified as those of major importance to all dams

irrespective of type. Example self weight, water & related seepage loads.
Secondary loads: are universally applicable although of lesser magnitude (e.g.
Silt load) or alternatively are of major importance only to certain types of dam
(e.g. thermal effects with in concrete dams).
Exceptional loads: are so designed on the basis of limited general applicability of
occurrence ( e.g. tectonic effects, or the inertia loads associated with seismic
activity)
a) Primary Loads
i. Water Load
Hydrostatic distribution of pressure with horizontal resultant force P1 (Note also
a vertical component exists in the case of an u/s batter, and equivalent tail water
may operate in the d/s face)
Refer figure 2.1
Where w unit weight of water =9.81 KN/m3

Pwv =w (area A1) KN/ m
Acting through centroid of A1
Pressure of any permanent tail water above the plane considered is:
ii. Self weight load: Determined with respect to an appropriate unit weight of the
material
Pm=c Ap KN/m
acts through the centroid of x- sectional area AP.
(c 23.5 KN/m3)
Where crest gates & other ancillary structures of considerable weight exist they
1
Hydraulic Structures-I for G3CE

must also be considered in determining Pm & their appropriate position of line of

action.
iii. Seepage & uplift load:

Equilibrium seepage patterns will establish within & under a dam eg. with
resultant forces identified as.
Pu =  Ah (Uw,avg)
if no drain functioning.
 is area reduction factor

Ah nominal plane area at a section considered.
If no drains functioning:
(m)
In modern dams internal uplift is controlled by the provision of vertical relief

drains close behind the u/s face. Mean effective head @ the line of drains, Zd can
be expressed as:
Zd = Z2+Kd(Z1-Z2)m
Kd is function of drain geometry (i.e. diameter, special & relative
location with u/s face.)
Kd= 0.33 (USBR)
Kd = 0.25 Tennase valley Authority
Kd= 0.25-0.5 appropriate to the site by the U.S corps of Engineers
The standard provision of deep grout curtain below the u/s face intended to limit
seepage also serves to inhibit pressure within the foundation. However, less
certain than efficient draw system & its effect is commonly disregarded in uplift
reduction.
b. Secondary loads
i. Sediment load:
Accumulated silt etc, generates a horizontal thrust, Ps. the magnitude additional
to Pwh is a function of sediment depth, Z3, submerged unit weight s’ & active
lateral pressure coefficient. Ka:
& acting @ Z3/3 above plane
s’ = s-w where s is sediment saturated unit weight.
Where: s is angle of shearing resistance.

For representative values of s 18-20KN/m3

s 300
Fig. 2.1 Gravity dam loading
Hydrodynamic wave Load

Transient load, Pwave, generated by wave action of water against the dam. It is not
normally significant & depends on the fetch & wind velocity.
F
H
Fig. 2.2 Hydrodynamic wave

Pwave =2w Hs2
Where Hs - significant wave height (is the mean height of the highest third
of
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the wave in train)
Hs range from 0.75 Hs for concrete dams to 1.3Hs for earth dams.
U= wind speed in km/hr

F= in km
Wind load: when the dam is full, wind acts only on the d/s side thus contribute to
stability. When empty the wind can act on the u/s face but insignificant
compared to hydrostatic load. For buttress dams load on the exposed surface
has to be considered.
Ice load: Not a problem in Ethiopia. It can be significant where ice sheets form to
appreciable thickness & persist for lengthy periods.
Pice =145 KN/m2 for ice > 0.6m thick, other wise neglected
Thermal & dam /foundation interaction effect: Cooling of large pours of mass
concrete following the exothermic hydration of cement & the subsequent
variation in ambient & water temperatures combine to produce complex & time
dependent temp. Gradients within the dam equally. Complex interaction develops
as a result of foundation deformation
C. Exceptional Loads
Seismic load: Horizontal & vertical inertia loads, are generated with respect to the
dam & the retained water by seismic disturbance. Horizontal & vertical
accelerations are not equal, the former being of greater in density. For design
purposes both should be considered operative in the sense last favorable to
stability of the dam, under reservoir full conditions the most adverse seismic
loading will then occur when the ground shock is associated with.
Horizontal foundation acceleration operating u/s, and

Vertical foundation acceleration operating downwards and vice-versa for
reservoir empty condition
Seismic coefficient analysis

Seismic acceleration coefficient. h for horizontal
v =0.5h for vertical
Representative seismic coefficient applied in design

Coff. h Modified mercali scale General damage U.S seismic zone
level
0.0 - Nil 0
0.25 VI Minor 1
0.10 VII Moderate 2
0.15 VIII-IX Major 3
4

0.20 Great 4
For more extreme circumstances eg. h=0.4 has been employed for dams in high
risk region in Japan, h =0.5 & h =0.6-0.8 damaged Koyna gravity dam, India (
1967) & Pacima arch dam USA (1971) respectively.
Inertia forces: Mass of dam

Horizontal Pemh =  h Pm
Vertical Pemv =  v Pm operating through centroid of the dam
Hydrodynamic forces: water action

Relative to any elevation @ depth Z1 below the water surface, the pressure pewh
pewh = Ceh.w Zmax. (KN/m2)
Zmax= Max. Water depth

Z1 = the depth @ section considered
Ce= dimensionless pressure factor
= f (Z1/Zmax, u) where u -inclination of u/s face to vertical
Total hydrodynamic load is given by.

Pewh = 0.66 Ce h Z1 w & acts @ 0.4 Z above section
pressure factor Ce.

Ratio z/z1 u =00 u = 1500
0.2 0.35 0.29
0.4 0.53 0.45
0.6 0.64 0.55
0.8 0.71 0.61
1.0 0.73 0.63
The vertical hydrodynamic load, Pewv, is
Pewv = v Pwv
Uplift load is assumed unaltered.
Resonance: results when period vibrations of the structure & earth quake period
are equal. For a concrete gravity dam of triangular X- section base thickness T
)
As an example, the natural frequency of vibration of monolithic gravity profiles
with nominal height of 20m & 50m are 15-25 & 6-9 HZ respectively ( if major
seismic shock frequency of 1-10 HZ). Thus it is only of concern for large dams &
vulnerable portion of the dam.
Load combinations
Different design authorities have differing load combinations. A concrete dam
should be designed with regard to the most rigorous groupings or combination
of loads which have a reasonable probability of simultaneous occurrence.
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Three nominated load combinations are sufficient for almost all circumstances.
In ascending order of severity we can have normal, unusual & extreme load
combination (NLC, ULC, ELC respectively)
With probability of simultaneous occurrence of load combination decreases,
factor of safety should also decrease.
DESIGN AND ANALYSIS OF GRAVITY DAMS

Criteria & Principles
The conditions essential to structural equilibrium & so to stability can be
summarized as
Assessed in relation to all probable conditions of loading, including reservoir

empty conditions the profile must have sufficient safety factor with respect to:
Rotation & overturning.
Translation & sliding and
Overstress & material failure.
Over turning
Sliding
X Stre X
ss
Overturning stability
Factor of safety against overturning, Fo, in terms of moment about the
downstream toe of the dam.
Fo > 1.25 may be acceptable, but Fo > 1.5 is desirable.

sliding stability
Factor of safety against sliding, Fs, estimated using one of the three definitions:
Sliding factor, FSS;
Shear friction factor, FSF or
3) Limit equilibrium factor, FLE.
The resistance to sliding or shearing which can be mobilized across a plane is
expressed through parameters C & tan.
1. Sliding Factor,Fss
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But for the foundation plane inclined @ small angle o
Fss should not be permitted to exceed 0.75, but under ELC up to 0.9 is
acceptable.
2. Shear friction factor,FSF : is the ratio of total resistance to shear & sliding which
can be mobilized a plane to the total horizontal load.
Where:
PH W
In some cases it may be appropriate to include d/s passive wedge resistance, pp,
as a further component of the resistance to sliding which can be mobilized.

Ww =weight of passive wedge.

Rw = sliding resistance in inclined plane.
=CAh +(Ww cosα+Hsinα) tan
This is affected by modifying the above equation, hence,

)
In the presence of horizon with low shear resistance it may be advisable to make
S=0.
Recommended shear friction factor, FSF (USBR 1987).

Load combination
Location of sliding plane Normal Unusual
Extreme
Dam concrete, base interface 3.0 2.0
>1.0
Foundation rock 4.0 2.7 1.3
C. Limit Equilibrium factor, FLE.

This follows conventional soil mechanics logic in defining FLE , as the ratio of
shear strength to mean applied stress across a plane i.e
FLE =
is expressed by Mohr Columb’s failure criteria, accordingly
is stress acting normal to plane of sliding

For single plane sliding mode.
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Note for  = 0 FLE =FSF.

This equation can be the developed for complicated failure plane
FLE =2.0 normal operation & FLE =1.3 under transmit condition embracing seismic
activity)
C. Stress analysis in gravity method

Gravity method is useful to analyses stress in straight dams which are not
geometrically complex. It is founded on 2-D elastic dam on uniformly rigid
foundation & linear variation of stress from u/s to d/s.
The stresses evaluated in a comprehensive analysis are:

Vertical normal stress, z, on horizontal planes.
Horizontal & vertical shear stress,
Horizontal normal stress, y ,on vertical planes and
Principal stress, 1 & 3 (direction & magnitude).
1. Vertical normal stress z.

Analysis is based on modified beam theory which is by combining axial &
bending load.
Where, v- resultant vertical load above the plane considered exclusive of uplift.
M* - summation of moments expressed w.r.t the centroid of the plane.
y’ - distance from the centroid to point of considerations
I - second moment of area of the plane w.r.t centroid.
For 2-D plane section of unit width Parallel to the dam axis, & with thickness T
normal to the axis:
and at y’=T/2
For reservoir full condition

At the u/s face
At the d/s face
Where e is the eccentricity of the resultant load, R, which must intersect the plane
d/s of its centroid for the reservoir full condition.
(The sign convention is reversed for reservoir empty condition of loading)

Where v - excludes uplift

For e > T/6, at u/s face –ve stress is developed, i.e. tensile stress. In design,
tensile stress has to be prohibited, but difficult to totally eliminate low tensile
stress in gravity dam. Total vertical stresses at either face are obtained by the
addition of external hydrostatic pressure.
2. Horizontal & vertical shear stresses

Numerically equal & complementary horizontal (zy) & vertical (yz) shear stresses
are generated @ any point as a result of variation of vertical normal stress over a
horizontal plane.
The variation b/n u/s & d/s stress is parabolic, & depend on rate of change of
variation of normal stress.
3. Horizontal normal stress, y

It can be determined by consideration of the equilibrium of the horizontal shear
force operating above & below a hypothetical horizontal element through the
dam. The difference in shear forces is balanced by the normal stresses on
vertical planes.
4. Principal stresses
1 & 3 may be determined from knowledge of z & y & construction of Mohr’s
circle diagram to represent stress conditions at a point, or by application of the
equation given below.
Major Principal Stress
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Minor principal stress
Where
The boundary values, 1 & 3 are determined by:

For upstream face
1u= zu (1+ tan2u)-Pw tan 2u
3u=Pw
For downstream face assuming no tail water
1d=zd (1+tan2d)
3d=0
Permissible stresses & cracking

The following table gives permissible compression stresses factor of safety for
gravity dam body & rock foundations. (USBR 1976)
load combination Minimum factor of safety on compressive

strength
Fc(concrete) Fr, (rock)
Normal 2
3.0 (max & 10 MN/m ) 4.0
Unusual 2
2.0 (max &15 MN/m ) 2.7
Extreme 1.0 max allowable stress 1.3
Horizontal cracking assumed to occur if zu min (without uplift) below limit set by
R
Vertical cross-section
T/2 e
T
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A B
Pressure diagram without
Uplift pressure
1
A A’ B
Uplift pressure diagram
4
T/2=T1
3
A A’ B
Combined pressure e’
diagram
3 4 T1/3
Combined base pressure & uplift pressure diagram. 5

When the uplift is introduced & the uplift pressure @ the U/s face is < A1, the
final stress may be computed by the above formula. If the uplift pressure @ the
upstream face is greater than A1. i.e. less than permissible tension stress.
Revise as follows.
1. A horizontal crack is assumed to exist & extend from the u/s face toward the
d/s face
to a point where the vertical stress of adjusted diagram is equal to the uplift
pressure @
the u/s face.
2. Taking moments about center of gravity & check whether the section is
adequate for
over turning, sliding & material failure.
Kd= 0.4 if drains are effective = 1.0 if no drains.

t’ = tensile bond strength of concrete.
Ft’= Factor of Safety [Ft’ =3 for NLC,
=2 for ULC,&
= 1.0 for ELC]
Design Gravity Dam profile

U/s face flare: the u/s face of a gravity profile is frequently modified by the
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introduction of a significant flare.
Design of small dams associated with provision of’ standard’ triangular profile of
u/s vertical face & d/s slope of 0.75 horizontal to 1.0 vertical.
In the case of large dams a unique profile should be determined to match the
specific conditions applicable. Two approaches are possible; the multi stage &
single stage.
The multistage approach defines a profile where the slopes are altered at
suitable intervals.
Design commences from crest level, & descends downwards through profile
stages corresponding to predetermined elevations. Each stage is proportioned
as to maintain stress level within acceptable limits. E.g. no tension under any
condition of loading.
The resulting profile allows marginal economics on concrete, but more expensive
to construct than the single –stage. Multi-stage profiles are now seldom
employed, even on large dams.
Single stage: is based on definition on a suitable & uniform d/s slope. The apex
of the triangular profile is set @ or just above DFL & initial base thickness T is
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determined for each loading combination in terms of F0. The critical value of T is
then checked for sliding stability & modified if necessary before checking heel &
toe stress @ base level.
For no tension @ u/s vertical face
Take =1.0
Advanced Analytical methods

When interaction b/n adjacent monolith result in loads transfer & complex
structural response, and further differential settlement exist, then alternative
analytical approaches called trial loads twist analysis & finite element analysis
exist.
Stabilizing and heightening

Remedial action to improve stability can be taken by pre-stressing provides an
additional vertical load with a resultant line of action close to the u/s face.
This improves F0 or Fs by operating adjunct to Pm.
Overturning design pre-stress required;
Where y2 is moment arm of Pps

Sliding
The pre-stressing tendons are typically located @ 3 to 7m centers to centers

along the crest. The pre-stress load required for each, PT (KN) is the appropriate
multiple of Pps . Pre-stressing is also useful for heightening of the dam.
Downstream shoulder
Contribution by weight of fill
WF =f*A
Pds= Ko..f . ZAB.Z KN/m
Where ZAB & Z as shown in the figure above.

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f unit weight of the fill

Ko is at ‘rest’ pressure coefficient
. Pds acts ZAB/3 above the base plane
Illusrative values of ko.
Shoulder fill Coeff. Ko
Compacted rock fill 0.2 – 0.3
Compacted sand 0.45 – 0.55
Compacted clay 1.0 – 2.0
Heavy compacted clay > 2.0
Buttress dams
A buttress dam consists of a slopping u/s membrane which transmits the water
load to
a series of buttress at right angle to the axis of the dam.
Buttress dam principally fall in to two groups, massive diamond or round-headed

buttress dams. The earlier but now largely obsolete flat slab (Amburson) &
decked buttresses constitute the minor types.
Relative to gravity dam, buttress dam has the advantages of saving in concrete,
major reduction in uplift and also offers greater ability to accommodate
foundation deformation without damage. However, the advantages offset by
considerably higher finished unit costs as a result of more extensive & non
repetitive formwork required. It also requires more competent foundation
because of stress concentration.
Buttress analysis & profile design

Buttress dam analysis parallels gravity dam practice in being conducted in two
phases
Stability investigation
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Stress within the profile

The form of buttress dam has two important consequences w.r.t. primary loads.
Uplift pressure confined to buttress head & result in modified uplift pressure
distribution; pressure relief drains are only necessary in exceptional cases
Pwv vertical component of water load enhanced. The concept of stability against
overturning is no longer valid.
In structural terms, massive buttress constructed of a series of independent
units, each composed of one buttress head & a supporting buttress or web
(length along the axis of the dam of about 12-15 m for each unit). Structural
analysis is therefore conducted w.r.t the unit as a whole.
Fss or more usually FSF shear friction factor analyzed in same way as gravity
profile with comparable minimum values for these factors.
Stress analysis of a buttress unit is complex & difficult. Modern practice is to
employ finite element analysis to assist in determining the optimum shape for
the buttress head to avoid undesirable stress concentrations @ its function with
the web.
Approximate analysis is possible by modified gravity method for parallel sided

d/s webs. The root of the buttress is usually flared to increase sliding resistance
& control the contact stress.
Profile design for buttress is not subject simplification as gravity dam. A trial
profile is established on the bases of previous experience. The profile details are
then modified & refined as suggested by initial stress analysis.
Arch Dams
The single-curvature arch dam & the double curvature arch/cupola were
introduced with concrete dams previously and the rock & valley conditions were
also outlined.
Valley suited for arch dams
Narrow gorges
Crest length to dam height.= 5 or less according to sarkaria
for Sv < 5 arch dam may be feasible

Arch & cupola dams transfer their loads to the valley sides than to the floor.
Overturning & sliding stability have little relevance here. If the integrity &
competence of the abutment is assumed failure can occur only as a result of
overstress. Arch dam design is therefore centered largely up on stress analysis
and the definition of an arch geometry which avoids local tension stress
concentration and /or excessive compressive stress. The area & cupola dam
offer great economics in volume of concrete.
Associated saving may also be realized in foundation excavation & preparation,

but the sophisticated form of arch dam leads to very much increased unit costs.
In case of complex geology of abetment saving can also be negated by
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requirement of ensuring abutment integrity under all conditions.
Arch geometry and profile.

The horizontal component of arch thrust must be transferred in to the abutment
at a safe angle.
ϴ=600 as indicated (assumed)
In general abutment entry angle of 450 to 700 is ok.
Arch & cupola profiles are passed on a member of geometrical forms.
Constant radius profile: has simplest geometry, U/s face of the dam is of
constant radii’s with a uniform radical d/s slope. (see fig). It is apparent that
central angle, 2ϴ, reaches a max. @ crest level.
In symmetrical valley minimum concrete volume when 2ϴ =1330, but entry angle
preclude this & 2ϴ ≤ 1100, the profile is limited to relatively symmetrical U-shaped
valley.
Constant angle profile, Central angle of different arch as have the same
magnitude from top to bottom & uses up to 70% of concrete as compared to
constant radius arch dam. But it is more complex as demonstrated in the figure.
It is best suited to narrow & steep-sided V-shaped valleys.
Cupola profile. Has a particularly complex geometry & profile, with constantly
varying horizontal & vertical radii to either face. A trial geometry selected from
programs (presented by Boss, 1975), & refined as necessary by material or
physical model.
Design & Analysis of Arch Dams
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Loads on arch dams :

Loads on arch dams are essentially the same as loads on gravity dams.
Uplift forces are less important, if no cracking occurs it can be neglected.
Internal stresses caused by temperature change, ice pressure, and fielding of
abutment are very important.
The design /analysis can be based on :
-The thin cylinder theory
-The thick cylinder theory.
-The elastic theory.
-Advanced method of analysis/ design –trial load analysis (TLA)
-Finite element analysis (FEA)
Thick & thin Ring, (cylinder) theory.

The theory envisages that the weight of concrete & that of water lie on the dam is
carried directly to the foundation not to the abutment
The horizontal water load is carried entirely by arch action.
The discrete horizontal arch elements are assumed to form pact of a complete
ring subjected to uniform radial pressure, Pw, from the water load & hence it is
assumed to have uniform radial deformation.
Thin Cylinder Theory
The theory assumes the arch to be simply supported @ the abutments & that the
stresses are approximately the same as in a thin cylinder of equal outside radius.
Consider thin ring 1-2 of unit height h = @ a depth of h below water surface.
Hydrostatic pressure acting radially against the arch is wh.
Let Ru = extrados radius Ri = intrados radius

Forces parallel to stream axis 2F sin  = 2Ru sin. wh.
F = wh Ru
The transverse unit stress
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For given stress the required thickness is
Since Ru = Rc+0.5T = Ri + T ;
Condition for least volume of concrete
V= A.R2θ = T*1*R2θ
 = 133 34 . (Most economical angle of arch with minimum

0 1
, gives
volume)
For 2 =1330341; R= 0.544B
Thick cylinder theory

At Radius R, the compressive ring stress is given by
Note in theory, T should diminish towards crown & increase towards abutments.
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In practice, T usually is constant at any elevation on a simple arch profile, and

correction for maximum stress at abutment made by factor, Kr, determined as a
function of θ & Ru /T from curves.
Elastic Arch theory

This theory also assumes complete transfer of load by arch action only.
Horizontal arch rings are assumed fixed to the abutments, but acting
independently of neighboring rings. Effects of temperature variation on arch
stress are considered. This method can be used for preliminary design to
determine adequacy of the section designed by the (cylinder theory).
The following formulae (modified by Cans equation) are used for calculating
thrusts & moments at the crown & abutments.
Thrust @ crown
Moment @ crown:
Thrust @ abutments:
Moment @ abutments:
After calculating thrusts & moments, stresses at intrados & extrados are
calculated from
Advanced method of analysis /design

The assumptions made in elastic ring analysis simplified & discrete independent
horizontal rings which are free of any mutual interaction and the uniform radial
deformation are both untenable. Easly recognition of the importance of arch-
cantilever & arch- abutment interactions led to the development to trial load
analysis (TLA) which is similar to trial load twist analysis used in gravity dam.
Finite element analysis (FEA) is also extensively applied in arch dam analysis.
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Although FEA is most powerful reliable & well proven approach it is a highly
specialist analytical method demanding experience.
Concrete dams design features & construction

All analysis are founded mainly based on assumption w.r.t leading regime,
material response, structural mechanism etc. application of the analytical
methods introduce in the proceeding sections represents only the initial phase of
the design process. The 2nd phase is to ensure by good detailed design the
assumptions made are fulfilled.
Design features divide in to three major categories

Those related to seepage
Those which accommodate deformation or relative moment
Features related to structural continuity i.e load transfer devices possibly
Those which facilitate construction
Cut-off & foundation grouting
Cut-offs are formed by grouting
Shallow trenches constructed under heel of dam contribute to seepage control
N.B curtain grouting & consolidation grouting refer Thomas (1976) & George
(1982) for grouting practice.
Uplift relief drains:
Drainage holes d/s of grout curtain
Holes are 75-100min.  & spacing of 3-5 centers & are drilled from inspection
gallery
Uplift with in the dam relived by holes running full height & of at least 150 mm 
to inhibit blocking by leached out material & located near to u/s face & spaced at
about 3m.
Relief drain efficiency is a function of drain geometry i.e spacing ,  distance
form u/s face
Internal design features

Inspection gallery
Collects inflow from seepage & inspection gallery.
Also gives access to appurtenance structures
Should not be less than 2x1.2m
Adequate ventilation & lighting is required
Transverse contraction joints ( inter- month invites)
Vertical contraction joints are formed @ regular intervals of 12-15m.
They permit minor differential moment
They are made necessary by shrinkage & thermal characteristics conc.
Construction joints ( inter-lift joints)
This is provided to prevent post construction shrinkage & cracking
Lift height is generally 1.5- 2.0m
Lift surface is generally constructed with a fall of about 4% towards the u/s face
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Load transfer & continuity

Although gravity dams designed on the basis of free standing vertical cantilevers,
load transfer is effected by interlocking vertical shear keys on the construction
joint face. In the case of arch & cupola dams it is essential to provide horizontal
continuity to develop arch action. The construction joint are grouted after the
structure is load
Pulvino or pad is heavy perimentral concrete, is constructed between the shell of
a cupola dam & the supporting rock to assist in distributing load in to the
abutments and foundation.
Concrete zoning : different concrete mix can be need in facing & hearting of
concrete dam.
Construction planning & exaction
Detailed pre of all activities involve must be prepared well in advance of sit
preparation, with the objective of ensuring optimum availability & utilization of all
resources the acting divided in to:
Initial phase - site preparation

Second phase -river diversion
Third phase - foundation excavation & preparation
Fourth phase – construction operation
Final phase- completion of ancillary work
Concrete for dams

The desirable characteristics comparable to concrete strength in concrete dams
are
satisfactory density n& strength
durability
low thermal volume change
resistance to cracking
low permeability &
economy
The primary constituents of concrete are cement, mineral aggregate & water.
Secondary constituents employed for dams include pozzolans & selected other
admixtures.
Rolled compacted concrete dams (RCCD)

This is a very recent idea to improve concrete dam construction how could you
change concrete (allow tension)
1. Rationale design principle (allow tension)
2. Alter design details (simple joint formworks)
3. ‘New type of concrete
4. Continuous construction use of rolled compacted concrete combines 3& 4
new conc. In a sense suitable for continuous construction.
Variants of RCC
lean RCC, USA use cement + pozz (PFA) < 100kg/m3 30 mm layers
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RCD method 700-100mm layer

Joints sawn
High paste Rcc USA, UK
Cement; the hydration of unmodified ordinary Portland cement (ASTM) type I)
equivalent ) is stroppy exothermic. It is preferable to employ a low heat (ASTM
type IV) or modified ordinary Portland cement (ASTM) type II) if available.
Thermal problems can also be alleviated by the use of pozzolan- blended
Portland cements (ASTM type 1P) In the absence of special cements pintail
replacement with pulverizing fuel ash (PFD) and or/ cooling are also effective in
containing heat build up.
Aggregates: used to act as cheap inert bulk filler in the concrete mix. Maximum
size aggregate (MSA) 75-100mm is optimum, with rounded or irregular natural
gravels etc, preferable to crushed rock aggregates.
In the fine aggregates, i.e < 4 4.67mm size natural sands are preferable to
crushed ones
and should be clean & free from surface weathering or impurities.
A general standard of water is that it should be fit for human consumption.
Pozzolana are silicious alumnious substances which react chemically with

calcium hydroxide from the cement to form additional compounds PFA an
artificial pozzolan is now universally employed. If available in partial replacement
of (25-50%) of cement PFA reduces total heat of hydration & delays the rate of
strength gain.
Long-term strength is generally enhanced, but strict quality control of PFA is
required.
Admixtures: the most common admixtures are air entraining agents (AFA) they
are employed to generate some 2-6% by volume of minute are bubles,
significantly improving the long term freeze than durability of the concrete. They
also reduce the water requirement of the fresh concrete & improve its handling
qualities. Water reducing admixtures (WRA) are sometimes employed to cut the
water requirement, typically by 7-8%. They are also effective in delaying setting
time under condition if ambient temperatures.
DESIGN PRINCIPLES OF EMBANKMENT DAMS

The embankment dam can be defined as a dam constructed from natural
materials excavated or obtained nearby. The materials available are utilized to
the best advantage, in relation to their characteristics as bulk fill zones within the
dam section. The natural fill materials are placed and compacted without the
addition of any binding agent, using high capacity mechanical plant.
An embankment dam is therefore a non-rigid dam which resists the forces

exerted up on it mainly by its shear strength. These dams usually provide the
23

most economical and most satisfactory solution for sites at which suitable
foundation at reasonable depth may not be available for a dam of concrete or
masonry.
The two main forms of embankment dams are Earth (earth fill) dams made
predominantly of earth or soil and Rock fill dams made predominantly of quarried
rock. However a composite earth and rock fill type of embankment dams are
also being widely used.
The design of an earth dam involves both a hydraulic and structural analysis. The
hydraulic analysis deals with the determination of the seepage patterns and the
magnitude of seepage as well as the internal hydrostatic seepage forces for both
the dam body and the foundation. Of particular importance is the investigation
for possible removal of fine particles near the toe by emerging seepage water
(piping). The structural analysis involves the study of the stability of the
embankment under the given conditions of seepage and other forces. Settlement
and stability studies of the foundation are also important.
3.1 Classification of Embankment Dams
Earth dams may be classified on the basis of methods of construction as:

Rolled-fill earth dam
Hydraulic-fill earth dam
Semi-hydraulic fill earth dams
ROLLED FILL EARTH DAM
In rolled-fill earth dams the embankment is constructed in successive

mechanically compacted layers. The material (sand, clay gravel etc) is
transported from the borrow pits to the dam site by truckers or scrapers. It is
then spread with in the dam section by bulldozers to form layers of 15 to 45 cm
thickness. Each layer is then thoroughly compacted and bonded with the
preceding layer by means of power operated rollers of proper design and weight.
HYDRAULIC FILL EARTH DAM

In the case of hydraulic-fill dam the materials are transported from borrow pits to
their final position (dam site) and placed through the agency of water. Thus in
this case, at the borrow pits the material is mixed with water to form a slurry
which is transported through flumes or pipes and deposited near the faces of
dam. The course materials of the slurry stay near the faces of the dam while the
finer ones move towards the center and get deposited there. This would provide
a dam section with shoulders of the course free draining particles and an
impervious central core of fine grained material such as clay and silt.
24

SEMI-HYDRAULIC FILL EARTH DAM

In the semi-hydraulic fill dam construction, the material is dumped near the
upstream and downstream face of the dam to form rough levees as in the case
of rolled fill dam without the use of water. Then the space b/n the levees are
filled with water and the material placed in or upon the levees is washed towards
the center of the dam. For this jets of water are directed on the dumped fill which
cause the finer material from the fill near the faces of the dam to be washed
away. The finer material moves towards the central portion of the dam and is
deposited there thus forming an impervious central core while course material
stays near the faces of the dam. However, in the absence of proper jetting action
the dumped fill at the faces of the dam may be more dense and impervious than
the material immediately below it on the inside of the dam which may result in
the failure of the dam.
Out of these three types, the rolled-fill earth dams are the most common. This is
so because in the case of the other two types lack of control in placing the
material may result in the failure of the dam.
Rolled Fill Embankments are of three types:
Homogenous type
Zoned type
Diaphragm type
A. HOMOGENOUS TYPE: purely homogeneous type of dam is composed of a

single kind of earth material except for the slope protection. It is used when only
a single type of material is economically and locally available. Such a section is
used only for low to moderately high dams and for dykes (an embankment
constructed to prevent flooding, keep out the sea, etc.) Large dams are rarely
designed as homogenous embankments.
For a completely homogeneous section it is inevitable that seepage will emerge

on the downstream slope regardless of its flatness and the impermeability of the
soil if the reservoir level is maintained for a sufficiently long time. At the
downstream slope up to 1/3 of the height may be saturated if internal drainage
arrangement is not provided. Besides larger sections (flat slopes) are required to
make it stable and safe against piping. Because of this an internal drainage
system such as a horizontal drainage layer and a rock toe is added so as to keep
the phreatic line well within the body of the dam. This permits the use of steeper
slopes and thus smaller sections.
The material comprising the dam must be sufficiently impervious to provide an

adequate water barrier & the slopes must be relatively flat for stability. To avoid
sloughing the upstream slope must be relatively flat if rapid draw down of the
reservoir is anticipated.
25

Although formerly very common in the design of small dams, the purely
homogenous section has been replaced by a modified homogeneous section in
which small amounts of carefully placed pervious materials control the action of
seepage so as to permit much steeper slopes. The modified homogeneous
section is the one provided with internal drainage filter system in the form of a
horizontal drainage blanket or a rock toe or a combination of both.
Homogeneous Embankment Dam Section

B. ZONED EMBANKMENT TYPE:
These are the most common for high dams of rolled fill type. They are provided
with a central impervious core, covered by a relatively pervious transition filter
which is finally surrounded by a more pervious outer zones or shells.
The core thickness should not be less than 3 m at any elevation or greater than
the embankment height above the corresponding section. The central core
checks the seepage; the transition filter zone prevents piping through cracks
which may develop in the core. The outer zones (shells) provide stability to the
core and also distribute the load over a larger foundation area. The core is
usually a mixture of clay and sand or gravel or silty clay. Pure clay that shrinks
and swells excessively is not suitable .Freely draining materials such as coarse
sands and gravels are used as the outer shells. This is necessary b/c the
26

downstream pervious zone should act as a drain to control the line of seepage.
If a variety of soils are readily available, the choice of type of earth fill dam should
always be the zoned embankment type b/c its inherent advantages will lead to
economies in cost of construction.
Zoned Dam Section
C. DIAPHRAGM TYPE: In this type of section the bulk of embankment is

constructed of pervious materials (sand, gravel or rock) and a thin diaphragm of
impermeable material is provided to form the water barrier. The position of this
barrier may vary from a blanket on the upstream face to central vertical core. If
the diaphragm is provided as an impervious blanket on the u/s face of the dam it
needs to be protected against shallow sloughs and slide during draw down and
from erosion by wave action. For this the diaphragm is held buried below a thin
layer of pervious material over which the upstream slope protection is provided.
The diaphragm may be of earth, Portland cement or asphalt concrete or other
material. If the core thickness at any elevation is less than 3m or less than the
embankment height above the corresponding section then the dam embankment
is considered to be the diaphragm type.
Diaphragm type
FOUNDATION REQUIREMENTS
The essential requirements of a foundation for an earth dam are that it provides
support for the embankment under all conditions of saturation and loading and
27

that it provides sufficient resistance to seepage to prevent excessive loss of

water. Although the foundation is not actually designed certain provisions for
treatment are made in designs to assure that essential requirements will be met.
Foundations are grouped in to three main classes according to their predominant

characteristics as rock foundation, Foundation of coarse-grained material
(pervious foundation) and foundations of fine grained materials (impervious
foundation).
Impervious Foundation: Foundations of fine silt and clay are impervious and have
very low shear strength. Shear failure may occur in such foundations. If the
foundation material is impervious and comparable to the compacted
embankment material in structural characteristics, little foundation treatment is
required. The minimum treatment for any foundation is stripping of the
foundation area to remove the topsoil with high content of organic matter & other
unsuitable material which can be disposed of by open excavation. In many cases
where the over burden is comparatively shallow the entire foundation is stripped
to bed rock.
Rock Foundation: Foundations of rock including hard shale do not present any
problem of bearing strength for small earth fill dam. The principal considerations
are dangerous erosive leakage and the excessive loss of water through joints,
crevices, permeable strata and along fault planes. Ordinarily, the design and
estimate for a storage dam should provide for the injection of grout under
pressure to seal seams, joints & other opening in the bed rock to a depth equal to
the reservoir head above the surface of the bed rock. Grouting is usually done
with neat cement and water starting with a ratio of 1:5. Pressures usually applied
are (0.25 D kg/sq cm). Where, D is the depth of grouting below the surface.
Pervious Foundations: Often the foundations for dams consist of recent alluvial
deposits composed of relatively pervious sand and gravel over lying impervious
geological formations. Two basic problems are found in pervious foundations.
One pertains to the amount of under seepage and the other is concerned with the
forces exerted by the seepage.
Quantity of Under Seepage and Seepage Forces: - To estimate the volume of

under seepage, it is necessary to determine the coefficient of permeability, k, by
Darcy’s formula, the accuracy of which depends on the homogeneity of the
foundation and the accuracy with which the coefficient of permeability is
determined.
Seepage forces are caused as a result of the friction b/n the percolating water
and the walls of the pores of the soil through which it flows. The forces are
exerted in the direction of flow and are proportional to the friction loss per unit
distance. As the water percolates up ward at the d/s toe of the dam, the seepage
force tends to lift the soil resulting in piping.
28

3.2 Causes of Failure of Earth Dams

Earth dam failures are caused by improper design, frequently based on
insufficient investigation and lack of control and maintenance. The various
causes may be grouped in to the following three broad categories:-
Hydraulic failure
Seepage failure
Structural failure
I. Hydraulic failure: - Caused by surface erosion of the dam by water. They include
wash out from overtopping, wave erosion of upstream face, scour from the
discharge of spillways & erosion of the d/s slope by rain.
II. Seepage failure: - uncontrolled or concentrated seepage through the dam body
or through the foundation may lead to piping and sloughing and subsequent
failure of the dam.
The following are the most common modes of seepage failure:-
Seepage through pervious foundation: - Presence of strata or lenses of sand or

gravel of high permeability or cavities and fissures in the foundation permit
concentrated flow of water from reservoir leading to piping.
Leakage through embankment: - This is mainly due to poor construction control,

in sufficient compaction adjacent to out let conduits, poor bond b/n embankment
& foundation or b/n successive layers of the embankment.
Conduit leakage: - failure may be either due to contact seepage along the conduit
or due to seepage caused by leakage in the conduit.
Sloughing: This occurs when the downstream portion of the dam becomes
saturated either due to choking or filter toe drain or due to presence of highly
pervious layer in the dam body.
III. Structural failure: - Consists of foundation slide and or embankment slide.
Foundation Slide: - When the foundation of soft soil such as fine silt, soft clay
etc. the entire dam may slide over the foundation. Partial failures of embankment
may also occur over part of the foundation where seams of fissured rock, shale’s
or soft clay may occur.
Embankment Slide: - When the embankment slopes are too steep for the
strength of the soil, they may slide causing dam failure. For the upstream slope
the critical condition is during sudden draw down and for the downstream slope
the full reservoir and steady seepage condition is the most critical.
3.3 Design Principles

Criteria for Safe Design of Earth Dam
29

An earth dam must be safe and stable during phases of construction and
operation of the reservoir. The practical criteria for the design of earth dams may
be stated briefly as follows.
No overtopping during occurrence of the inflow design flood.
appropriate design flood
Adequate spillway
Sufficient outlet works
Sufficient free board
No seepage failure
Phreatic (seepage) line should exit the dam body safely without sloughing
downstream face.
Seepage through the body of the dam, foundation and abutments should be
controlled by adapting suitable measures.
The dam and foundation should be safe against piping failure.
There should be no opportunity for free passage of water from U/S to D/S both
through the dam and foundation.
No Structural failure
Safe U/S & D/S slope during construction
Safe U/S slope during sudden draw down condition.
Safe D/S slope during steady seepage condition
Foundation shear stress within the safe limits.
Earth quake resistant dam
Proper slope protection against wind & rain drop erosion.
Proper drainage
Economic section
Selection of an Earth Dam
The preliminary design of an earth dam is done on the basis of past experience
and on the basis of the performance of the dams built in the past. We shall
discuss here the preliminary selection of the following terms:
Top width
Free board
Casing or outer shells
Central impervious core
Cut-off trench
Downstream drainage system.
Top width. The crest width of an earth dam depends on the following
considerations:
Nature of the embankment materials and minimum allowable percolation
distance through the embankment at the normal reservoir level.
Height of the structure
Importance of the structure
Width of highway on the top of the dam
Practicability of construction
Protection against earthquake forces.
Following are some of the empirical expressions for the top width b of the earth
30

dam, in terms of the height H of the dam:

For very low dam (H<10m)
1/2
b=0.55H + 0.2H For medium dam (10m<H<30m)
b=1.65(H+1.5)1/3 For large dam (H>30m)
Free board . Free board is the vertical distance between the horizontal crest of the
embankment and the reservoir level. Normal free board is the difference in the
level between the crest or top of the embankment and normal reservoir level.
Minimum free board is the difference in the elevation between the crest of the
dam and the maximum reservoir water surface that would result and spillway
function as planned. Sufficient free board must be provided so that there is no
possibility whatsoever of the embankment being overtopped.
The U.S.B.R suggests the following free boards:
Table 3.1: U.S.B.R practice for free board
Nature of spillway Height of dam Free Board

Free Any Minimum 2m and maximum 3m
over the maximum flood level
Controlled Less than 2.5 above the top of gates
Controlled Over 60m 3m above the top gates
Casing or outer shells. The function of casing or outer shells is to impart stability
and protect the core. The relatively pervious materials, which are not subjected to
cracking on direct exposure to atmosphere, are suitable for casing. Table 10.2 (a)
gives recommendations for suitability of soils used for earth dams as per IS:
8826-1978.
Table 3.2 (a) Suitability of Soils for Construction of Earth Dams
Relative Suitability Homogenou Zoned earth dam

s section Previous casing Impervious core
1. very suitable GC SW,GW GC
2. Suitable CL,CI GM CL,CI
3. Fairly suitable SP, SM,CH SP,GP CM,GC,SM SC,CH
4. Poor - - ML,MI,MH
3. Not suitable - - OL, NI, OH ,Pt
The design slopes of the upstream and downstream embankments may vary
widely, depending on the character of the materials available, foundation
conditions and the height of the dam. The slopes also depend up on the type of
the dam (i.e. homogeneous, zoned or diaphragm).
The upstream slope may vary from 2:1 to as flat as 4:1 for stability. A storage
31

dam subjected to rapid drawdown of the reservoir should have an upstream zone
with permeability sufficient to dissipate pore water pressure exerted outwardly in
the upstream part of the dam. If only materials of low permeability are available,
it is necessary to provide flat slope for the rapid drawdown requirement.
However, a steep slope may be provided if free draining sand and gravel are
available to provide a superimposed weight for holding down the fine material of
low permeability. The usual downstream slopes are 2:1, where embankment is
impervious.
Table 3.3 (b): Side slopes for earth dams according to Terzaghi
Type of material Upstream Downstream
slope slope
Homogeneous well graded 2:1 2:1
material
Homogeneous coarse silt 3:1
2 :1
Homogeneous silty clay or
clay 2:1
2 :1
H less than 15 m
2 :1
3:1
H more than 15 m
Sand or sand and gravel with 3:1
2 :1
clay core
Sand or sand and gravel with 2:1
2 :1
R.C core wall
Table 3.4 (c): Preliminary dimensions of earth dams (According to strange)
Height of dam Height of dam Top U/S D/S

above above H.F.L width slope slope
foundation (m) (m)
level (m)
Up to 4.5 1.2 to 1.5 1.8 1:1
1 :1
4.5 to 7.5 1.5 to 1.8 1.85
2 :1 2 :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
Seepage Analysis
Seepage analysis: is used
To determine the quantity of water passing through the body of the dam and
32

foundation.
To obtain the distribution of pore water pressure.
Assumptions to be made in seepage analysis
The rolled embankment and the natural soil foundation of the earth dam are
incompressible porous media. The size of the pore spaces do not change with
time, regardless of water pressure (Isotropic).
The seeping water flows under a hydraulic gradient which is due only to gravity
head loss, or Darcy’s law for flow through porous medium is valid.
There is no change in the degree of saturation in the zone of soil through which
the water seeps and the quantity flowing in to any element of volume is equal to
quantity which flows out in the same length of time.
(Steady flow)
The hydraulic boundary conditions at entry and exit are known.
Laplace equation for two dimensional flows

In earth dams, the flow is essentially two dimensional. Hence we shall consider
only two dimensional flows.
Vy+(∂Vy/∂y)Δy
Δy
Vx Vx+(∂Vx/∂x)Δx
Δx
Vy
Consider an element of soil is size x, y and of unit thickness perpendicular to
the plane of the paper. Let Vx and Vy be the entry velocity components in x and y
direction. Then
will be the corresponding velocity components at the exit of the element.

According to assumption 3 stated above, the quantity of water entering the
element is equal to the quantity of water leaving it. Hence, we get
From which
… (i)
This is the continuity equation.
According to assumption 2:
33

…. (ii)
And ….(iii)
Where h = hydraulic head under which water flows.

Kx and Ky are coefficient of permeability in x and y direction.
Substituting (ii) and (iii) in (i), we get
… (3.1)
For an isotropic soil,

Ky = Kx = K
Hence we get from eq. (3.1)
Substituting velocity potential =  = K*h , we get

… (3.2)
This is the Laplace equation of flow in two dimensions. The velocity potential 
may be defined as a scalar function of space and time such that its derivative
with respect to any direction gives the fluid velocity in that direction.
This is evident, since we have
=Kh
The solution of Eq. 3.2 can be obtained by

analytical methods
graphical method
experimental methods
The solution gives two sets of curves, know as equipotential lines and stream
lines (or flow lines), mutually orthogonal to each other, as shown in Fig. below.
The equipotential lines represent contours of equal head (potential). The
direction of seepage is always perpendicular the equipotential lines. The paths
along which the individual particles of water seep through the soil are called
stream lines or flow lines.
34

Figure 3.6: Flow net

Computation of rate of seepage from flow net
A network of equipotential lines and flow lines is known as a flow net. Fig.3.6
shows a portion of such a flow net. The portion between any two successive flow
lines is known as flow channel. The portion enclosed between two successive
equipotential lines and successive flow lines is known as field such as that
shown hatched in Fig. 3.6.
Let: b and l be the width and length of the field.
h = head drop through the field.
q = discharge passing through the flow channel.
H = total head causing flow
= difference between upstream and downstream heads
Then, from Darcy’s law of flow through soils:
… (i) (Considering unit thickness)
If Nd = total number of potential drops in the complete flow net,
Then
… (ii)
Hence the total discharge through the complete flow net is given by
Where Nf = total number of flow channels in the net. The field is square and
hence b=l
Thus,
This is the required expression for the discharge passing through a flow net, and
is valid only for isotropic soils in which
Phreatic Line in Earth Dam

Phreatic line / seepage line / Saturation line is the line at the upper surface of
35

the seepage flow at which the pressure is atmospheric.
Figure 3.8: Phreatic line in Earth dam

Phreatic line for a homogeneous Earth dam with horizontal
Drainage blanket
Figure below shows a homogeneous earth dam with horizontal drainage blanket
FK at its toe. The phreatic line in this case coincides with the base parabola ADC
except at the entrance. The basic property of the parabola which is utilized for
drawing the base parabola is that the distance of any point p from the focus is
equal to the distance of the same point from the directrix. Thus
Distance PF = Distance PR where, PR is the horizontal distance of P from
the
Directrix EG
Figure 3.9
Graphical method
Steps:
Starting point of base parabola is @ A AB = 0.3L
F is the focal point
Draw a curve passing through F center @ A
Draw a vertical line EG which is tangent to the curve
EG is the directrix of the base parabola
Plot the various points P on the parabola in such a way that PF = PR
Analytical method
PF = PR
From point A (known), x = b and y = h
36

Equation of parabola … (3.6)

Discharge through the body of Earth dam
From parabola equation,
…………. (3.7)
Phreatic line for a dam with no filter

General solution by Casagrande
Figure below shows a homogeneous dam with no horizontal drainage filter at the
d/s side. The focus in this case will be the lowest point F of the d/s slope.
Fig 3.10: Dam with no drainage filter.

And the base parabola BKC will evidently cut the d/s slope at K and extend
beyond the limits of the dam, as shown by dotted line. However, according to exit
conditions, the phreatic line must emerge out at some point M, meeting the d/s
face tangentially at J. The portion JF is then known as discharge face and always
remains wet. The correction a, by which the parabola is to be shifted
downwards, is found by the value of given by Casagrande for various
values of the slope of the discharge face. The slope angle  can even exceed
the value of 900. Thus we observe that
= value found from table … (i)
a+ a=KF from Fig 3.10 … (ii)

Solving (i) and (ii), the value a and a can be found.
Table for the value of with slope angle 
37

0
30 0.36
600 0.32
900 0.26
1200 0.18
1350 0.14
1500 0.10
1800 0.0
Discharge through the body of Earth dam
Figure 3.11
a. Analytical Solution of Schaffernak and Van Iterson for < 300 (Fig.3.11)
In order to find the value of a analytically, Schaffernak and Van Iterson assumed
that the energy gradient
This means that the gradient is equal to the slope of the line of
seepage, which is approximately true so long as the slope is gentle (i.e. <300).
For the vertical section JJ1
but
and y= JJ1= a sin 

Substituting in (i), we get
q = k (a sin) (tan) … (3.8)

This is the expression for discharge.
Again
Integrating between the limits:

38

x= a (Cos ) to x = b
y= a (sin  ) to y = h , we get
and
From which, we obtain, after simplification,
… (3.9)
b. Analytical solution of Casagrande for 300< <600

It will be observed that the previous solution gives satisfactory results for slope <
300. For steeper slopes, the deviation from correct values increases rapidly
beyond tolerable limits. Casagrande suggested the use of sin  instead of tan.
In other words, it should be taken as (dy/ds) instead of (dy/dx), where s is the
distance measured along the phreatic line.
Figure 3.12
Thus (3.10)
At J, s= a and y = a sin  then,

Where s = distance measured along the curve.
Substituting in (3.10), we get
q = k. (sin) (a sin ) = k(a sin2) …(3.11)
This is the expression for the discharge.
Again
 a (sin2 ) ds = ydy
Integrating between the following limits (s = a to s =S)
Where S = total length of the parabola
And (y = a sin to y=h), we get
39

From which …. (3.12)
Taking S (h2+b2)1/2 we get
… [3.13]
Phreatic line for homogenous Earth dam with rock toe
Figure 3.13
Phreatic line for zoned Earth dam with central core
Figure 3.14
Characteristics of Phreatic line (Seepage line)
Based on the above discussions, the characteristics of the phreatic line may be
summarized below:
At the entry point, the phreatic line must be normal to the upstream face since
the upstream face is a 100% equipotential line. For other entry condition
40

(Fig.3.15), the phreatic line starts ta11ngentially with the water surface.
Fig 3.15: Entry conditions of phreatic line

The pressure along the phreatic line is atmospheric. Hence the only change in the
head along it is due to drop in the elevation of various points on it. Due to this,
the successive equipotential lines will meet it at equal vertical intervals.
The focus of the base parabola lies at the break out point of the bottom flow line,
where the flow emerges out from relatively impervious medium to a highly
pervious medium.
When horizontal filter or drainage toe is provided, the phreatic line would tend to
emerge vertically.
In the absence of any filter, the seepage line will cut the downstream slope at
some point above the base. The location of this point, and the phreatic line itself,
is not dependent on the permeability or any other property, so long as the dam is
homogeneous. The geometry of the dam alone decides these.
The presence of pervious foundation below the dam does not influence the
position of phreatic line.
In the case of a zoned dam with central impervious core, the effect of outer
shells can be neglected altogether. The focus of the base parabola will be
located at the downstream. Toe of the core (Fig. 3.14)
Graphical determination of flow net
After having located phreatic line in an earth dam the flow net can be plotted by
trial and error by observing the following properties of flow net (Fig 3.16), and by
following the practical suggestions given by A Casagrande.
41

Fig 3.16: Flow net by graphical

Properties of flow net
The flow lines and equipotential lines meet at right angles to each other.
The fields are approximately squares, so that a circle can be drawn touching all
the four sides of square.
The quantity flowing through each flow channel is the same similarly, the same
potential drop occurs between two successive equipotential lines.
Smaller the dimensions of the field, greater will be the hydraulic gradient and
velocity of flow through it.
In a homogeneous soil, every transition in the shape of curves is smooth, being
either elliptical or parabolic in shape.
Stability Analysis
Stability analyses under the following four heads are generally needed:
Stability analysis of down stream slope during steady seepage.
Stability of up stream slope during sudden Draw down.
Stability of up stream & down stream slope during and immediately after
construction.
Stability of foundation against shear.
Swedish Circle Method of Slope Stability
It is one of the most generally accepted methods of checking slope stability. In
this method the potential surface is assumed to be cylindrical, and the factor of
safety against sliding is defined as the ratio of average shear strength, as
determined by Coulomb’s equation S = C +  tan to the average shearing stress
determined by static’s on the potential sliding surface. In order to test the
stability of the slope, a trial slip circle is drawn, and the soil material above
assumed slip surface is divided in to a convenient number of vertical strips or
slices. The trail sliding mass (i.e. the soil mass contained with in the assumed
failure surface) - is divided in to a number (usually 5 to8) of slices which are
usually, but not necessarily, of equal width. The width is so chosen that the chord
and arc subtended at the bottom of the slice are slice passes through material of
one type of soil.
The forces between the slices are neglected and each slice is assumed to act
independently as a column of soil of unit thickness and width b. The weight W of
42

each slice is assumed to act at its centre. If this weight of each slice is resolved
in normal (N) and tangential (T) components, then the normal component will
pass through the center of rotation (O), and hence does not cause any driving
moment on the slice. However, the tangential component T cause a driving
moment = T (T*r), Where r is the radius of the slip circle. The tangential
components of the few slices at the base may cause resisting moment; in that
case T is considered negative.
If c is the unit cohesion and L is the curved length of each slice, then resisting
force from Column’s equation is = c L + N tan
For the entire slip surface AB, we have
Driving moment Md = rT
Resisting moment Mr. = r Where T = sum of all tangential
components
N = sum of all normal
components
L= L= length AB of slip circle r =the radius of the entire slip
circle
Hence factor of safety against sliding is c = the unit cohesion
= ….(3.14)
43

Figure 3.17: A portion of slip surface for slices

Method of locating center of critical slip circle
Fellenius gave the method of locating the locus on which probable centers of
critical slip circle may lie. He gives direction angles to be plotted at heel
measured from the outer slope and to be plotted from horizontal line above the
top surface of the dam. These two lines plotted with given direction angle
intersect at point P. Point P is one of the centers. To obtain the locus we obtain
point Q by taking a line H m below the base of the dam and 4.5 H m away from
toe. When the line PQ is obtained, trial centers are selected around P on the line
PQ and factor of safety corresponding to each centre calculated from Equation
given above as ordinates on the corresponding centers, and a smooth curve is
obtained. The centre corresponding to the lowest factor of safety is then the
critical centre.
44

Figure 3.18: Location of center of critical slip circle

Stability of downstream slope during steady seepage
Critical condition for d/s slope occurs when the reservoir is full and percolation is
at its maximum rate. The directions of seepage forces tend to decrease stability.
In other words, the saturated line reduces the effective stress responsible for
mobilizing shearing resistance.
….. (3.15)
When U is the total pore pressure on the slope surface
Fig 3.19: Stability of downstream slope during steady seepage

The pore-water pressure at any point is represented by the piezometric head (hw)
at that point. Thus the variations of pore water pressure along a likely slip
surface is obtained by measuring at each of its intersections with an
equipotential line, the vertical height from that intersection to the level at which
the equipotential line cuts the phreatic line. The pore pressure represented by
vertical height so obtained are plotted to scale in a direction normal to the sliding
surface at the respective point of intersection. The distribution of pore water
pressure on the critical slope surface during steady seepage is shown hatched in
fig.3.19.The area of U- diagram can be measured with help of a planimeter.
In the absence of a flow net, the F.S of the d/s slope can approximately be from
45

the equation
… (3.16)
The following unit weights may be used for the calculation of and whe
n pore pressure are otherwise not included in the stability analysis, however the
Phreatic line needs to be drawn.
Location Driving force Resisting force

Below phreatic surface Saturated weight Submerged weight
Above phreatic surface Moist weight Moist weight
46

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Design Principles of Dam 2016

2.1 Concrete Dams

2.1.1 Forces Acting on Concrete dams

Primary loads: are identified as those of major importance to all dams

Where w unit weight of water =9.81 KN/m3

Hydraulic Structures-I for G3CE

must also be considered in determining Pm & their appropriate position of line of

iii. Seepage & uplift load:

 is area reduction factor

In modern dams internal uplift is controlled by the provision of vertical relief

s’ = s-w where s is sediment saturated unit weight.

Where: s is angle of shearing resistance.

Hydraulic Structures-I for G3CE

For representative values of s 18-20KN/m3

Fig. 2.1 Gravity dam loading

Hydrodynamic wave Load

Fig. 2.2 Hydrodynamic wave

Hydraulic Structures-I for G3CE

the wave in train)

U= wind speed in km/hr

Horizontal foundation acceleration operating u/s, and

Seismic coefficient analysis

Representative seismic coefficient applied in design

Hydraulic Structures-I for G3CE

Inertia forces: Mass of dam

Hydrodynamic forces: water action

Zmax= Max. Water depth

Total hydrodynamic load is given by.

pressure factor Ce.

Hydraulic Structures-I for G3CE

DESIGN AND ANALYSIS OF GRAVITY DAMS

Assessed in relation to all probable conditions of loading, including reservoir

Fo > 1.25 may be acceptable, but Fo > 1.5 is desirable.

Hydraulic Structures-I for G3CE

But for the foundation plane inclined @ small angle o

Hydraulic Structures-I for G3CE

Ww =weight of passive wedge.

This is affected by modifying the above equation, hence,

Recommended shear friction factor, FSF (USBR 1987).

C. Limit Equilibrium factor, FLE.

is expressed by Mohr Columb’s failure criteria, accordingly

is stress acting normal to plane of sliding

Hydraulic Structures-I for G3CE

Note for  = 0 FLE =FSF.

C. Stress analysis in gravity method

The stresses evaluated in a comprehensive analysis are:

1. Vertical normal stress z.

For reservoir full condition

At the d/s face

Hydraulic Structures-I for G3CE

Where v - excludes uplift

2. Horizontal & vertical shear stresses

3. Horizontal normal stress, y

Major Principal Stress

Hydraulic Structures-I for G3CE

Minor principal stress

The boundary values, 1 & 3 are determined by:

Permissible stresses & cracking

load combination Minimum factor of safety on compressive