Gravity dams

ABSTRACT
Gravity dams are solid concrete structures that maintain their
stability against design loads from the geometric shape, mass and
strength of the concrete The three-dimensional flow in continuous
permeable rocks under concrete dams is discussed particularly the
influence of the drains in the determination of the uplift pressures
needed for stability analysis. Proper consideration of the uplift
pressure at the base of a concrete gravity dam is of great importance
in practical engineering, since it is crucial to the safety of the dam,
specifically for a cracked dam under seismic conditions. However,
constant uplift pressure, which is suitable for the static case only,
was adopted in almost all the seismic analyses of cracked concrete
gravity dams. To adequately estimate the seismic behavior of
cracked concrete gravity dams, a seismic uplift pressure model is
proposed for a penetrated crack. In this model, the amount and the
distribution of the uplift pressure along the assumed rigid crack walls
are determined by the earthquake acceleration, the water heads, the
aperture of the crack, and the opening/closing velocity. Application
of the model to a typical concrete gravity dam with a penetrated
crack at the base reveals that the seismic behavior of the dam is
markedly affected by the seismic uplift pressure. In general, the
residual downstream sliding is considerably enlarged compared to
that of constant uplift pressure. Computations show that the seismic
uplift pressure can be several times higher than the constant one,
increasing the dynamic instability of the cracked dam. It is also
revealed that the dynamic water flow plays the role of a wedge while
the upper mouth of the crack is closing. When the dam rocks back to
upstream, the uplift pressure increases until it is so high that the
pivot at the toe is raised up and the whole dam loses its contact.
Then the resultant uplift pressure remains constant until the dam is
inclined to the upstream. During this period of time, the cracked dam
is normally drifting towards the downstream due to the hydro
pressure.

CONTENTS
1. INTRODUCTION
2. TYPES OF DAMS
3. FORCES ON GRAVITY DAM
a. WATER PRESSURE FORCE
b. UPLIFTPRESSUREFORCE
c. SILTPRESSUREFORCE
d. ICEPRESSURE FORCE
e. WAVEPRESSURE FORCE
f. EARTHQUAKEFORCES
g. WIND PRESSUREFORCE
h. SELF WEIGHTOF DAM
4. CONCLUSION
5. REFERENCES

INTRODUCTION
A Dam is a structure built across a river for the impoundment of water.
It is one of the main works of the civil engineering. It takes years to
complete and its cost run in Crores. Thus it needs to be designed in
such a way that it is economical as well as safe. For the designing of
the Dam we need to determine forces acting on a Dam and their line
of action. The various forces acting on a Dam include
1.Weight of Dam
2. Water pressure force
3.Uplift pressure force
4.Earthquake forces
5.Silt pressure force
6.Wind pressure force
7.Wave pressure force
Weight of the Dam is the main stabilizing force in Gravity Dam which
holds the Dam. The water pressure which acts laterally is the main de-
stabilizing force which tends to overturn the Dam. Due to presence of
pores in the Dam and at its foundation gives rise to the Uplift pressure
which reduces the weight of the Dam. The Wave pressure arises when
the winds blow over Dam. Due to the Silting, the silt exerts a pressure
same as that of backfill in the retaining wall. In the earthquake prone
zones, earthquake forces shall also be determined. Earthquake can
impart either vertical or horizontal acceleration on the Dam and the
water stored. If there are fast blowing winds, wind pressure shall also
be considered in the design of the Dam.

GRAVITY DAM
A dam is a barrier that stops or restricts the flow of water or
underground streams. Reservoirs created by dams not only` suppress
floods but also provide water for activities such as irrigation, human
consumption, industrial use, aquaculture, and navigability.
Hydropower is often used in conjunction with dams to generate
electricity. A dam can also be used to collect water or for storage of
water which can be evenly distributed between locations. Dams
generally serve the primary purpose of retaining water, while other
structures such as floodgates or levees (also known as dikes) are used
to manage or prevent water flow into specific land regions.
There are vrious types of Dams.On the basis of their structural
behaviour they are classified as:
 GRAVITY DAM
 EARTHEN DAM
 ROCKFILL DAM
 ARCH DAM
GRAVITY DAMS
`In a gravity dam, the force that holds the dam in place against the
push from the water is Earth's gravity pulling down on the mass of
the dam. The water presses laterally (downstream) on the dam,
tending to overturn the dam by rotating about its toe (a point at the
bottom downstream side of the dam). The dam's weight counteracts

that force, tending to rotate the dam the other way about its toe.
The designer ensures that the dam is heavy enough that the dam's
weight wins that contest. In engineering terms, that is true whenever
the resultant of the forces of gravity acting on the dam and water
pressure on the dam acts in a line that passes upstream of the toe of
the dam.
Furthermore, the designer tries to shape the dam so if one were to
consider the part of dam above any particular height to be a whole
dam itself, that dam also would be held in place by gravity. i.e. there
is no tension in the upstream face of the dam holding the top of the
dam down. The designer does this because it is usually more
practical to make a dam of material essentially just piled up than to
make the material stick together against vertical tension.
Note that the shape that prevents tension in the upstream face also
eliminates a balancing compression stress in the downstream face,
providing additional economy.
For this type of dam, it is essential to have an impervious foundation
with high bearing strength.
When situated on a suitable site, a gravity dam can prove to be a
better alternative to other types of dams. When built on a carefully
studied foundation, the gravity dam probably represents the best
developed example of dam building. Since the fear of flood is a
strong motivator in many regions, gravity dams are being built in
some instances where an arch dam would have been more
economical.
Gravity dams are classified as "solid" or "hollow" and are generally
made of either concrete or masonry

A Gravity Dam is a dam constructed from concrete or stone masonry
and designed to hold back water by primarily utilizing the weight of
the material alone to resist the horizontal pressure of water pushing
against it. Gravity dams are designed so that each section of the dam
is stable, independent of any other dam section.
Gravity dams generally require stiff rock foundations of high bearing
strength (slightly weathered to fresh); although they have been built
on soil foundations in rare cases. The bearing strength of the
foundation limits the allowable position of the resultant which
influences the overall stability. Also, the stiff nature of the gravity
dam structure is unforgiving to differential foundation settlement;
which can induce cracking of the dam structure

FORCES ACTING ON A GRAVITY DAM
In the design of a dam, the first step is the determination of various
forces which acts on the structure and study their nature. Depending
upon the situation, the dam is subjected to the following forces:
1. WATER PRESSURE FORCE
2. UPLIFT PRESSURE FORCE
3. SILT PRESSURE FORCE
4. ICE PRESSURE FORCE
5. WAVE PRESSURE FORCE
6. EARTHQUAKE FORCES
7.WIND PRESSURE FORCE
8.SELF WEIGHT OF THE DAM

WATER PRESSURE FORCE
Water pressure (P) is the most major external force acting on such a
dam. The horizontal water pressure, exerted by the weight of the
water stored on the upstream side on the dam can be estimated
from rule of hydrostatic pressure distribution ; which is triangular in
shape. When the upstream face is vertical, the intensity is zero at the
water surface and equal to WH at the base ; where W is the unit
weight of water and H is the depth of water. The resultant force due
to this external water 1/2 WH2
, acting at H/ 3 from base.

When the upstream face is partly vertical and partly inclined the
resulting water force can be resolved into horizontal component and
vertical component. The horizontal component 1/2WH2
acts at H/3
from the base ; and the vertical component can be calculated as the
weight of water acting through the cg. For convenience the inclined
surface is divided into some simple figures, in order to calculate the
area. The weight of water per unit length is calculated as the product
of area water stored and specific weight of the water
Where,
PH=Horizontal Pressure acting per unit length of Dam
PV=Vertical component of pressure acting per unit length Dam

UPLIFT PRESSURE FORCE
When a concrete dam impounds a body of water, it will experience a
load or force commonly referred to as Hydrostatic Pressure. A variety
of other forces such as Uplift pressure, earth pressure, silt pressure,
wave pressure, wind pressure, ice pressure, seismic acceleration,
hydrodynamic pressure, and thermal stress from ambient
temperature changes can also act on the dam depending upon
site conditions. Though it is imperative to analyze all applicable force
combinations specific to a given site when evaluating an
existing gravity dam or designing a new one, history has proven that
the consideration of uplift pressure is especially important.
Uplift is an active force that exists within both the foundation and
the concrete structure itself. This pressure is present in cracks, pores,
and joints of the concrete within a dam, at the interface between the
dam and the foundation, and in cracks, pores, and seams within the
foundation rock. Large uplift pressures can compromise the
structural adequacy of concrete gravity dams and serve as
the principal cause of failure. Because uplift pressures can greatly
impact the stability of concrete gravity dams, they must be analyzed
and accounted for during design and evaluation of such structures.
Uplift depends upon :
Area factor : Initially it was assumed that the uplift pressure occurs
on only 1/3 to 2/3 area but later on different experiments were
carried out by Terzaghi etc and it was assumed that uplift pressure
occurs on entire horizontal area.

Intensity of pressure : Uplift pressure corresponds to the depth of
the water. At the upstream face at the base of dam it corresponds to
the full depth of water, while as at the downstream face it
corresponds to the tail water depth. If tail water depth is zero then
uplift pressure at the downstream face is zero. It varies linearly from
upstream face to downstream face.
Direct reduction of uplift pressures can be accomplished by the
incorporation of a drain curtain, also known as drainage or relief wells.
These internal drainage systems consist of a series of vertical or
vertically-inclined wells or boreholes that facilitate the draining of the
foundation and abutments in order to relieve the uplift pressure
caused by impounded water. Effectiveness in reducing
uplift pressures through drainage systems is dependent upon drain
hole size, depth, spacing, and maintenance as well as the character

of the foundation. In addition, a grout curtain positioned upstream of a
drain curtain within the dam’s base can also facilitate the reduction of
uplift pressures by eliminating or decreasing the number of seepage
paths.
To address the potential for highly variable nature of foundation rock
and concrete properties as well as construction quality within a given
structure “the current design practice [for estimating uplift pressures in
concrete gravity dams] relies heavily on simple empirical rules… It is
assumed that uplift pressure at the base of a dam without drains
varies linearly from full reservoir pressure at the heel to tailwater at the
toe. For dams with foundation drains, the pressure is assumed to
follow a bi-linear tailwater plus some fraction of the difference between
headwater and tailwater at the line of drains, to tailwater at the toe.
Prior to the 1920s, many gravity dams in the United States were
designed without any allowance for uplift. The general view was that
uplift could not develop at the base of a gravity dam to any significant
degree since the dam by its own weight placed the structure in positive
contact with its foundation. After some highly publicized dam failures in

the early 1900s, engineers began to pay more attention to accounting
for this force. At that time, the practice consisted of two components.
The first component related to “uplift intensity” which assumed that
uplift varied linearly from full reservoir pressure at the upstream face to
zero or tailwater pressure at the downstream face. The second
component related to the proportion of the horizontal area of the
structure’s base or partial section above the base in which uplift acted
upon. Depending upon foundation rock characteristics and whether or
not grout and drain curtains were to be included, uplift intensity was
applied to one-third, one-half, two-thirds, or the full horizontal base
area. It wasn’t until the 1950s that engineers began to adopt the more
conservative approach of applying uplift to the full base area
regardless of whether or not grout and drain curtains were to be
included. Since uplift can be a significant destabilizing force, any design
or evaluation should properly account for it. In certain cases, it may be
appropriate to install instrumentation to measure and confirm the
validity of uplift assumptions.
Remnants of Austin (Bayless) Dam one day after failure. The dam's failure
due to sliding can be directly attributable to the designer admittedly
neglecting to account for uplift pressure due to a misguided approach in
crediting certain design features with the ability to completely eliminate this
force.

SILT PRESSURE FORCE
All rivers contain sediments: a river, in effect, can be considered a
body of flowing sediments as much as one of flowing water. When a
river is stilled behind a dam, the sediments it contains sink to the
bottom of the reservoir. The proportion of a river’s total sediment
load captured by a dam – known as its "trap efficiency" – approaches
100 per cent for many projects, especially those with large reservoirs.
As the sediments accumulate in the reservoir, so the dam gradually
loses its ability to store water for the purposes for which it was built.
Every reservoir loses storage to sedimentation although the rate at
which this happens varies widely. Despite more than six decades of
research, sedimentation is still probably the most serious technical
problem faced by the dam industry.
CAUSES :
The origin of the increased sediment transport into an area may be
erosion on land, or activities in the water.
In rural areas the erosion source is typically soil degradation due to
intensive or inadequate agricultural practices, leading to soil erosion,
especially in fine-grained soils such as loess. The result will be an
increased amount of silt and clay in the water bodies that drain the
area. In urban areas the erosion source is typically construction
activities, since this involves clearing the original land-covering
vegetation and temporarily creating something akin to an urban
desert from which fines are easily washed out during rainstorms.
In water the main pollution source is sediment spill from dredging,
from the transportation of dredged material on barges, and the
deposition of dredged material in or near water. Such deposition
may be made to get rid of unwanted material, such as the offshore
dumping of material dredged from harbours and navigation

channels. The deposition may also have as purpose to build up the
coastline, artificial islands, or for beach replenishment.
Climate change also affect siltation rates.
The silt elevation should be determined by hydrographic surveys.
Vertical pressure exerted by saturated silt is determined as if silt were
a saturated soil. The magnitude of pressure varies directly with the
depth. Horizontal pressure exerted by the load is calculated in the
same manner as submerged earth backfill.
acting at from the base. Where,
= coefficient of active earth pressure of silt =
= angle of internal friction of soil, cohesion neglected.
= submerged unit weight of silt material.
h = height of silt deposited

If the upstream face is inclined, the vertical weight of the silt
supported on the slope also acts as a vertical force.
In the absence of any reliable data for the type of silt that is going
to be deposited, U.S.B.R. recommendations may be adopted. In
these recommendations, deposited silt may be taken as
equivalent. to a fluid exerting a force with a unit wt. equal to 3.6
lcN/m3
in the horizontal direction and a vertical force with a unit
wt. of 9.2 kN/m 3. Hence, the total horizontal force will be 3 . 6%
= 1.8 h 2
kN/m run, and vertical force will be 9 2. 4=4.6 h 2
kN/m
run.
In most of the gravity-dam designs, the silt pressure is neglected.
The basis for neglecting this force is that :
Initially, the silt load is not present, and by the time itbecomes
significant, it gets consolidated to some extent and, therefore,
acts less like a fluid. Moreover, silt deposited in the reservoir is
somewhat impervious and, therefore, will help to minimise the
uplift under the dam.

ICE PRESSURE FORCE
Formation of a thick sheet of ice occurs in winter in cold
countries where the air current temperatures go as low as to 10°F. In
such case, ice sheet forms on the top surface of the sheet will be at
the temperature of blowing wind well below the freezing point, while
the temperature varies from below the freezing point at the top to
+32°F at the bottom surface. If the sides of the dam provide restraint,
then the pressure exerted will be comparatively more, than when the
sides do not provide any constraint
Where the dam is provided with an overflow spill way, the spill
way crest is usually some distance below the maximum water level.
The maximum level occurs only at times of maximum flow and a
solidly frozen sheet at that time is highly improbable. It is usual to
assume that the worst ice condition will occur only with water at the
spill way lip.
Nothing is known of the action of ice during an earth quake, and its
earth-quake effect on the stability of the dam is ignored.
The thrust exerted by expanding Ice sheet varies with the thickness
of Ice sheet, air temperature rise, and the restraint. The magnitude of
this force varies from 250 to 1500 kN/m 2

WAVE PRESSURE FORCE
The upper portions of dams are subject to the wave action; the
dimensions of the waves depend upon the extent of the water (Fetch)
surface and the velocity of wind.
A knowledge of the wave heights is important, if over-topping by waves
is to be avoided.
MOLITER, STEVENSON’S FORMULA FOR WAVE HEIGHT
IfV is the velocity of the wind in KM/hour and F is the fetch in kilometers,
then the height of the wave is given by
hw 0.032 Rt(VF) + 0.763 0.271F1/4
And when F > 32 km, then hw = 0.032 Rt(VF)
Where ‘hw’ is the height of the wave, from the trough to the crest,
and 2/3 ‘h of the crest of the wave above the still water level. Free board
for the dam should be at least 1.5 times the wave height ‘hw’. When the
wave vertical force hits of the dam, again rides up the face of the dam to
a height of 1/3 ’hw’ above the still water level as shown in the
figure. for earth dams having flat slopes, it is assumed that the waves
ride up the slope, a vertical distance above the still water to level, 1.4 ‘hw’.
The maximum wave pressure to Pw occurs at 0.125 hw above the still
water level and is given by the equation
Pw = 2.4whw or Pw = 24 hw (in Kilopascals)
The total wave force is given by Pw = 2 w hw2 or Pw = 20 hw2 (n
kilo Newtons) and acts
at 0.375 hw above still water level, where ‘w’ is t
And hw is height of wave in metres.

where hw = height of water from top of crest to bottom of trough
in metres.
V = wind velocity in km/hr
F = Fetch or straight length of water expanse in km.
The maximum pressure -intensity-due to wave-action may be given
by
PW = 2.4 hw and acts at hw/2 metres above the still water surface.
The pressure distribution may be assumed to be triangular, of height
5hw/3
The total wave force is given by
Pw = 2 w hw2 or Pw = 20 hw2 (n kilo Newtons)
And acts at 0.375 hw above still water level where ’w’ is
specific gravity of water and ‘hw’ is height of wave in meters.

EARTHQUAKE FORCES
If the dam to be designed, is to be located in a region which is
susceptible to earthquakes, allowance must be made for the
stresses generated by the earthquakes.
An earthquake produces waves which are capable of shaking the
Earth upon which the dam is resting, in every possible direction.
The effect of an earthquake is, therefore, equivalent to
imparting an acceleration to the foundations of the dam in the
direction in which the wave is travelling at the moment. Earthquake
wave may move in any direction, and for design purposes, it has to
be resolved in vertical and horizontal components. Hence, two
accelerations, i.e. one horizontal acceleration (Uh) and one vertical
these generally expressed as percentage of the acceleration due-to
gravity
In India, the entire country has been divided into five seismic zones
depending upon the severity of the earthquakes. Zone V is the most
serious zone and includes Himalayan regions of North India. A map
and description of these -zones is available in "Physical and
Engineering Geology" (1999 edition) by the same author, and can be
referred to, in order to obtain an idea of the value of the (1 which
should be chosen for designs. On an average, a value of α equal to 0.1
to 0.15 g is generally sufficient for high in seismic zone. However, for
areas not subjected to extreme earthquakes, α = 0.1 g and 04=0.05 g
may by used. In areas of no earthquakes or very less earthquakes,
these forces may be neglected. In extremely seismic regions and in
conservative designs, even a value upto 0.3 g may sometimes be
adopted.

Effect of vertical acceleration : A vertical acceleration may
either act downward or upward. When it is acting in the upward
direction, then the foundation of the dam will be lifted upward and
becomes closer to the body of the dam, and thus the effective
weight of the dam will increase and hence, the stress developed
will increase.
When the vertical acceleration is acting downward, the
foundation shall try to move downward away from the dam body
thus reducing the effective weight and the stability of the dam, and
hence is the worst case for designs.
Such acceleration will, therefore, exert an inertia force given by
In other words vertical acceleration reduces the unit weight of Dam
material

Hydrodynamic pressures : Horizontal acceleration acting towards the
reservoir causes a momentary increase in the water pressure, as the
foundation and dam accelerate towards the reservoir and the water
resists the movement owing to its inertia. The extra pressure exerted
by this process is known as hydrodynamic pressure.
According to Von-Karman the amount of this hydrodynamic pressure
Pe is given by:
Pe=0.455khW. H2
It acts at the height of 4h/3π from the base
Kh=fraction of gravity adopted
W=unit weight of water

WIND PRESSURE FORCE
The top exposed portion of the Dam is small and hence the wind
pressure is negligible, however in the areas which are prone to speedy
winds an allowance should be made in the designing of the Dam. In
these areas about 150kg/m2 for the exposed surface area of the
upstream and downstream faces should be considered.

SELF WEIGHT OF THE DAM
The weight of dam is the main stabilizing force in case of gravity dams..
Technically a concrete gravity dam derives its stability from the force
of gravity of the materials in the section and hence the name. The
gravity dam has sufficient weight so as to withstand the forces and the
overturning moment caused by the water impounded in the reservoir
behind it. It transfers the loads to the foundations by cantilever action
and hence good foundations are pre requisite for the gravity dam. The
weight of dam per unit length is calculated as the product of the
specific weight of concrete and area of dam. For convenience the dam
is divided into simple set of geometrical areas to calculate area and
their center of gravity. Weight is calculated as the product of the area
and specific weight. It acts through center of gravity. For the
preliminary purposes the specific weight of concrete may be taken as
24kN/m³,however for the detailed study the specific weight of
concrete is experimentally found which depends on different
properties of concrete like proportioning, water-cement ratio, specific
weight of aggregate etc.

CONCLUSION
The correct calculation of the forces on the dam is the main aim of
engineers in the analysis of dam since it helps in the cost
minimization. Furthermore, the realistic calculation of loads may
reduce the chances of dam failure which otherwise may cause
heavy damage both to life as well as property. that it is the most
economic section and satisfies all the conditions and
requirements of stability. The preliminary dam section is selected
based on the U.S.B.R. recommendations, and the stability and
stress conditions of the high concrete gravity dam are
approximated and analyzed for varying horizontal earthquake
intensity and unvarying other loads, using two-dimensional
gravity method and finite element method. The horizontal earth-
quake intensities are perturbed from 0.10 g - 0.30 g with 0.05g
increment, keeping other loads unchanged, to calculate the total
horizontal and vertical forces and moments at the toe of the
gravity dam, and to examine the stability and stress conditions of
the dam using the two methods. Dealing with the U.S.B.R.
recommended initial dam section, the stabilizing moments are
found to de- crease significantly with the increment of horizontal
earthquake intensity, indicating endanger to the dam stability,
thus larger dam section is designed to increase the stabilizing
moments and to make it safe against failure. The results of the
horizontal earthquake intensity perturb- bation suggest that the
stability of the gravity dam en- dangers with the increment of
horizontal earthquake intensities unless the dam section is
enlarged significantly.

REFERENCES
1. Design of Gravity Dams, Bureau of Reclamation,1976
2. Design of Small Dams, Bureau of Reclamation, 1987
3. Gravity Dam Design,
4. U.S. Army Corps of Engineers, EM 1110-2-2200, June 1995
5. U.S. Army Corps of Engineers, ‘Gravity Dam Design’
Engineering Manual,EM 1110-2-2200,
6. Irrigation Water Power & Water Resource Engineering By
KR Arora
7. Irrigation Engineering and Hydraulic Structures by Santosh
Kumar Garg

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