1. ZAKIR HUSSAIN COLLEGE OF ENGINEERING & TECHNOLOGY
ALIGARH MUSLIM UNIVERSITY
Certificate
This to certify that the project entitled " Design Of Concrete Gravity Dam "
being submitted by SYED MOHD. SALMAN NAQVI, MD GULNAWAZ
KHAN, ABDUL HANNAN KHAN, MOHD. JUNAID KHAN, ADIL NISHAT in
partial fulfilment of the requirement for the award of degree of
BACHOLAR OF ENGINEERING in Civil Engineering from “Zakir Husain
College of Engineering and Technology”, ALIGARH MUSLIM
UNIVERSITY. This is record of candidate's own work carried out under our
supervision and guidance of the undersigned during the session 2014-15.
Dr. Javed Alam Prof. Mohd. Athar Alam
(Dept.Of Civil Engineering) (Dept. Of Civil Engineering)

2. Dedicated to Engineers
DEPARTMENT OF CIVIL ENGINEEERING
ZAKIR HUSSAIN COLLEGE OF ENGG. & TECH.
ALIGARH MUSLIM UNIVERSITY
ALIGARH(U.P), 202002 – INDIA

3. Acknowledgement
I owe my deep sense of gratitude to my teachers Dr.Javed
Alam and Prof. Mohd. Athar Alam, Department of civil
engineering, A.M.U, Aligarh. They have been moving
sprit behind all my efforts in executing the present work
and encouraged us by making scholarly suggestions and
furtherance of this work. Despite their fully busy schedule
they spared their valuable time to go through and
scrutinize our project work. Their scholastic corrections
furnish adequate guidelines. I express my profound sense
of obligation to them.
It would be deemed an act of ingratitude if I
fail to take this opportunity to thank all the civil
engineers and scientists whose work has been utilized at
all stages of this project work. I am grateful to my
colleagues without whom this project would not have
come in present face.
SYED MOHD SALMAN NAQVI
MD GULNAWAZ KHAN
ADIL NISHAT
ABDUL HANNAN KHAN
MOHAMMAD JUNAID KHAN

4. CONTENTS
CHAPTER 1………………………. INTRODUCTION TO DAMS
(1-29)
CHAPTER 2……… CONCRETE GRAVITY DAM & IT’S DESIGN
(30-61)
CHAPTER 3…….…..……………….. FORCES ACTING ON DAM
STRUCTURE
(62-75)
CHAPTER 4 …………………………...…...……….. CASE STUDY
(76-97)
CHAPTER 5……………………………….… IMPACTS OF DAMS
(98-104)
CHAPTER 6…….……….CALCULATION FOR DESIGN OF DAM
ON EXCEL SHEET
(104-

5. 1
CHAPTER - 1
INTRODUCTION TO DAMS
1(a) Definition - A dam is a hydraulic structure of fairly impervious
material built across a river to create a reservoir on its upstream side for
impounding water for various purposes. It is a barrier that impounds water or
underground streams. Dams generally serve the primary purpose of retaining
water. Dams are probably the most important hydraulic structure built on the
rivers. These are very huge structure and require huge money, manpower and
time to construct. Dams are generally constructed in the mountainous reach of
the river where the valley is narrow and the foundation is good.
1(b) Uses and purpose of dam –
Water is essential for sustenance of all forms of life on earth. It is not evenly
distributed all over the world and even its availability at the same locations is
not uniform over the year. While the parts of the world, which are scarce in
water, are prone to drought, other parts of the world, which are abundant in
water, face a challenging job of optimally managing the available water
resources. No doubt the rivers are a great gift of nature and have been playing a
significant role in evolution of various civilizations, nonetheless on many
occasions, rivers, at the time of floods, have been playing havoc with the life
and property of the people. Management of river waters has been, therefore, one
of the most prime issues under consideration. Optimal management of river

6. 2
water resources demands that specific plans should be evolved for various river
basins which are found to be technically feasible and economically viable after
carrying out extensive surveys. Since the advent of civilization, man has been
constructing dams and reservoirs for storing surplus river waters available
during wet periods and for utilization of the same during lean periods. The dams
and reservoirs world over have been playing dual role of harnessing the river
waters for accelerating socio-economic growth and mitigating the miseries of a
large population of the world suffering from the vagaries of floods and
droughts. Dams and reservoirs contribute significantly in fulfilling the following
basic human needs: -
 WATER FOR DRINKING AND INDUSTRIAL USE
 IRRIGATION
 FLOOD CONTROL
 HYDRO POWER GENERATION
 INLAND NAVIGATION
In ancient times, dams were built for the single purpose of water supply or
irrigation. As civilizations developed, there was a greater need for water supply,
irrigation, flood control, navigation, water quality, sediment control and energy.
Therefore, dams are constructed for a specific purpose such as water supply,
flood control, irrigation, navigation, sedimentation control, and hydropower. A
dam is the cornerstone in the development and management of water resources
development of a river basin. The multipurpose dam is a very important project
for developing countries, because the population receives domestic and
economic benefits from a single investment.
Water supply for domestic and industrial use –

7. 3
It has been stressed how essential water is for our civilization. It is important to
remember that of the total rainfall falling on the earth, most falls on the sea and
a large portion of that which falls on earth ends up as runoff. Only 2% of the
total is infiltrated to replenish the groundwater. Properly planned, designed and
constructed and maintained dams to store water contribute significantly toward
fulfilling our water supply requirements. To accommodate the variations in the
hydrologic cycle, dams and reservoirs are needed to store water and then
provide more consistent supplies during shortages.
Inland navigation –
Natural river conditions, such as changes in the flow rate and river level, ice and
changing river channels due to erosion and sedimentation, create major
problems and obstacles for inland navigation. The advantages of inland
navigation, however, when compared with highway and rail are the large load
carrying capacity of each barge, the ability to handle cargo with large-
dimensions and fuel savings. Enhanced inland navigation is a result of
comprehensive basin planning and development utilizing dams, locks and
reservoirs which are regulated to provide a vital role in realizing regional and
national economic benefits. In addition to the economic benefits, a river that has
been developed with dams and reservoirs for navigation may also provide
additional benefits of flood control, reduced erosion, stabilized groundwater
levels throughout the system and recreation.

8. 4
Flood control –
Dams and reservoirs can be effectively used to regulate river levels and flooding
downstream of the dam by temporarily storing the flood volume and releasing it
later. The most effective method of flood control is accomplished by an
integrated water management plan for regulating the storage and discharges of
each of the main dams located in a river basin. Each dam is operated by a
specific water control plan for routing floods through the basin without damage.
This means lowering of the reservoir level to create more storage before the
rainy season. This strategy eliminates flooding. Flood control is a significant
purpose for many of the existing dams and continues as a main purpose for
some of the major dams of the world currently under construction.
Hydropower –
Electricity generated from dams is by very far the largest renewable energy
source in the world. More than 90% of the world's renewable electricity comes
from dams. Hydropower also offers unique possibilities to manage the power

9. 5
network by its ability to quickly respond to peak demands. Pumping-storage
plants, using power produced during the night, while the demand is low, is used
to pump water up to the higher reservoir. That water is then used during the
peak demand period to produce electricity. This system today constitutes the
only economic mass storage available for electricity.
Irrigation by dam –
Dams and reservoirs are constructed to store surplus waters during wet periods,
which can be used for irrigating arid lands. One of the major benefits of dams
and reservoirs is that water flows can be regulated as per agricultural
requirements of the various regions over the year.
Dams and reservoirs render unforgettable services to the mankind for meeting
irrigation requirements on a gigantic scale.
It is estimated that 80% of additional food production by the year 2025 would
be available from the irrigation made possible by dams and reservoirs.
Dams and reservoirs are most needed for meeting irrigation requirements of
developing countries, large parts of which are arid zones.
There is a need for construction of more reservoir based projects despite
widespread measures developed to conserve water through other improvements
in irrigation technology.

10. 6
A major portion of water stored behind dams in the world is withdrawn for
irrigation which mostly comprises consumptive use, that is, evapotranspiration
(ET) needs of irrigated crops and plantations. On the submerged land, there are
often possibilities for seasonal irrigation. A majority of dams built in the world
are multipurpose in nature, but irrigation is the largest user of the waters
withdrawn. This does not necessarily mean that irrigation is also the biggest
user of storage. The dams were responsible a few decades ago, for bringing
under cropping, additional areas and ushering in the green revolution through
high yielding crops and application of fertilisers, imparting food security in the
face of evergrowing population.
FUTURE WATER DEMAND PROJECTIONS:
(BILLION CUBIC METERS: BCM)
Scenarios Year 2010 Year 2025 Year 2050
Low 489 619 830
Medium 536 688 1008
High 536 734 1191
Source : GOI 1990b: 8-9
1(c) History of dam’s construction –
Ancient dams-
Early dam building took place in Mesopotamia and the Middle East. Dams were
used to control the water level, for Mesopotamia's weather affected
the Tigris and Euphrates rivers, and could be quite unpredictable. The earliest
known dam is the Jawa Dam in Jordan, 100 kilometres (62 mi) northeast of the
capital Amman. This gravity dam featured an originally 9 m (30 ft) high and
1 m (3 ft 3 in) wide stone wall, supported by a 50 m (160 ft) wide earth rampart.
The structure is dated to 3000 BC.
The Ancient Egyptian Sadd-el-Kafara Dam at Wadi Al-Garawi, located about
25 km (16 mi) south of Cairo, was 102 m (335 ft) long at its base and 87 m
(285 ft) wide. The structure was built around 2800 or 2600 BC. as a diversion
dam for flood control, but was destroyed by heavy rain during construction or
shortly afterwards. During the XIIth dynasty in the 19th century BC, the
Pharaohs Senosert III, Amenemhat III and Amenmehat IV dug a canal 16 km

11. 7
long linking the Fayum Depression to the Nile in Middle Egypt. Two dams
called Ha-Uar running east-west were built to retain water during the annual
flood and then release it to surrounding lands. The lake called "Mer-wer" or
Lake Moeris covered 1700 square kilometers and is known today as Berkat
Qaroun. By the mid-late 3rd century BC, an intricate water-management system
within Dholavira in modern day India, was built. The system included 16
reservoirs, dams and various channels for collecting water and storing it.
The Kallanai is constructed of unhewn stone, over 300 m (980 ft) long, 4.5 m
(15 ft) high and 20 m (66 ft) wide, across the main stream of the Kaveri river
in Tamil Nadu, South India. The basic structure dates to the 2nd century
AD and is considered one of the oldest water-diversion or water-regulator
structures in the world, which is still in use. The purpose of the dam was to
divert the waters of the Kaveri across the fertile Delta region for irrigation via
canals.
Roman engineering -
The Roman dam at Cornalvo in Spain has been in use for almost two millennia.
Roman dam construction was characterized by "the Romans' ability to plan and
organize engineering construction on a grand scale". Roman planners
introduced the then novel concept of large reservoir dams which could secure a
permanent water supply for urban settlements also over the dry season. Their
pioneering use of water-proof hydraulic mortar and particularly Roman
concrete allowed for much larger dam structures than previously built, such as
the Lake Homs Dam, possibly the largest water barrier to that date, and
the Harbaqa Dam, both in Roman Syria. The highest Roman dam was

12. 8
the Subiaco Dam near Rome; its record height of 50 m (160 ft) remained
unsurpassed until its accidental destruction in 1305.
Roman engineers made routine use of ancient standard designs like
embankment dams and masonry gravity dams. Apart from that, they displayed a
high degree of inventiveness, introducing most of the other basic dam designs
which had been unknown until then. These include arch-gravity dams, arch
dams, buttress dams and multiple arch buttress dams, all of which were known
and employed by the 2nd century AD. Roman workforces also were the first to
build dam bridges, such as the Bridge of Valerian in Iran.
Remains of the Band-e Kaisar dam, built by the Romans in the 3rd century AD.
In Iran, bridge dams such as the Band-e Kaisar were used to
provide hydropower through water wheels, which often powered water-raising
mechanisms. One of the first was the Roman-built dam bridge in Dezful, which
could raise water 50 cubits in height for the supply to all houses in the town.
Also diversion dams were known.
Milling dams were introduced which the Muslim engineers called the Pul-i-
Bulaiti. The first was built at Shustar on the River Karun, Iran, and many of
these were later built in other parts of the Islamic world. Water was conducted
from the back of the dam through a large pipe to drive a water wheel
and watermill. In the 10th century, Al-Muqaddasi described several dams in
Persia. He reported that one in Ahwaz was more than 910 m (3,000 ft) long, and
that and it had many water-wheels raising the water into aqueducts through
which it flowed into reservoirs of the city. Another one, the Band-i-Amir dam,
provided irrigation for 300 villages.

13. 9
Middle Ages -
In the Netherlands, a low-lying country, dams were often applied to block rivers
in order to regulate the water level and to prevent the sea from entering the
marsh lands. Such dams often marked the beginning of a town or city because it
was easy to cross the river at such a place, and often gave rise to the respective
place's names in Dutch. For instance the Dutch capital Amsterdam (old name
Amstelredam) started with a dam through the river Amstel in the late 12th
century, and Rotterdam started with a dam through the river Rotte, a minor
tributary of the Nieuwe Maas. The central square of Amsterdam, covering the
original place of the 800 year old dam, still carries the name Dam Square or
simply the Dam.
Industrial era -
An engraving of the Rideau Canal locks at Bytown.
The Romans were the first to build arch dams, where the reaction forces from
the abutment stabilizes the structure from the external hydrostatic, but it was
only in the 19th century that the engineering skills and construction materials
available were capable of building the first large scale arch dams.
Three pioneering arch dams were built around the British Empire in the early
19th century. Henry Russel of the Engineers oversaw the construction of
the Mir Alam dam in 1804 to supply water to the city of Hyderabad (it is still in
use today). It had a height of 12 meters and consisted of 21 arches of variable
span.
In the 1820s and 30s, Lieutenant-Colonel John By supervised the construction
of the Rideau Canal in Canada near modern-day Ottawa and built a series of
curved masonry dams as part of the waterway system. In particular, the Jones
Falls Dam built by John Red path, was completed in 1832 as the largest dam

14. 10
in North America and an engineering marvel. In order to keep the water in
control during construction, two sluices, artificial channels for conducting
water, were kept open in the dam. The first was near the base of the dam on its
east side. A second sluice was put in on the west side of the dam, about 20 feet
(6 meters) above the base. To make the switch from the lower to upper sluice,
the outlet of Sand Lake was blocked off.
Masonry arch wall, Parramatta, New South Wales, the first engineered dam built in Australia.
Hunts Creek near the City of Parramatta, Australia was dammed in the 1850s, to
cater for the demand for water from the growing population of the city. The
masonry arch dam wall was designed by Lieutenant Percy Simpson who was
influenced by the advances in dam engineering techniques made by the Royal
Engineers in India. The dam cost £17,000 and was completed in 1856 as the
first engineered dam built in Australia, and the second arch dam in the world
built to mathematical specifications.
The first such dam was opened two years earlier in France. It was also the first
French arch dam of the industrial era, and it was built by François Zola in the
municipality of Aix-en-Provence to improve the supply of water after the 1832
cholera outbreak devastated the area. After royal approval was granted in 1844,
the dam was constructed over the following decade. Its construction was carried
out on the basis of the mathematical results of scientific stress analysis.
The 75-miles dam near Warwick, Australia was possibly the world's first
concrete arch dam. Designed by Henry Charles Stanley in 1880 with an
overflow spillway and a special water outlet, it was eventually heightened to 10
meters.

15. 11
In the latter half of the nineteenth century, significant advances in the scientific
theory of masonry dam design were made. This transformed dam design, from
an art based on empirical methodology to a profession based on a rigorously
applied scientific theoretical framework. This new emphasis was centered
around the engineering faculties of universities in France and in the United
Kingdom. William John Macquorn Rankine at the University of
Glasgow pioneered the theoretical understanding of dam structures in his 1857
paper On the Stability of Loose Earth. Rankine theory provided a good
understanding of the principles behind dam design. In France, J. Augustin
Tortene de Sazilly explained the mechanics of vertically faced masonry gravity
dams and Zola's dam was the first to be built on the basis of these principles.
Large dams -
The Hoover Dam by Ansel Adams, 1942.
The era of large dams was initiated with the construction of the Aswan Low
Dam in Egypt in 1902, a gravity masonry buttress dam on the Nile River.
Following their 1882 invasion and occupation of Egypt, the British began
construction in 1898. The project was designed by Sir William Will cocks and
involved several eminent engineers of the time, including Sir Benjamin
Baker and Sir John Aird, whose firm, John Aird & Co., was the main
contractor. Capital and financing were furnished by Ernest. When initially
constructed between 1899 and 1902, nothing of its scale had ever been
attempted; on completion, it was the largest masonry dam in the world.
The Hoover Dam was a massive concrete arch-gravity dam, constructed in
the Black Canyon of the Colorado River, on the border between the US states

16. 12
of Arizona and Nevada between 1931 and 1936 during the Great Depression. In
1928, Congress authorized the project to build a dam that would control floods,
provide irrigation water and produce hydroelectric power. The winning bid to
build the dam was submitted by a consortium called Six Companies, Inc.Such a
large concrete structure had never been built before, and some of the techniques
were unproven. The torrid summer weather and the lack of facilities near the
site also presented difficulties. Nevertheless, Six Companies turned over the
dam to the federal government on 1 March 1936, more than two years ahead of
schedule.
Most dams constructed during the second half of the 19th
century in 1850-1900 in the earlier part of the period, were small by nature of
the needs they served, and mainly constructed of earth and rock. As the turn of
the century neared, and technology improved, larger concrete dams emerged.
The Lower Crystal Springs Dam provided a significant example of a
CONCRETE GRAVITY DAM that set precedence for future dam design. Built
in 1888 near the San Andreas Fault, the Lower Crystal springs Dam withstood
the 1906 San Francisco earthquake with little damage.
1(e) Different types of dams –
Dams can be classified on the basis of following points –
A – Based on use of dam .
B – Based on hydraulic design.
C – Based on material of construction.
D – Based on mode of resistance offered by dam against external
Forces.

17. 13
A – Based on use of dam -
(a)Storage dam :
They are constructed to store water during the rainy season when there is a large
flow in the river. Many small dams impound the spring runoff for later use in
dry summers. Storage dams may also provide a water supply, or improved
habitat for fish and wildlife. They may store water for hydroelectric power
generation, irrigation or for a flood control project. Storage dams are the most
common type of dams and in general the dam means a storage dam unless
qualified otherwise.
(b) Diversion dam :

18. 14
A diversion dam is a dam that diverts all or a portion of the flow of a river from
its natural course. Diversion dams do not generally impound water in
a reservoir. Instead, the water is diverted into an artificial water course or canal,
which may be used for irrigation or return to the river after passing
through hydroelectric generators, flow into a different river or be itself dammed
forming a reservoir.
The earliest diversion dam—and the second oldest dam of any kind known—is
the Ancient Egyptian Sadd el-Kafara Dam at Wadi Al-Garawi, which was
located about twenty five kilometres south of Cairo. Built around 2600 BC for
flood control, the structure was 102 metres long at its base and eighty seven
metres wide. It was destroyed by a flood while it was still under construction.
(c) Retention dam :
Detention dams are constructed for flood control. A detention dam retards the
flow in the river on its downstream during floods by storing some flood water.
Thus the effect of sudden floods is reduced to some extent. The water retained
in the reservoir is later released gradually at a controlled rate according to the
carrying capacity of the channel downstream of the detention dam. Thus the
area downstream of the dam is protected against flood.
(d) Water spreading dam :
These are low height dam whose main objective isto recharge ground water.
(e) Debris dam :

19. 15
A debris dam is constructed to retain debris such as sand, gravel, and drift wood
flowing in the river with water. The water after passing over a debris dam is
relatively clear.
B – Based on hydraulic design-
(a)Non overflow dam :
It is constructed such that water is not allowed to overflow over its crest. In
most cases, dams are so designed that part of its length is designed as an
overflow dam (this part is called the spillway) while the rest of its length is
designed as a non-overflow dam. In some cases, these two sections are not
combined.
(b) Overflow dam :
It is constructed with a crest to permit overflow of surplus water that cannot be
retained in the reservoir. Generally dams are not designed as overflow dams for
its entire length. Diversion weirs of small height may be designed to permit
overflow over its entire length.
C – Based on material –
(a)Rigid dam :
It is constructed with rigid material such as stone, masonry, concrete, steel, or
timber. Steel dams (steel plates supported on inclined struts) and timber dams
(wooden planks supported on a wooden framework) are constructed only for
small heights (rarely).
 Steel dam –

20. 16
A steel dam consists of a steel framework, with a steel skin plate on its upstream
face. Steel dams are generally of two types: (i) Direct-strutted, and (ii)
Cantilever type . In direct strutted steel dams, the water pressure is transmitted
directly to the foundation through inclined struts. In a cantilever type steel dam,
there is a bent supporting the upper part of the deck, which is formed into a
cantilever truss. This arrangement introduces a tensile force in the deck girder
which can be taken care of by anchoring it into the foundation at the upstream
toe. Hovey suggested that tension at the upstream toe may be reduced by
flattening the slopes of the lower struts in the bent. However, it would require
heavier sections for struts. Another alternative to reduce tension is to frame
together the entire bent rigidly so that the moment due to the weight of the
water on the lower part of the deck is utilised to offset the moment induced in
the cantilever. This arrangement would, however, require bracing and this will
increase the cost. These are quite costly and are subjected to corrosion. These
dams are almost obsolete. Steel dams are sometimes used as temporary coffer
dams during the construction of the permanent one. Steel coffer dams are
supplemented with timber or earthfill on the inner side to make them water
tight. The area between the coffer dams is dewatered so that the construction
may be done in dry for the permanent dam.
Examples of Steel type: Redridge Steel Dam (USA) and Ashfork-Bainbridge
Steel Dam (USA).
 Timber dam :
Main load-carrying structural elements of timber dam are made of wood,
primarily coniferous varieties such as pine and fir. Timber dams are made for

21. 17
small heads (2-4 m or, rarely, 4-8 m) and usually have sluices; according to the
design of the apron they are divided into pile, crib, pile-crib, and buttressed
dams. The openings of timber dams are restricted by abutments; where the
sluice is very long it is divided into several openings by intermediate supports:
piers, buttresses, and posts. The openings are covered by wooden shields,
usually several in a row one above the other.
(b) Non rigid dam :
It is constructed with non-rigid material such as earth, tailings, rockfill etc.
 Earthen dam –
An earth dam is made of earth (or soil) built up by compacting successive
layers of earth, using the most impervious materials to form a core and placing
more permeable substances on the upstream and downstream sides. A facing of
crushed stone prevents erosion by wind or rain, and an ample spillway, usually
of concrete, protects against catastrophic washout should the water overtop the
dam. Earth dam resists the forces exerted upon it mainly due to shear strength of
the soil. Although the weight of the this structure also helps in resisting the
forces, the structural behaviour of an earth dam is entirely different from that of
a gravity dam. The earth dams are usually built in wide valleys having flat
slopes at flanks (abutments).The foundation requirements are less stringent than
those of gravity dams, and hence they can be built at the sites where the
foundations are less strong. They can be built on all types of foundations.
However, the height of the dam will depend upon the strength of the foundation
material.Examples of earthfill dam: Rongunsky dam (Russia) and New Cornelia
Dam (USA).

22. 18
 Rockfill dam –
A rockfill dam is built of rock fragments and boulders of large size. An
impervious membrane is placed on the rockfill on the upstream side to
reduce the seepage through the dam. The membrane is usually made of
cement concrete or asphaltic concrete. In early rockfill dams, steel and
timber membrane were also used, but now they are obsolete. A dry rubble
cushion is placed between the rockfill and the membrane for the
distribution of water load and for providing a support to the membrane.
Sometimes, the rockfill dams have an impervious earth core in the middle
to check the seepage instead of an impervious upstream membrane. The
earth core is placed against a dumped rockfill. It is necessary to provide
adequate filters between the earth core and the rockfill on the upstream
and downstream sides of the core so that the soil particles are not carried
by water and piping does not occur. The side slopes of rockfill are usually
kept equal to the angle of repose of rock, which is usually taken as 1.4:1
(or 1.3:1). Rockfill dams require foundation stronger than those for earth
dams.
Examples of rockfill dam: Mica Dam (Canada) and Chicoasen Dam
(Mexico).
 Rubber dam –

23. 19
A symbol of sophistication and simple and efficient design, this most recent
type of dam uses huge cylindrical shells made of special synthetic rubber and
inflated by either compressed air or pressurized water. Rubber dams offer ease
of construction, operation and decommissioning in tight schedules. These can
be deflated when pressure is released and hence, even the crest level can be
controlled to some extent. Surplus waters would simply overflow the inflated
shell. They need extreme care in design and erection and are limited to small
projects.
Example of Rubber type: Janjhavathi Rubber Dam (India).
D – Based on mode of resistance –
(a) Gravity dam :
A gravity dam is a massive sized dam fabricated from concrete and designed to
hold back large volumes of water. By using concrete, the weight of the dam is
actually able to resist the horizontal thrust of water pushing against it. This is
why it is called a gravity dam. Gravity essentially holds the dam down to the
ground, stopping water from toppling it over. Gravity dams are well suited for
blocking rivers in wide valleys or narrow gorge ways. Since gravity dams must

24. 20
rely on their own weight to hold back water, it is key that they are built on a
solid foundation of bedrock. In fact, an earth rockfill dam is a gravity dam.
Straight gravity dam – A gravity dam that is straight in plan.
Curved gravity plan – A gravity dam that is curved in plan.
Curved gravity dam (Arch gravity dam) – It resists the forces acting on it by
combined gravity action (its own weight) and arch action.
Solid gravity dam – Its body consists of a solid mass of masonry or concrete
Hollow gravity dam – It has hollow spaces within its body.
Most gravity dams are straight solid gravity dams.
(b) Arched dam :
 It is a curved masonry or concrete dam, convex upstream, which resists
the forces acting on it by arch action. transfers the water pressure and
other forces mainly to the abutments by arch action. These type of dams
are concrete or masonry dams which are curved or convex upstream in
plan
 Its shape helps to transmit the major part of the water load to the
abutments
 Arch dams are built across narrow, deep river gorges, but now in recent
years they have been considered even for little wider valleys.

25. 21
The only arch dam in India – Idukki dam (double curvature in plan) –
concrete arch dam.
(c) Buttress dam :
It consists of water retaining sloping membrane or deck on the u/s which is
supported by a series of buttresses. These buttresses are in the form of equally
spaced triangular masonry or reinforced concrete walls or counterforts. The
sloping membrane is usually a reinforced concrete slab. In some cases, the u/s
slab is replaced by multiple arches supported on buttresses (multiple arch
buttress dam) or by flaring the u/s edge of the buttresses to span the distance
between the buttresses (bulkhead buttress dam or massive head buttress dam).
In general, the structural behaviour of a buttress dam is similar to that of a
gravity dam.
 Buttress Dam – Is a gravity dam reinforced by structural supports
 Buttress – a support that transmits a force from a roof or wall to another
supporting structure
 This type of structure can be considered even if the foundation rocks are
little weaker.
1(f) Basic terms of dam characteristics –
The following is a list of terms and their definitions that are frequently used
when discussing the physical characteristics of dams.

26. 22
ABUTMENT: The part of the valley side against which the dam is constructed.
May also refer to an artificial abutment sometimes constructed as a concrete
wall. Right and left abutments are those on respective sides as an observer when
viewed looking downstream.
BASE WIDTH: The width of the dam measured along the dam/foundation
interface.
BREACH: An opening or a breakthrough of a dam sometimes caused by rapid
erosion of a section of earth embankment by water.
CONDUIT: A closed channel to convey the discharge through or under a dam.
Usually pipes constructed of concrete or steel.
CORE (IMPERVIOUS CORE) (IMPERVIOUS ZONE): A zone of material
of low permeability in an embankment dam, hence the terms central core,
inclined core, puddle clay core, and rolled clay core.
CREST LENGTH: The developed length of the top of the dam. This includes
the length of the spillway, powerhouse, navigation lock, fish pass, etc., where
these structures form part of the length of the dam. If detached from the dam,
these structures should not be included.

27. 23
CREST OF DAM: The term crest of dam is often used when top of spillway
and top of dam should be used for referring to the overflow section and dam
proper, respectively.
CUTOFF: An impervious construction by means of which seepage is reduced
or prevented from passing through foundation material.
CUTOFF WALL: A wall of impervious material, e.g., concrete, wood pilings,
steel sheet piling, built into the foundation to reduce seepage under the dam.
DRAINAGE LAYER OR BLANKET: A layer of pervious material placed
directly over the foundation material or downstream slope to facilitate seepage
drainage of the embankment. May also use an upstream blanket placed on the
impoundment floor and upstream embankment to prevent seepage entering the
dam.
DRAWDOWN: The resultant lowering of water surface level due to release of
water from the reservoir.
EMBANKMENT: Fill material, usually earth or rock, placed with sloping
sides.
EMERGENCY ACTION PLAN: A predetermined plan of action to be taken
to reduce the potential for property damage and loss of lives in an area affected
by a dam break.
FACE: With reference to a structure, the external surface that limits the
structure, e.g., the face of the wall or dam.
FLASHBOARDS: Lengths of timber, concrete, or steel placed on the crest of a
spillway to raise the operating water level but that may be quickly removed in
the event of a flood either by tripping a supporting device or by designing the
flashboard supports to fail under specified conditions.
FOUNDATION OF DAM: The natural material on which the dam structure is
placed.
FREEBOARD: The vertical distance from the water surface to the lowest
elevation at which water would flow over the dam at a section not designed to
be overflowed.

28. 24
GATE: In general, a device in which a leaf or member is moved across the
waterway from an external position to control or stop the flow.
CREST GATE (SPILLWAY GATE): A gate on the crest of a spillway that
controls overflow or reservoir water level.
FLAP GATE: A gate hinged along one edge, usually either the top or bottom
edge. Examples of bottom-hinged flap gates are tilting gates and fish belly gates
so called from their shape in cross section.
OUTLET GATE: A gate controlling the outflow of water from a reservoir.
RADIAL GATE (TAINTER GATE): A gate with a curved upstream plate
and radial arms hinged to piers or other supporting structures.
SLIDE GATE (SLUICE GATE): A gate that can be opened or closed by
sliding in supporting guides.
HEEL OF DAM: The junction of the upstream face of a gravity or arch dam
with the foundation surface. In the case of an embankment dam the junction is
referred to as the upstream toe of the dam.
INTAKE: Any structure in a reservoir, dam, or river through which water can
be drawn into an outlet pipe, flume, etc.
LOW LEVEL OUTLET (BOTTOM OUTLET): An opening at a low level
from the reservoir generally used for emptying the impoundment.
OUTLET: An opening through which water can be freely discharged for a
particular purpose from a reservoir.
PERVIOUS ZONE: A part of the cross section of an embankment dam
comprising material of high permeability.
RIPRAP: A layer of large uncoursed stones, broken rock, or precast blocks
placed in random fashion on the upstream slope of an embankment dam, on a
reservoir shore, or on the sides of a channel as a protection against wave and ice
action.
SEEPAGE COLLAR: A projecting collar usually of concrete or steel built
around the outside of a pipe, tunnel, or conduit, under an embankment dam, to
lengthen the seepage path along the outer surface of the conduit.

29. 25
SPILLWAY: A structure over or through which flood flows are discharged. If
the flow is controlled by gates, it is considered a controlled spillway; if the
elevation of the spillway crest is the only control, it is considered an
uncontrolled spillway.
AUXILIARY SPILLWAY (EMERGENCY SPILLWAY): A secondary
spillway designed to operate only during exceptionally large floods.
OGEE SPILLWAY (OGEE SECTION): An overflow spillway, which in
cross section the crest, downstream slope, and bucket have an “S” or ogee form
of curve. The shape is intended to match the underside of the nappe at its upper
extremities.
SPILLWAY CHANNEL (SPILLWAY TUNNEL): A channel or tunnel
conveying water from the spillway to the river downstream.
STOPLOGS: Large logs, timbers or steel beams placed on top of each other
with their ends held in guides on each side of a channel or conduit so as to
provide a cheaper or more easily handled means of temporary closure than a
bulkhead gate.
STRUCTURAL HEIGHT: The vertical distance from the lowest point of
natural ground on the downstream side of the dam to the highest part of the dam
which would impound water.
TOE OF DAM: The junction of the downstream face of a dam with the natural
ground surface. This is also referred to as the downstream toe. For an
embankment dam the junction of the upstream face with ground surface is
called the upstream toe.
TOP OF DAM: The elevation of the upper most surface of a dam, usually a
road or walkway, excluding any parapet wall, railings, etc.
TOP THICKNESS (TOP WIDTH): The thickness or width of a dam at the
top of the dam. In general, the term thickness is used for gravity and arch dams,
width is used for other dams.
TRAINING WALL: A wall built to confine or guide the flow of water.

30. 26
1(g) Factors governing the selection of a particular
type of dam-
Before constructing a dam, it is necessary to choose its type on the basis of
economy, ease of construction etc. these are some important factors on which
the selection of dam depends-
 Topography – topography dictates the first choice of type of dams.
e.g – A narrow U- shaped valley, i.e a narrow stream flowing between
high rockey walls, would suggest a concrete overflow dam.
1. A low , rolling plain country, would naturally suggest an earth fill dam with a
separate spill way.
2. A narrow V – shaped valley indicates the choice of arch dam. It is preferable
to have the top width of valley less then one fourth of its height. But a separate
site of spill way must be available.
 Geological and foundation conditions-
The various kinds of foundation generally encountered are discussed below –
1. Solid rock foundation –
Solid rock foundations such as granite, gneiss etc. have a strong bearing power.
They offer high resistance to erosion and percolation, almost every kind of dam
can be built on such foundations. Sometimes seems and fractures are present in
the rocks. They must be grouted and sealed properly.
2. Gravel Foundations-
Coarse sands and gravels are unable to bear the weight of the high concrete
gravity dams and are suitable for earthen and rock-fill dams. Low concrete
gravity dams up to a height of 15 m may also be suggested on such foundations.
These foundations have high permeability and therefore subjected to water
percolation at high rates. Suitable cut-offs must be provided to avoid danger of
undermining.

31. 27
3. Silt And Fine Sand Foundations- They suggest the adoption of
earthen dams or very low gravity dams (up to a height of 8m). Seepage through
such a foundation may be excessive. Settlement may also be a problem. They
must be properly designed to avoid such dangers. The protection of foundations
at the downstream toe erosion must also be ensured.
4. Clay Foundations- Unconsolidated and high moisture clays are likely
to cause enormous settlement of dam. They are fit for concrete gravity dams,
but that too , after special treatment.
 Availability of material-
In order to achieve economy in the dam, the materials required for its
construction must be available locally or at short distances from the
construction site.
 Earthquake zone-
If the dam is to be situated in an earthquake zone, its design must include the
earthquake forces.
 Height of dam –
Earthen dams are usually not provided for heights more than 30m or so. Hence,
for greater heights, gravity dams are generally preferred.
1(h) Selection of dam site –

32. 28
When selecting a dam site, an exhaustive study of the potential alternatives
should be conducted, including both physical and socio-economic factors. The
villagers of the area are the most important sources of practical information for
such a study, and they often have immediate proposals on suitable sites.
However, it is important to consult as many stakeholders as possible to avoid
personal biases from individuals or small groups. Possible dam sites must be
compared carefully, and a number of site visits are essential to identify critical
features.
A dam may be over topped due to the resulting wave action or rise of the water
surface on account of a major slide into the reservoir. If the reservoir site is
likely to be affected by the slides and cannot be abandoned, some restraining
steps in reservoir operation should be taken to avoid serious failure. These steps
could be in the form of limiting the filling and draw-down rates or imposing the
maximum allowable water surface at a level lower than the maximum normal
water surface. Alternatively, installation of drains to relieve water pressure
along likely slip surfaces, some form of impervious lining, and pinning the
unstable mass of its parent formation by rock bolting can be resorted to for
preventing slides.

33. 29
Stabilization of the unstable mass can also be achieved by
strengthening or replacing weak material. Grouting is the most common remedy
for strengthening such weak masses. It may be desirable to plan the steps to be
taken to mitigate the effects of potential slide after it has occurred in spite of all
preventive steps. Reservoir water loss either to the atmosphere or to the ground
can be a controlling factor in the selection of a site for a conservation reservoir.
For a flood control reservoir, water loss is of concern only if it relates to the
safety of the project. The lining of the surface through which seepage is
expected is one of the preventive measures to reduce the reservoir water loss to
the ground. At times, a blanket of impervious material extending from the heel
of the dam is required. This too serves to control the seepage from the reservoir.
Loss of reservoir water to the atmosphere occurs due to direct
evaporation from the reservoir surface. The evaporation losses are affected by
the climate of the region, shape of the reservoir, wind conditions, humidity, and
temperature. From considerations of evaporation, a reservoir site having a small
surface area to volume ratio will be better than a saucer-shaped reservoir of
equal capacity. Evaporation-retardant chemicals increase the surface tension of
water by forming a monomolecular film and thus reduce evaporation. Bank
storage is the water which spreads out from a body of water, filling interstices
of the surrounding earth and rock mass. This water is assumed to remain in the
surrounding mass and does not continue to move to ultimately join the ground
water or surface water as seepage water does. The bank storage is not mitigable.
It must, however, be estimated for feasibility investigations and measured
during reservoir operation for providing guidelines for reservoir regulation
The following factors need to be considered very carefully:
 Physical suitability of the site for dam construction.
 Ownership of the dam site and its catchment area. To avoid conflicts, care
should be taken in areas where the dam site is owned or used by two or
more villages.
 Height of embankment. This will help determine whether the dam can be
constructed by the villagers on their own, or if outside assistance is
required.

34. 30
 Type, suitability and availability of construction materials. This will help
to decide what type of dam is to be constructed. A rock-fill dam is
obviously not a good choice if there are no stones in the area.
 Loss of good arable land by inundation.
 Interference with cemeteries, graves or other areas of cultural importance.
 Location of irrigable areas in relation to the dam.
 Size, topography, vegetation cover and other physical characteristics of
the catchment area.
After identifying possible dam sites, they must be ranked in order of priority.
Consider the factors above and also the following features as added advantages:
 A narrow river or streambed that would minimize the embankment
volume
 Rock outcrops available for spillway and foundation
 Flat reservoir areas of low-value land that can store a relatively large
volume of water with a low embankment height.
To assure community support, frequent meetings should be organized to discuss
the advantages and disadvantages of different sites with the villagers.
CHAPTER – 2
CONCRETE GRAVITY DAM &
IT’S DESIGN
Introduction -
Dams constructed out of masonry or concrete and which rely solely on its self-
weight for stability fall under the nomenclature of gravity dams. Masonary
dams have been in use in the past quite often but after independence, the last
major masonry dam structure that was built was the Nagarjunsagar Dam on
river Krishna which was built during 1958-69. Normally, coursed rubble

35. 31
masonry was used which was bonded together by lime concrete or cement
concrete. However masonry dam is no longer being designed in our country
probably due to existence of alternate easily available dam construction material
and need construction technology. In fact, gravity dams are now being built of
mass concrete, whose design and construction aspects would be discussed in
this chapter. There are other dams built out of concrete like the Arch/Multiple
Arch or Buttress type. These have however not been designed or constructed in
India, except the sole one being the arch dam at Idukki on river Periyar. For
concrete dams, the stress developed at the junction of the base becomes quite
high, which the foundation has to resist. Usually concrete gravity dams are
constructed across a river by excavating away the loose overburden till firm
rock is encountered which is considered as the actual foundation. The quality of
foundation not only affects the design, it also guides the type of dam that would
be suited at a design site. Hence, discussions on the ground foundation aspects
have been introduced in this lesson as well. It may also be realized that
designing a dam based on field data (like the geometry of the river valley, the
foundation allowable bearing capacity .etc.) is not the only part that a water
resource engineer has to do. He has to get it constructed at the design site which
may easily take anywhere between 5 to 10 years or even more depending on the
complexity of the work and the volume and type of the structure. It may easily
be appreciated that constructing a massive structure across a flowing river is no
easy task. In fact tackling of the monsoon flows during the years of construction
is a difficult engineering task.
Concrete gravity dam and apparent structures- basic
layout-
The basic shape of a concrete gravity dam is triangular in section with the top
crest often widened to provide a roadway The increasing width of the section
towards the base is logical since the water pressure also increases linearly with
depth as shown in Figure 1a. In the figure, h is assumed as the depth of water
and γh is the pressure at base, where γ is the unit weight of water (9810 N/m³),
W is the weight of the dam body. The top portion of the dam (Figure 1b) is
widened to provide space for vehicle movement. A gravity dam should also
have an appropriate spillway for releasing excess flood water of the river during
monsoon months. This section looks slightly different from the other non-
overflowing sections. A typical section of a spillway is shown in Figure.

36. 32
The flood water glides over the crest and downstream face of the spillway and
meets an energy dissipating structure that helps to kill the energy of the flowing
water, which otherwise would have caused erosion of the river bed on the
downstream. The type of energy dissipating structure shown in Figure 2 is
called the stilling basin which dissipates energy of the fast flowing water by
formation of hydraulic jump at basin location. This and other types of spillway
and energy dissipators are discussed in a subsequent section. Figure 3 shows the
functioning of this type of spillway. Usually, a spillway is provided with a gate,
and a typical spillway section may have a radial gate as shown in Figure 4. The
axis or trunnion of the gate is held to anchorages that are fixed to piers.

37. 33
Also shown in the figure is a guide wall or training wall that is necessary to
prevent the flow crossing over from one bay (controlled by a gate) to the
adjacent one. Since the width of a gate is physically limited to about 20m
(limited by the availability of hoisting motors), there has to be a number of bays
with corresponding equal number of gates separated by guide walls in a
practical dam spillway. The upstream face of the overflowing and non-
overflowing sections of a gravity dam are generally kept in one plane, which is
termed as the dam axis or sometimes referred to as the dam base line. Since the
downstream face of the dam is inclined, the plane view of a concrete gravity
dam with a vertical upstream face would look like as shown in Figure .

38. 34
If a concrete gravity dam is appreciably more than 20 m in length measured
along the top of the dam from one bank of the river valley to the other, then it is
necessary to divide the structure into blocks by providing transverse
contraction joints. These joints are in vertical planes that are at the right angle
to the dam axis and separated about 18-20 m. The spacing of the joints is
determined by the capacity of the concreting facilities to be used and
considerations of volumetric changes and attendant cracking caused by
shrinkage and temperature variations. The possibilities of detrimental cracking
can be greatly reduced by the selection of the proper type of the cement and by
careful control of mixing and placing procedures. The contraction joints allow
relieving of the thermal stresses. In plan, therefore the concrete gravity dam
layout would be as shown in Figure 7, where the dam is seen to be divided into
blocks separated by the contraction joints.

39. 35
The base of each block of the dam is horizontal and the blocks in the centre of
the dam are seen to accommodate the spillway and energy dissipators. The
blocks with maximum height are usually the spillway blocks since they are
located at the deepest portion of the river gorge, as shown in Figure 7. The
upstream face of the dam is sometimes made inclined (Figure 8a) or kept
vertical up to a certain elevation and inclined below (Figure 8b).

40. 36
Concrete Gravity Dams-
 Stability requirement
 Load Combinations
 Modes of failure of a gravity dam
 Overturning
 Sliding
 Crushing
 Tension
 Principal and Shear Stresses
 Elementary and Practical Profile

41. 37
1. Load combinations -
Gravity dam design should be based on the most adverse load combination A,
B, C, D, E, F or G given below using the safety factors prescribed-
 Load Combination A (Construction Condition) – Dam completed but no
water in reservoir and no tailwater.
 Load Combination B (Normal Operating Condition) – Full reservoir
elevation, normal dry weather tailwater, normal uplift; ice and silt (if
applicable).
 Load Combination C (Flood Discharge Condition) – Reservoir at
maximum flood pool elevation, all gates open, tailwater at flood
elevation, normal uplift, and silt (if applicable ).
 Load Combination D - Combination A, with earthquake.
 Load Combination E - Combination B, with earthquake but no ice.
 Load Combination F - Combination C, but with extreme uplift (drains
inoperative).
 Load Combination G - Combination E, but with extreme uplift (drains
inoperative).
2. Requirements for Stability-
Specific stability criteria for a particular loading combination are dependent
upon the degree of understanding of the foundation structure interaction and site
geology, and to some extent, on the method of analysis. Assumptions used in
the analysis should be based upon construction records and the performance of
the structures under historical loading conditions. In the absence of available
design data and records, site investigations may be required to verify
assumptions. Safety factors are intended to reflect the degree of uncertainty
associated with the analysis. Uncertainty resides in the knowledge of the
loading conditions and the material parameters that define the dam and the
foundation. Uncertainty can also be introduced by simplifying assumptions
made in analyses. When sources of uncertainty are removed, safety factors can
be lowered.
Modes of failure of a gravity dam:
 Overturning
 Sliding
 Compression or Crushing

42. 38
 Tension
The design shall satisfy the following requirements of stability:
 The dam shall be safe against sliding on any plane or combination of
planes within the dam, at the foundation or within the foundation;
 The dam shall be safe against overturning at any plane within the dam, at
the base, or at any plane below the base; and
 The safe unit stresses in the concrete or masonry of the dam or in the
foundation material shall not be exceeded.
The shape of a dam and curvature in its layout are pertinent in regard to the
stability and more favourable stress conditions. Wherever possible dam and
foundation designs should take advantage of the favourable conditions accruing
from curved shapes, gradual transitions and fillets. For consideration of
stability the following assumptions are made:
 That the dam is composed of individual transverse vertical elements each
of which carries its load to the foundation without transfer of load from or
to adjacent elements. (NOTE - However. In the stability analysis of a
gravity dam, it becomes frequently necessary to make an analysis of the
whole block, wherever special features of foundation and large openings
so indicate).
 That the vertical stress varies linearly from upstream face to downstream
face on any horizontal section.
3. Reaction of Foundations-
 The resultant of all horizontal and vertical forces should be balanced by
an equal and opposite reaction at the foundation consisting of the total
vertical reaction and the total horizontal shear and friction at the base and
the resisting shear and friction of the passive wedge, if any.
 For the dam to be in static equilibrium the location of this force is such
that the summation of moments is equal to zero.
 The distribution of the vertical reaction is assumed as trapezoidal for
convenience only, with knowledge that the elastic and plastic properties
of both the foundation material and the concrete do affect the actual
distribution.
 The problem of determining the actual distribution is complicated by the
horizontal reaction, internal stress relations and other theoretical
considerations.
4. Overturning-

43. 39
 The overturning of the dam section takes place when the resultant force at
any section cuts the base of the dam downstream of the toe.
 In that case the resultant moment at the toe becomes clockwise (or -ve).
 On the other hand, if the resultant cuts the base within the body of the
dam, there will be no overturning.
 For stability requirements, the dam must be safe against overturning.
 The factor of safety against overturning is defined as the ratio of the
righting moment (+ ve MR) to the overturning moments (- ve M0) about
the toe.
The factor of safety against overturning should not be less than 1.5
IS Code Recommendation-
 Before a gravity dam overturns bodily, other types of failures may occur,
such as cracking of the upstream material due to Tension, increase in
uplift, crushing of toe material and sliding.
 A gravity dam is, therefore, considered safe against overturning if the
criteria of n tension on the upstream face, the resistance against sliding as
well as the quality and strength of concrete/masonry of the dam and its
foundation is satisfied assuming the dam and foundation as a continuous
body.
5. Sliding Resistance-
 Many of the loads on the dam are horizontal or have horizontal
components which are resisted by frictional or shearing forces along
horizontal planes in the body of the dam, on the foundation or in the
foundation.
 A dam will fail in sliding at its base, or at any other level, if the horizontal
forces causing sliding are more than the resistance available to it at that
level.
 The resistance against sliding may be due to friction alone, or due to
friction and shear strength of the joint.
 Shear strength develops at the base if benched foundations are provided
and at other joints if the joints are carefully laid so that a good bond
develops.

44. 40
 Shear strength also comes into play because of the interlocking of stone
in masonry dams.
 The factor of safety against sliding shall be computed from the following
equation and shall not be less than 1.0
Where,
FS = factor of safety against sliding,
ΣW = dead load of the dam,
ΣPU = total uplift force,
μ = tan φ = coefficient of internal friction of the material (varies from 0.65 to
0.75 for concrete),
= cohesion of the material or permissible shear stress at the plane considered
(=1.4 N/mm2 for concrete),
A = area under consideration for cohesion,
Fφ = partial factor of safety in respect of friction,
Fc = partial factor of safety in respect of cohesion,
ΣFH = total horizontal force.
The partial factor of safety in respect of friction and partial factor of safety in
respect of cohesion are follows-
For final designs, the value of cohesion and internal friction shall
be determined by actual laboratory and field tests.
6. Compression & crushing-

45. 41
In order to calculate the normal stress distribution at the base, or at any section,
let ΣFH be the total horizontal force,
ΣFV be the total vertical force and
R be the resultant force cutting the base at an
Eccentricity e from the centre of the base of width b, which is equal to where⎯x
is the distance of the resultant force R from the toe given by-
The normal stress at any point on the base will be the sum of the Direct stress
and the bending stress. The direct stress is-
Bending stress at any fibre at distance y from Neutral Axis is-

46. 42
For rectangular section of 1 m wide and b m deep-
and for extreme fibre at toe or heel, y = b/2 hence the total normal stress pn is
given by-
The positive sign will be used for calculating normal stress at the toe, since the
Bending stress will be compressive there, and negative sign will be used for
calculating normal stress at the heel.
The normal stress distributions for a general case when e < b/6 the stress at both
toe and heel are compressive. Evidently, the max compressive stress occurs at
the toe and for safety, this should not be greater than the allowable compressive
stresses both for the dam and foundation materials. When the eccentricity e is
equal to b/6 we get-
7. Tension-

47. 43
If e > b/6, the normal stress at the heel will be -ve or tensile. When the
eccentricity e is greater than b/6 a crack of length will develop due to tension
which can be calculated as-
 No tension should be permitted at any point of the dam under any
circumstance for moderately high dams.
 For no tension to develop, the eccentricity should be less than b/6.
 Or, the resultant should always lie within the middle third.
Effect of Tension Cracks-
 Since concrete cannot resist the tension, a crack develops at the heel,
which modifies the uplift pressure diagram.
 Due to tension crack, the uplift pressure increases in magnitude and net
downward vertical force or the stabilizing force reduces.
 The resultant force gets further shifted towards toe and this leads to
further lengthening of the crack.
 The base width thus goes on reducing and the compressive stresses on toe
goes on increasing, till the toe fails in compression or sliding.
8. Principal and Shear Stresses-

48. 44
Consider an elementary triangular section at either the heel or the toe of the dam
section such that stress intensities may be assumed to be uniform on its faces.
The face of the dam will be a principal plane as water pressure acts on it in the
perpendicular direction, with no accompanying shear stress. Since the principal
planes are mutually at right angle, the plane AB, right angle to AC, will have
only a normal stress on it, and will be the other principal plane. The forces
acting on the elementary section are shown in Fig-
Principal Stresses-
Let ds, dr and dy be the lengths of AC, AB and BC; p = intensity of water
pressure; σ1 = principal stress on plane AB; τ = shear stress; and pn = normal
stress. Considering unit length of the dam, the normal forces on the planes AB,
BC and CA are respectively σ1 dr, pn dy and p ds. Resolving all the forces
in the vertical direction, we get-
 The principal stress relationship is applicable to both u/s and d/s faces.

49. 45
 It should be noted, however, that for the u/s face σ1 will always be less
than p. Hence σ1 is the minor principal stress and p is the major
principal stress for the u/s face.
 For the d/s face σ1 will always be greater than p, so σ1 is the major
principal stress and p is the minor principal stress.
 For the d/s side, the worst condition will be when there is no tailwater,
and hence p will be zero and σ1 will be maximum.
 If pe is the intensity of hydrodynamic pressure of tailwater due to an
earthquake the principal stress at the d/s becomes-
Shear stresses-
Resolving all the forces in the horizontal direction, we get-
Substituting the value of σ1 we get-
 The above equation is applicable for d/s side only.
 For the u/s side, the magnitude of τ will be the same but its direction will
be reversed.
 If tailwater is neglected (p = zero), the shear stress at the d/s side will be
maximum.
 Considering the hydrodynamic pressure due to earthquake, the shear
stresses at d/s and u/s are given by-
9. Elementary Profile of a Gravity Dam-
 In the absence of any force other than the forces due to water, an
elementary profile will be triangular in section, having zero width at the

50. 46
water level, where water pressure is zero, and a maximum base width b,
where the maximum water pressure acts.
 The section of the elementary profile is of the same shape as the
hydrostatic pressure distribution diagram.
Consider main three forces acting on the elementary profile of a gravity dam-
1. Weight of the dam-
2. Water pressure-
3. Uplift pressure-
where C = uplift pressure intensity factor
Base width of the Elementary Profile-
(A).No Tensile Stress Criterion:-

51. 47
For the reservoir full condition, for no tension to develop, the resultant R must
pass through the outer third point. Taking the moment of all forces about M2
andequating it to zero (since the moment of R about M2 is zero), we get-
where Sc = specific gravity of dam material
(B).No Sliding Criterion:-
For no sliding to occur, horizontal force causing sliding should be balanced by
the frictional forces opposing the same. Hence,
The width provided for the elementary profile should be greater of the width
given by the both criteria. If both criteria are satisfied simultaneously then-
Stresses developed in the Elementary Profile-
(A). Base width from No Tension Criterion:-
Principal Stress:
For full reservoir condition in elementary profile e = b/6 and
Hence, the normal stresses at the toe and heel are

52. 48
Corresponding principal stress at the toe (tan φ = b/H and no
tailwater or p = 0) will be
Shear Stress:
Following similar procedure, shear stress at the toe will be-
Substituting b from no tension criterion-
Since the normal stress at the heel is zero, the principal stress and shear stress
will be zero at heel.
(B). Reservoir Empty Condition:-
When the reservoir is empty, the only force acting on the elementary profile will
be its weight, acting through the first third point M1. Hence, ΣFV = W, and
e = -b/6 so shear stress is zero and the maximum compressive normal stress
equal to principal stress at the heel or toe thus-
Limiting Height of a Gravity Dam-
The only variable in the expression for the principal stress σ1 at the toe is H.
The maximum value of this principal stress should not exceed the allowable
stress σper for the material ie σ1 ≤ σper. In the limiting case-

53. 49
From which, the limiting height Hlim is-
For finding Hlim, it is usual not to consider the uplift. For C = 0, we get-
 If the height of the dam is more than Hlim, the max compressive stress
will exceed the permissible stress and that condition is undesirable.
 Classification of gravity dam
 Low gravity dam (H < Hlim )
 High gravity dam (H > Hlim )
 For a concrete dam (Sc = 2.40 and σper = 3.0 N/mm2), the limiting height
is about 88 m.
 If higher grade concrete (σper ≥= 3.0 N/mm2) is used then the limiting
height would be more.
 If the height of the dam to be constructed is more than that Hlim , the
section will have to be given extra slopes to the u/s and d/s sides, below
the limiting height, to bring the compressive stress within the permissible
limits.
Practical Profile of a Gravity Dam-

54. 50
 The elementary profile of a gravity dam is triangular in shape, having
zero width at the top.
 However, a truly triangular section is not practical nor is it necessarily the
most economical section.
 The elementary profile of the gravity dam is only a theoretical profile
because such a profile is not possible in practice.
 Deviation from the elementary profile is due to the provision of
 freeboard
 Top width or roadway at the top
 Additional loads due to the roadway
Effect of Freeboard-
 Freeboard is the margin provided between the top of dam and H.F.L. in
the reservoir to prevent the splashing of the waves over the non-overflow
section.
 It also takes care of any unforeseen floods in the reservoir.
 The freeboard adopted shall be 1.5 times the corresponding wave height
hw above normal pool elevation or maximum reservoir level, whichever
gives the higher crest elevation for the dam.
 The freeboard above maximum reservoir level shall, however, be in no
case less than 0.9 m
 Current practice is to provide a max freeboard equal to 3 to 4 % of the
dam height, though free board equal to 5 % or more might prove
economical.
Effect of Topwidth-
 If some top width T = AD is provided for the elementary section ABC,
the resultant of the dam section will be shifted to the u/s when the
reservoir is empty.
 AM1 is the inner third point line, and MI is the line passing through the
centroid of the added triangle ADE. Both these lines intersect at point H.
 For all sections below plane FHG, the resultant will, therefore, be shifted
to the left of line AM1, causing tension at the down stream face when the
reservoir is empty.
 This will require the provision of u/s batter FC1 below the plane FHG.

55. 51
In order to find the depth h' of the plane FHG below which u/s batter is
required, we have-
Thus for heights greater than h’, u/s batter will have to be provided. The
centroidal line MIJ intersects with the outer-third point line AM2 at J. Hence,
when the reservoir is full, the resultant of all sections below the plane KJE is
shifted to the u/s side.
 In order to bring the resultant back to the outer third point line, for the
sake of economy, the slope of d/s face may be flattened, bringing it from
EB to position EB1.
 Thus, due to the provision of some top width T, the net economical
section will be ADEB1C1F
 It can be seen that as the top width is increased, the u/s batter is increased
while the d/s slope is decreased.
 Increase in concrete volume due to provision of top width is counter-
balanced by the reduction in the d/s slope at lower levels.
 The concrete added for the provision of top width decreases, rather than
increases, the total concrete volume in the dam.

56. 52
 However, the most economical top width is the function of height of
dam.
 Creager has shown that the most economical top width, without,
considering earthquake effects, is found to be about 14 % of the height of
dam.
 However, for dams of low height, the top width provided on the basis of
economy (ie.14 % of height) may have to be increased from other
practical considerations, such as provision of roadway on the top etc.
 Thus due to provisions of freeboard and top width, some concrete is to be
provided to the upstream side and some concrete is removed from the
downstream side to eliminate tension and/or to economize.
Stability Analysis of dam-
The stability analysis of gravity dams may be carried out by various methods, of
which the gravity method is described here. In this method, the dam is
considered to be made up of a number of vertical cantilevers which act
independently for each other. The resultant of all horizontal and vertical forces
including uplift should be balanced by an equal and opposite reaction at the
foundation consisting of the total vertical reaction and the total horizontal shear
and friction at the base and the resisting shear and friction of the passive wedge,
if any. For the dam to be in static equilibrium, the location of this force is such
that the summation of moments is equal to zero. The distribution of the vertical
reaction is assumed as trapezoidal for convenience only. Otherwise, the problem
of determining the actual stress distribution at the base of a dam is complicated
by the horizontal reaction, internal stress relations, and other theoretical
considerations. Moreover, variation of foundation materials with depth, cracks
and fissures which affect the resistance of the foundation also make the problem
more complex. The internal stresses and foundation pressures should be
computed both with and without uplift to determine the worst condition. The
stability analysis of a dam section is carried out to check the safety with regard
to-
1. Rotation and overturning

57. 53
2. Translation and sliding
3. Overstress and material failure
Stability against overturning
Before a gravity dam can overturn physically, there may be other types of
failures, such as cracking of the upstream material due to tension, increase in
uplift, crushing of the toe material and sliding. However, the check against
overturning is made to be sure that the total stabilizing moments weigh out the
de-stabilizing moments. The factor of safety against overturning may be taken
as 1.5. As such, a gravity dam is considered safe also from the point of view of
overturning if there is no tension on the upstream face.
Stability against sliding
Many of the loads on the dam act horizontally, like water pressure, horizontal
earthquake forces, etc. These forces have to be resisted by frictional or shearing
forces along horizontal or nearly-horizontal seams in foundation. The stability
of a dam against sliding is evaluated by comparing the minimum total available
resistance along the critical path of sliding (that is, along that plane or
combination of plans which mobilizes the least resistance to sliding) to the total
magnitude of the forces tending to induce sliding.
The stability of gravity dam can be approximately and
easily analysed by two dimensional( gravity method) and by three dimensional
methods such as slab analogy method, trial load twist method, or by
experimental studies on model. Two dimensional gravity method is discussed
below-
Gravity Method (Two Dimensional Stability Analysis)-
The preliminary analysis of all gravity dams can be made easily by isolating a
typical cross-section of the dam of a unit width. This section is assumed to
behave independently of the adjoining sections. In other words, the dam is

58. 54
considered to be made up of a number of cantilevers of unit width each, which
act independently of each other. This assumption of independent functioning of
each section, disregards the beam action in the dam as a whole.
If vertical transverse joint of dam are not grouted or keyed together, this
assumption is nearly true. Hence for wide U-shaped valleys, where transverse
joints are not generally grouted, this assumption is nearly satisfied. But for
narrow V-shaped valleys, where the transverse joints are generally keyed
together and the entire length of the dam acts monolithically as a single body,
this assumption may involve appreciable errors. In such cases, preliminary
designs may be done by gravity method and precise final designs may be
carried out by any of the available three dimensional methods.
Assumptions-
The various assumptions made in the two dimensional design of gravity dams
are summarised below:
(i) . The dam is considered to be composed of number of cantilevers, each of
which is 1 m thick and each of which acts independent of the other.
(ii).No loads are transferred to the abutments by beam action.
(iii).The foundation and the dam behave as a single unit; the joint being perfect.
(iv).The material in the foundation and the body of the dam are isotropic and
homogeneous.
(v).The stress developed in the foundation and the body of the dam are within
elastic limits. (vi).No movements of the foundation are caused due to
transference of loads. (vii).Small opening made in the body of the dam do not
affect thegeneral distribution of stress and they only produce local effects asper
St. Venant's principle.
Procedure-
Two dimensional analysis can be carried out analytically .
Analytical Method. The stability of the dam can be analysed in the following
steps:
(i). Consider unit length of the dam.

59. 55
(ii). Work out magnitude and directions of all vertical forces acting on the dam
and their algebraic sum, i.e. ∑V.
(iii). Similarly, work out all horizontal forces and their algebraic sum, i.e ∑H.
(iv). Determine lever arm of all these forces about toe.
(v). Determine the moments of all these forces about toe and find out the
algebraic sum of all those moments, i.e.∑M. (vi). Find out the location of the
resultant forces by determining its distance from the toe, =
(vii).Find out the eccentricity (e) of the resultant (R) using = . It must be
less than B/6 in order to ensure that no tension is developed anywhere in the
dam. (vii).Determine the vertical stress at the toe and heel.
(viii). Determine the max normal stress i.e. principal stress at the toe and the
heel. They should not exceed the max allowable value. The crushing strength of
concrete varies between 1500 to 3000 kN/ depending upon its grade M15 to
M30.
(ix). Determine the factor of safety against overturning as equal to -
=
(x). Determine the factor of safety against sliding, using sliding factor Should
lie between 1.2 to 1.5
Construction of concrete gravity dam-
River diversion-
Regardless of the type of dam, whether concrete or embankment types, it is
necessary to de-water the site for final geological inspection, for foundation
improvement and for the construction of the first stage of the dam. In order to
carry out the above works the river has to be diverted temporarily. The
magnitude, method and cost of river diversion will depend upon the cross-
section of the valley, the bed material in the river, the type of dam, the expected
hydrological conditions during the time required to complete the dam

60. 56
construction works, and finally upon the consequences of failure of any part of
the temporary works. For concrete dams, it may be necessary to divert the river
during the first phase of the construction of the dam. Once this is complete, the
river may be allowed to overtop the dam and flow without causing serious
damages to the structure or its foundation. For concrete dams, sluice openings
are left open in the first stage of concreting and the higher stages constructed. If
the second stage outlets are too small for the flood to pass, they would be
submerged after the whole works.
Diversion Channels-
A concrete or masonry dams could be allowed to get overtopped during floods
when construction activity is not in progress. The resulting damage is either
negligible or could be tolerated without much concern. Therefore, it is
customary to adopt diversion flood which is just adequate to be handled during
non monsoon season, when construction activity of the dam is continued.
Generally the largest observed non-monsoon flood or non-monsoon flood of
100 year return period is adopted as a diversion flood. This is generally a small
fraction of the design flood of the spillway and, therefore, diversion channel
required to handle this flood is obviously small. Advantage is also taken of
passing the floods over partly completed dam or spillway blocks, thereby
keeping the diversion channel of relatively smaller size. In such a case a small
excavated channel either in the available width of the river or one of the banks
of the river proves to be adequate. Construction sluices are located in such
excavated channels which allow passage of non-monsoon flows without
hindrance to the construction activity. Such sluices are subsequently plugged
when the dam has been raised to adequate height. If the pondage is not allowed
even when the dam has been raised to sufficient height, the river outlets are
often provided in the body of the non overflow or overflow dam to pass the non
monsoon flows which later on are kept for permanent use after completion of
construction. If the diversion channel is excavated on one of the river banks, it
is possible to use the same for locating an irrigation outlet, a power house or a
spillway depending upon the magnitude and purpose of the project. Figures
show typical layouts of diversion channel for masonry/concrete dams in wide
and narrow rivers respectively.

61. 57
Preparation of foundation for dam construction-
A concrete gravity dam intended to be constructed across a river valley would
usually be laid on the hard rock foundation below the normal river overburden

62. 58
which consists of sand, loose rocks and boulders. however at any foundation
level the hard rock foundation, again, may not always be completely
satisfactory all along the proposed foundation and abutment area, since locally
there may be cracks and joints, some of these (called seams) being filed with
poor quality crushed rock. Hence before the concreting takes place the entire
foundation area is checked and in most cases strengthened artificially such that
it is able to sustain the loads that would be imposed by the dam and the
reservoir water, and the effect of water seeping into the foundations under
pressure from the reservoir. Generally the quality of foundations for a gravity
dam will improve with depth of excavation. Frequently the course of the river
has been determined by geological faults or weaknesses. In a foundation of
igneous rock, any fault or seam should be cleaned out and backfilled with
concrete. A plug of concrete of depth twice the width of the seam would usually
be adequate for structural support of the dam, so that depth of excavation will,
on most occasions depend upon the nature of infilling material, the shape of the
excavated zone and the depth of cutoff necessary to ensure a acceptable
hydraulic gradient after the reservoir is filled. An example of this type of
treatment for Bhakra dam is shown in Figure .
Improvement of the foundation for a dam may be effected by the following
major ways:
1. Excavation of seams of decayed or weak rock by tunneling and backfilling
with concrete.
2. Excavation of weak rock zones by mining methods from shafts sunk to the
zone and backfilling the entire excavated region with concrete.
3. Excavation for and making a subterranean concrete cutoff walls across
leakage channels in the dam foundation where the where the water channels are
too large or too wet for mining or grouting
4. Grouting the foundation to increase its strength and to render it impervious.

63. 59
Grouting of the foundation of the dam to consolidate the entire foundation rock
and consequently increasing its bearing strength is done by a method that is
referred to as consolidation grouting. This is a low pressure grouting for which
shallow holes are drilled through the foundation rock in a grid pattern. These
holes are drilled to a depth ranging from 3 to 6 m. prior to the commencement
of the grouting operation, the holes are thoroughly washed with alternate use of
water and compressed air to remove all loose material and drill cuttings. The
grout hole are then tested with water under pressure to obtain an idea of the
tightness of the hole which is necessary to decide the consistency of the grout to
be used and to locate the seams or other openings in the rock which are to be
plugged . The grout is then injected with these holes at relatively low pressure
which is usually less than about 390 KN/m². Since this is a low pressure
grouting it is accomplished before any concrete for the dam is laid. This
grouting results in the consolidation of the foundation into more or less
monolithic rock by bonding together the jointed or shattered rocks.

64. 60
Construction of Galleries in Gravity Dams-
Galleries are horizontal or sloping openings or passages left in the body of the
dam. They may run longitudinally (i.e. parallel to dam axis) or transversely (i.e.
normal to dam axis) and are provided at various elevations. All the galleries are
interconnected by steeply sloping passages or by vertical shafts fitted with stairs
or mechanical lifts. The size of a gallery will depend upon the size of the dam
and the function of the gallery.
Functions and type of galleries in dams-

65. 61
(1). Foundation Gallery-
A gallery provided in a dam may serve one particular purpose or more than one
purpose. For example, a gallery provided near the rock foundation, serve to
drain off the water which percolates through the foundations. This gallery is
called a foundation gallery or drainage gallery. It runs longitudinally and is
quite near to the u/s face of the dam. Its size usually varies from 1.5 m x 2.2 m
to 1.8 m x 2.4 m. Drain holes are drilled from the floor of this gallery after the
foundation grouting has been completed. Seepage is collected through these
drain holes. The size of gallery should be sufficient to accommodate at least a
drilling machine. Besides drainage off seepage water, it may be helpful for
drilling and grouting of the foundations, when this cannot be done from the
surface of dam.
(2). Inspection Galleries-
The water which seeps through the body of dam is collected by means of a
system of galleries provided at various elevations (say at heights of 15 m or so)
and interconnected by vertical shafts, etc. All these galleries, besides draining
off seepage water, serve inspection purpose. They provide access to the interior
of the dam and are, therefore, called Inspection Galleries. However, galleries in
dams are seldom provided for purely inspection purposes. They generally serve
other purpose along with this purpose. Their main function are summarised
below-
(a). They intercept and drain off water seeping through the dam body.
(b). They provide access to dam interior for observing and controlling the
behaviour of dam.
(c). They provide enough space for carrying pipes, etc during artificial cooling
of concrete.
(d).They provide access for grouting the contractions joints when this cannot be
done from the face of the dam.
(e).They provides access to all outlets and spillway gates, valves etc, by
housing their electrical and mechanical controls. All these gates, valves etc can
be easily control by men, from inside the dam itself. (f). They provide space for

66. 62
drilling and grouting of foundations, then it cannot be done from the surface of
the dam. Generally, the foundation gallery is used for this purpose.
Cross-section of Dam Galleries-
Dam galleries are formed as the concrete is placed and its size depends upon
the function of gallery and also upon the size of the dam. The provision of
gallery in a dam body, changes the normal pattern of stress in the body of the
dam. Stress concentration may, therefore, occur at corners, and hence, in order
to minimise this stress concentrations, the corners must be rounded smoothly.
Tension and compression zones may be worked out and proper reinforcements,
etc are provided to counter act them.
CHAPTER - 3
FORCES ACTING ON DAM
STRUCTURE
Fundamentally a gravity dam should satisfy the following criteria-

67. 63
1. It shall be safe against overturning at any horizontal position within the dam
at the contact with the foundation or within the foundation.
2. It should be safe against sliding at any horizontal plane within the dam, at the
contact with the foundation or along any geological feature within the
foundation.
3. The section should be so proportional that the allowable stresses in both the
concrete and the foundation should not exceed. Safety of the dam structure is to
be checked against possible loadings, which may be classified as primary,
secondary or exceptional. The classification is made in terms of the applicability
and/or for the relative importance of the load.
1. Primary loads are identified as universally applicable and of prime
importance of the load.
2. Secondary loads are generally discretionary and of lesser magnitude like
sediment load or thermal stresses due to mass concreting.
3. Exceptional loads are designed on the basis of limited general applicability or
having low probability of occurrence like inertial loads associated with seismic
activity.
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 forces that give stability
to the dam include:
1. Weight of the dam
2. Thrust of the tail water
The forces that try to destabilize the dam include:
1. Reservoir water pressure
2. Uplift
3. Forces due to waves in the reservoir
4. Ice pressure
5. Temperature stresses
6. Silt pressure
7. Seismic forces
8. Wind pressure
The forces to be resisted by a gravity dam fall into two categories as given
below:
1. Forces, such as weight of the dam and water pressure which are directly
Calculated from the unit weight of materials and properties of fluid pressure and
2. Forces such as uplift, earthquake loads, silt pressure and ice pressure which
are assumed only on the basis of assumptions of varying degree of reliability. In

68. 64
fact to evaluate this category of forces, special care has to be taken and reliance
placed on available data, experience and judgement.
Figure shows the position and direction of the various forces expected in a
concrete gravity dam. Forces like temperature stresses and wind pressure have
not been shown. Ice pressures being uncommon in Indian context have been
omitted.
For consideration of stability of a concrete dam, the following assumptions are
made:
1. That the dam is composed of individual transverse vertical elements each of
which carries its load to the foundation without transfer of load from or to
adjacent elements. However for convenience, the stability analysis is commonly
carried out for the whole block.
2. That the vertical stress varies linearly from upstream face to the downstream
face on any horizontal section.

69. 65
The Bureau of Indian Standards code IS 6512-1984 “Criteria for design of solid
gravity dams recommends that a gravity dam should be designed for the most
adverse load condition of the seven given type using the safety factors
prescribed.
Depending upon the scope and details of the
various project components, site conditions and construction programme one or
more of the following loading conditions may be applicable and may need
suitable modifications. The seven types of load combinations are as follows:
1. Load combination A (construction condition): Dam completed but no water
in reservoir or tailwater.
2. Load combination B (normal operating conditions): Full reservoir elevation,
normal dry weather tail water, normal uplift, ice and silt (if applicable)
3. Load combination C: (Flood discharge condition) - Reservoir at maximum
flood pool elevation ,all gates open, tailwater at flood elevation, normal uplift,
and silt (if applicable)
4. Load combination D: Combination of A and earthquake
5. Load combination E: Combination B, with earthquake but no ice
6. Load combination F: Combination C, but with extreme uplift, assuming the
drainage holes to be Inoperative
7. Load combination G: Combination E but with extreme uplift (drains
inoperative) It would be useful to explain in a bit more detail the different
loadings and the methods required to calculate them. These are explained in the
following sections.
The significant loadings on a concrete gravity dam include the self-
weight or dead load of the dam, the water pressure from the reservoir, and the
uplift pressure from the foundation. There are other loadings, which either occur
intermittently, like earthquake forces, or are smaller in magnitude, like the
pressure exerted by the waves generated in the reservoir that hits the upstream
of the dam face. These loadings are explained in the following section.
Dead load-
The dead load comprises of the weight of the concrete structure of the dam body
in addition to pier gates and bridges, if any over the piers. The density of
concrete may be considered as 2400 kg/m³. Since the cross section of a dam
usually would not be simple, the analysis may be carried out by dividing the
section into several triangles and rectangles and the dead load (self weight) of
each of these sections (considering unit width or the block width) computed

70. 66
separately and then added up. For finding out the moment of the dead load
(required for calculating stresses), the moments due to the separate sub–parts
may be calculated individually and then summed up.
Water pressure on dam-
The pressure due to water in the reservoir and that of the tailwater acting on
vertical planes on the upstream and downstream side of the dam respectively
may be calculated by the law of hydrostatics. Thus, the pressure at any depth ‘h’
is given by ‘γh’ kN/m² acting normal to the surface. When the dam has a
sloping upstream face, the water pressure can be resolved into its horizontal and
vertical components, the vertical component being given by the weight of the
water prism on the upstream face and acts vertically downward through the
centre of gravity of the water area supported on the dam face.
In spillway section, when the gates are closed, the water pressure can be worked
out in the same manner as for non–overflow sections except for vertical load of
water on the dam itself. During overflow, the top portion of the pressure triangle
gets truncated and a trapezium of pressure acts (Figure 24).
Uplift pressures-
Uplift forces occur as internal pressure in pores, cracks and seams within the
body of the dam, at the contact between the dam and its foundation and within
the foundation. The recent trends for evaluating uplift forces is based on the
phenomenon of seepage through permeable material. Water under pressure
enters the pores and fissures of the foundation material and joints in the dam.
The uplift is supposed to act on the whole width plane, that is being considered,

71. 67
either at the base or at any position within the dam. The uplift pressure on the
upstream end of the considered horizontal plane is taken as ‘γ ’ where ‘ ’
is the depth of water above the plane. On the downstream the value is ‘γ ’
where ‘ ’ is again the depth of water above the plane.
Figure 25 illustrates the uplift pressure on a concrete gravity dam’s non
overflow section through two planes – one at the base and the other at the
horizontal plane which is above the tail water level. In Figure 25, the drainage
holes either in the body of the dam, or within the foundation has not been
considered. If the effects of the drainage holes are considered, then the uplift
pressure diagram gets modified as shown in Figure 26. If there is crack at any
plane of the dam, or at the base then the uplift pressure diagram gets further
modified as shown in Figure27.

72. 68
As such, the uplift pressure is assumed to act throughout the base area. Further
it is also assumed that they remain unaffected by earthquakes.
Silt pressure-
The weight and the pressure of the submerged silt are to be considered in
addition to weight and pressure of water. The weight of the silt acts vertically
on the slope and pressure horizontally, in a similar fashion to the corresponding
forces due to water. It is recommended that the submerged density of silt for
calculating horizontal pressure may be taken as 1360 kg/m³. Equivalently, for
calculating vertical force, the same may be taken as 1925 kg/m³.
Earthquake (seismic) forces-
Earthquake or seismic activity is associated with complex oscillating patterns of
acceleration and ground motions, which generate transient dynamic loads due to
inertia of the dam and the retained body of water. Horizontal and vertical
accelerations are not equal, the former being of greater intensity. The
earthquake acceleration is usually designated as a fraction of the acceleration
due to gravity and is expressed as α⋅g, where α is the Seismic Coefficient. The
seismic coefficient depends on various factors, like the intensity of the
earthquake, the part or zone of the country in which the structure is located, the
elasticity of the material of the dam and its foundation, etc. For the purpose of
determining the value of the seismic coefficient which has to be adopted in the
design of a dam, India has been divided into five seismic zones, depending upon
the severity of the earthquakes which may occur in different places. A map

73. 69
showing these zones is given in the Bureau of Indian Standards code IS: 1893-
2002 (Part-1) “Criteria for earthquake resistant design of Structures (fourth
revision)”, and has been reproduced in Figure 28.
The BIS code also indicates two methods that may be used for determining the
Coefficient α.
These are:
1. The Seismic Coefficient Method (for dam height up to 100m)
α=βΙα0 ….(2)
2. The Response Spectrum Method (for dams taller than 100m)
α=βΙΦ0 (Σα/γ) ….(3)
where,
β = Soil-foundation system factor, which may be taken as 1.0 for dams
FIG. 28 SHOWING SEISMIC ZONES IN INDIA

74. 70
I = Importance factor, which may be taken as 2.0 for dams
α0=The basic seismic Coefficient, the value of which for each of the five zones
is given the following table:
F0 = The seismic Zone Factor for average acceleration spectra, the value of
which for each of the five zones is given in the following table:
Sa/g = the average acceleration coefficient that has to be read from Figure 29,
corresponding to the appropriate natural period of vibration and damping of the
structure.
The natural (or fundamental) period of vibration of a gravity dam may be
determined by the following expression:
Where,
T = The natural period of vibration of the dam, in seconds
H = The height of the dam, in m
B = The base width of the dam, in m
γm = Specific weight of the material with which the dam is constructed. For
concrete dams, it may be taken as about 26.5KN/m3
g = Acceleration due to gravity (=9.8m/s2)
α0

75. 71
Es = Modulus of elasticity of the dam material. For concrete dams, it may be
taken as about 32.5 GPa.
Using the value obtained for the natural period of vibration (T) of the dam, and
Assuming the recommended value of 5 percent damping, as per IS: 1893-1984,
the value of (Sa/g) may be obtained from Figure 29, and the value of the
seismic coefficient computed using the appropriate equation.
As mentioned earlier, the earthquake forces cause both the dam structure as well
as the water stored in the reservoir to vibrate. The forces generated in the dam
are called the Inertia Force and that in the water body, Hydrodynamic Force.
Since the earthquake forces are generated due to the vibration of the earth itself,
which may be shaking horizontally in the two directions as well as vibrating
vertically. For design purpose, one has to consider the worst possible scenario,
and hence the combination that is seen to be the least favourable to the stability
of the dam has to be considered. When the dam has been newly constructed, and
the reservoir has not yet been filled, then the worst combination of vertical and
horizontal inertia forces would have to be taken that cause the dam to topple
backward as shown in Figure 30. The notations used in the figure are as
follows:
: Horizontal earthquake force acting in the upstream direction
: Horizontal earthquake force acting in the downstream direction
: Vertical earthquake force acting upwards
: Vertical earthquake force acting downwards

76. 72
Under the reservoir full condition, the worst combination of the inertia forces is
the one which tries to topple the dam forward, as shown in Figure 31.
In the Seismic Coefficient method, the horizontal and vertical acceleration
coefficients, αh and αv, respectively, are assumed to vary linearly from base of
the dam to its top as shown in Figure 32.

77. 73
In order to find the force generated due to the acceleration, it would be
necessary to divide the dam into horizontal strips, finding out the force on each
strip, and then integrating for the total dam height (Figure 33). This has to be
done for both horizontal force H and vertical force V. Taking moment of these
forces for each strip about any point in the dam body (say the heel or the toe)
and integrating over the dam height would give the moment due to horizontal
and vertical earthquake forces.
In the Response Spectrum method, the horizontal seismic coefficient
is assumed to be equal to the value of the seismic coefficient α obtained by