9
1. INTRODUCTION
1.1. THE NEED FOR DAMS
Dams are built to impound water and discharge it for a variety of purposes into
channels, tunnels and conduits, to create head of water needed for hydropower
generation and to protect the land against the ravages of floods. Above all, however
they provide active storage for the management of water, which is for striking a
balance between natural flow regimes on the one hand and patterns of demand, which
are normally quite different on the other. Depending on the size of the reservoir, this
equalizing function may occupy a daily, weekly or annual cycle, or even tide over
multiannual periods.
All the dams, with only very few exceptions, offer security against two extremes: (1)
Against a lack of water bringing draught, power failures, dried out river beds and
falling ground water levels and (2) Against too much water, especially too much too
quickly, in the form of raging floods causing devastating inundation to farmland and
people's homes.
The primary function of dams worldwide is to provide reliable water supplies to a
major proportion of the approximately 2 700 000 km2 presently under irrigation in the
world. And for the future the United Nations Development Programme (UNDP)
requires a 3% compound rate of annual growth to meet the needs of an extra one
billion people in the next ten years.
The control of floods, which still cause 40% of fatalities from natural catastrophes
worldwide, has always been particularly significant motive for dam construction
everywhere, and sometimes its primary purpose. In many other cases flood control is
a valuable spin-off from dams built primarily to serve other purposes, which also
represent the subsequent source of revenue, in particular power production.
With a total annual generation of 2.1 million GWh, hydropower today account for
20% of electricity consumption worldwide. Even at a conservative estimate, the total
exploitable potential is at least six times larger - an incentive for the further
development of this source of clean, renewable energy.
Storage reservoirs form the backbone of innumerable water supply systems, and many
more of them will still be needed for this purpose. Efforts to supply water have to
keep up with the unprecedented growth in population that already face a serious
scarcity of safe water.
Augmentation of low flows in rivers, the improvement of water quality, the
enhancement of tourism, recreation areas and fishery are all additional assets rightly
claimed for many dams and their reservoirs.
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At present reservoirs behind the dams store some 5500 km3 of water, of which about
3600 km3 is available for regular use. This figure is of the same magnitude as the
worldwide water withdrawals for consumptive use, estimated at present at about 3700
km3/year, of which 68% is used for the irrigation of croplands, 24% for industry and
8% for domestic and industrial purposes. The sheer magnitude of these figures shows
how much dams and appurtenant reservoirs have become an integral part of our large-
scale engineered infrastructure, of our man-made basis of survival. At the same time
the rate of growth in the world population and the pressures that growth is creating in
terms of water, food and energy supplies require the continued creation and
maintenance of further storage volumes.
Today about 45 000 large dams (higher than 15 m) and an estimated 800 000 smaller
ones improve the living conditions of many of the world's six billion people. Yet
about 1.5 billion of these people have no reliable access to clean water and hygienic
conditions, a fundamental human right. Moreover the world population continues to
grow, in some regions at a rapid rate and in concentrated areas.
Dams provide all these benefits, but there is usually also a cost. People, other life
forms and the natural environment are affected when dams and reservoirs are built,
and the impact may require resettlement and relocation. The challenge is to balance
the benefits and costs in the short and long term. When the needs are water supply,
food production, flood control and electricity production, what realistic options and
alternatives does society have, and what are the short and long-term consequences?
Along with the growth in size of the dams and their reservoirs their environmental
impact and the awareness thereof increased as well. In the late 1960's these aspects
became the object of public debates, which, at times degenerated into bitter
controversy.
Besides the change of landscapes - by no means always negative - dam constructions
had drastic consequences whenever large numbers of people had to be resettled from
the reservoir area. Unfortunately, several of these operations were poorly planned
and/or badly managed.
As is the case in other fields of technology, is not the dam construction that should be
blamed if anything goes wrong. To blame is the abuse that occurs for often short-lived
and/or particular advantages. Through a long history, dam engineers have acquired the
ability to serve both goals – need of water storage and environmental and social
compatibility-efficiently, securely and in an environmentally safe way.
Looking ahead, people will continue to build dams for many purposes, especially in
the developing world. The reason is that dams in very many cases will be judged to
represent the best option among the feasible alternatives to satisfy critical human and
societal needs. As the world's population continues to increase in water-scarce
regions, additional water resources must be developed. The only practical way to
achieve this on the scale required is to increase storage capacity and that means to
build more dams.
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1.2. BRIEF HISTORY OF CONCRETE DAM EVOLUTION
The predecessors of modern dams are masonry dams dating back more than 2000
years, and some of these still remain in excellent conditions. In such dams the
upstream and downstream faces have been formed by dressed masonry and the main
body comprises rubble masonry bedded in lime mortar. With the advent in the last
century of Portland cement concrete and the increased labor costs of stone quarrying,
the concrete dam has largely replaced the masonry dam, especially in industrialized
countries.
Along the years the concrete dam has developed into a number of specific types such
as the double curvature arch and the buttress. More recently still, the increased use of
earth moving plant has firmly established roller compaction as the frequently
preferred method for mass concrete construction (Figure 1.1).
Fig.1.1. Development of concrete dam types
In their simplest forms both masonry and concrete dams are gravity structures with
near-vertical upstream faces and downstream slopes in the order of 0.8:1. The water
thrust from upstream is resisted by assumed sliding planes within the dam body and
ultimately through sliding resistance at the base. Friction is the principal
consideration, although in many cases some acknowledgement of effective cohesion
is also used. The science of designing such dams really developed in the last century
with the increased awareness of internal and foundation uplift pressures and their
fundamental importance to the stability of such dams.
RCC dam
FSHD
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Gravity dams are relatively understressed structures, and attempts at economy have
been made by forming voids. Such hollow gravity dams are not common nowadays.
The logical progression from these has been the buttress dam, where a series of
"counterforts" or upstream/downstream walls are used to support a continuous facing.
The facing, or buttress heads, can be profiled to ensure that the head stays in overall
compression, thus minimizing reinforcement requirements.
In buttress and some hollow gravity dams, the foundations between the buttresses are
open, thus eliminating uplift pressure. The upstream faces are also typically sloped to
encourage additional hydraulic load to improve overall stability. In the cases of both
buttress and hollow gravity dams, stresses are higher than in conventional gravity
dams, and therefore the qualities of concrete and foundations needed are also higher.
The use of both types has waned, as a result of the increased costs of labor and
shuttering compared with simple gravity construction.
Arch dams, in masonry form, have been constructed for some several hundred years.
However, the last 50 years has seen the use of advanced mathematical techniques
such as finite element analyses, now enhanced by increased computing power and
availability, to optimize double curvature design. Such dams can of course only be
constructed where the topography and geology are appropriate. The requirement for
good quality concrete is generally high and complications such as joints grouting and
pre-and/or post-cooling of the concrete inevitably increase the cost.
The arch-gravity dam is sometimes seen as a type of dam in its own right; however,
simple analyses generally demonstrate that, in normal working conditions, the arch
action tends to be minimal and, indeed, the dam functions normally as a slender
gravity dam.
Perhaps the biggest advantage which concrete dams have over earth dams is their
ability to tolerate diversion floods with minimal damage and their ability to
accommodate, or act as, spillways, eliminating the need for special separate
structures.
In the case of concrete dams, the most recent revolution has been re-establishing the
concrete gravity dam as an economic alternative, given the introduction of roller
compacted concrete techniques. Initially, three schools emerged. At one extreme was
the use of a relatively lean and porous mix at dams. At the other extreme was the use
of a high paste mix. In the latter case, however, the tendency has been to increase
specification requirements, as problems have developed, and to lose some of the
benefits of cheap roller compaction.
In this sense the evolution of the concrete dam has in fact regressed back to the
largely gravity section by the use of a different construction method, although
examples also exist of both arch and arch-gravity RCC structures.
An intermediate form of gravity dam is the FSHD or "hardfill" dam. This form of
dam, in effect, represents a very weak form of RCC, but with cohesion and more self-
supporting than pure rockfill. The dam would slope both upstream and downstream.
Such a dam can be expected to be permeable and, therefore, some form of upstream
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facing is required such as those currently used on concrete faced rockfill dams. Such a
facing can be incorporated in the dam construction, while a number of concrete dams
have now been waterproofed upstream with geomembranes.
Another intriguing option could be the fully drained gravity dam, which is a simple
gravity dam with an impermeable face founded on a confined layer of rockfill. A
secure, impermeable barrier, with drainage provision, would protect the main body
from water penetration, while a free-draining layer of rockfill under the dam would
mean that foundation seepage pressure could be relieved, eliminating upthrust.
Eliminating uplift can, in theory, reduce the downstream slope of a simple gravity
dam from 0.8:1 to 0.5:1.
1.3. BRIEF HISTORY OF EMBANKMENT DAM EVOLUTION
The basic concept of the embankment dam can be traced back 4500 years to the
earliest well known example of the Sadd-el-Kafara dam on the River Nile. This was a
zoned dam, although generally the earliest dams, and even today the simplest dams,
are homogeneous earth embankments: that is, the material used for the construction
remains essentially constant throughout. The material therefore has to provide both
sufficient impermeability to give the dam its purpose, while at the same time it must
have sufficient strength to retain its shape and resist water loads. Internal water
pressures will be based on a phreatic seepage line. Even when attempts are made at
zoning by using the same material compacted to different densities, the result, in
practice, is frequently homogeneity.
Figure 1.2. Simplified development of embankment dam types
The inevitable development from the homogeneous embankment was the zoned dam,
and there are good historic examples of these (Figure 1.2). In the case of the zoned
Bro
ad
ev
olu
tio
na
ry d
irec
tion
Homogenous
Embankment
Zoned
Embankment
Embankment with
Waterproof
Facing
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earthfill or rockfill dam, materials are selected and used for their specific properties
and in proportions guided by local site availability. Typically, the central core of the
dam will be made of a relatively impermeable material such as clay, silt or moraine.
This will be supported upstream and downstream by shoulders, often of random
material. Cores have also been constructed of bitumen, concrete and, less commonly,
steel and plastic.
Key elements in the design of a zoned dam also include the transitions or filters
between the core and the adjacent shoulder material. These can be particularly critical
on the downstream side, where they will act both as filters to retain the migration of
the fine core material and as drainage layers to avoid pressures building up in the
downstream shoulder. Vertical chimney drains may be supplemented, where appro-
priate, by horizontal drains through the shoulders. It should be noted that in the case
of such a zoned embankment with a narrow core, the hydraulic thrust is resisted
almost entirely by the downstream shoulder. It will do this by internal friction and
cohesion, both through the material itself and at and through the foundations. Many
thick cores transfer a major portion of thrust directly into the foundation via shear.
The construction of zoned embankment dams has advanced greatly in the last century
as a result of the efforts of engineers such as Terzaghi who, through rigorous research
and testing, enhanced the art of dam design with sound engineering science. It is
gratifying to the designer, however, to note that design still retains an element of both
art and science. One change which has accompanied the science of earth dams has
been the increased use of optimal compaction densities, a trend which is being relaxed
in circumstances such as wet core construction in high rainfall areas.
Rockfill as a principal construction medium for embankment dams has also advanced
considerably since the 1950s. Early construction often used quarry-run rockfill,
dumped relatively dry.
The next great change came in the 1960s with the increased compaction effected by
vibratory rollers. This permitted increased heights for all types of rock-fill
embankment but, in particular, resulted in a considerable increase of confidence in the
construction of faced rockfill dams. In such dams, the principal body is composed
entirely of rockfill, and the waterproof membrane is placed on the sloping upstream
face. Modern facings tend to be of reinforced concrete or asphalt, although early
examples also included steel and timber. Good design guidelines and precedents exist
now for the confident design of such dams to heights well in excess of 100 m. Careful
attention is needed to aspects such as the peripheral joint and to local seepage
gradients at the lower plinth.
In the case of such dams it should be noted that the entire rockfill body remains
protected from the reservoir and also acts to resist hydraulic water loads. Indeed, the
upstream sloping face will attract a stabilizing vertical load from the water upstream.
In very recent years rockfill embankments have been built which can withstand
overtopping. The design of embankments to overtop is, however, still rare.
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1.4. DAM WORLD SITUATION
Figure 1.3 shows the evolution in the total number of large dams in operation
(according to International Commission of Large Dams a large dam is the one that is
higher than 15 m). At the beginning of the 20-century the total number of large dams
was only 427. In 1950 the dam number reached 5268. Since the World War II the
number of dams has increased considerably, especially in Asia. The last accurate
inventory of large dams was in 1992, when a total number of 36,235 large dams in
operation were registered.
Fig.1.3. Evolution of the number of large dams in the world
The significant increase of in dams since 1992 does not result only from new
constructions but is largely because of the correction of statistics made by China.
In the 21st century the dam construction is expected to maintain its rate of
development at least in Asia and Latin America. It should be noted that in
industrialized countries most of the potential dam construction sites have already been
exploited.
In 2001, a total number of 361 large dams with heights of more than 60 m, and 35
with heights of more than 150 m, were under construction in the world. China,
Turkey, India, Japan and Iran hold the first five places on the list.
Selecting the highest concrete dams, the list of dams under construction includes:
Gravity dams – Kishau (India), H = 236 m; Three Gorges (China), H = 175 m;
Shafaroud (Iran), H = 159 m.
Arch dams – Ertan (China), H = 240 m; Karun IV- Monj (Iran), H = 230 m;
Nukui (Japan), H = 156 m.
The multiple arch dam – Berke (Turkey), H = 201 m.
Selecting the highest embankment dams, the list of dams under construction includes:
Europe
Asia
America
Africa
Australia
TOTAL
Year
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Earthfill dams – Yusufeli (Turkey), H= 270 m; Tehri (India), H= 261 m;
Gotrand (Iran), H=180 m; Xianolangdi (China), H= 154 m.
Impervious core rockfill dams – San Roque (Philippines), H= 200 m; Sykia
(Greece), H= 175 m; Yacambu (Venezuela), H= 158 m.
Concrete face rockfill dams – La Miel (Colombia), H=188 m; Tianshengqiao
(China), H= 178 m; Ita (Uruguay), H= 154 m.
On the other hand in Europe, once the location of all the dam records, only four
concrete dams with heights of more than 100 m were under construction (all of them
gravity dams), three in Spain and one in Italy.
Figure 1.4. shows the evolution of maximum dam heights around the world. The two
main types of dams are presented: concrete dams and embankment dams. For concrete
dams the world record is still held by the Grande Dixance gravity dam built in 1962 in
Switzerland at 285 m. For embankment dams the world record is held by Nurek earth
core rockfill dam built in 1980 in Russia at 308 m.
Fig. 1.4. Evolution of maximum dam heights
The highest arch dam in the world is Vaiont dam (Italy), with a total height of 262 m.
Since the reservoir behind the Vaiont dam is empty due to an unfortunate accident of
the reservoir slopes, the height record among the arch dams belongs to Mauvoisin
(Switzerland) with 237 m.
The records in the field of buttress dams are differentiated by dam types. Among the
massive head buttress dams the highest is Hatanagi (Japan), H = 125m. The highest
hollow gravity dam was completed in 1986 for the Itaipu waterpower development,
with a total height of 186 m. The highest multiple arch dam is Daniel Johnson (built
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in 1970Canada), H + 214 m. As far as flat slab and buttress dams are concerned they
are of a smaller size, the record being realized in 1949 in Argentina, with a height of
88 m.
Although more recently developed, RCC dams are also very well represented in the
list of the highest dams. La Miel I dam in Colombia, commissioned in 2003, has a
height of 188 m. Two other high dams were recently built in Japan: Urayama (H =
156 m, in 1999) and Miyagase (H = 155 m, in 2001).
After Nurek, the second clay core rockfill dam in terms of height is Chicoasen dam in
Mexic, with a total height of 261 m.
The record in the field of earthfill dams is held by Mica dam built in 1973 in Canada,
as a dam with an incined central core. Oroville dam in USA with a height of 230 m is
the second of the same concept.
The highest concrete face rockfill dam in operation is Tianshengqiao, in China, with a
total height of 178 m. Storglomvatn dam in Norway, with a maximum height of 125
m is the highest rockfill dam with asphaltic core in the world.
Looking at history, it can be observed that the welfare of human beings has always
related to the development of hydraulic schemes, among which the most important
civil engineering works are the dams. In the future, hydraulic schemes and dams will
retain this fundamental importance for humanity.
BIBLIOGRAPHY
Hoeg, K. Lecture presented at the World Water Forum, The Hague, in March 2000.
Hydropower and dams. World Atlas 2000.
Hydropower and dams. World Atlas 2000.
Mason, P., J. The evolving dam. Hydropower and dams, Issue five, 1997.
Schnitter, N. A history of dams – the useful pyramids. A.A.Balkema, 1994.
Schleiss,A.,J. The importance of hydraulic schemes for sustainable development in
the 21st century. Hydropower and dams, Issue one, 2000.
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2. GRAVITY DAMS
2.1. INTRODUCTION
Gravity dams are dams that by their own weight resist the forces imposed on them
with a desired factor of safety. Gravity dams are designed so that every unit of length
is stable, independent of every other unit of length; hence, the dams can be straight,
curved or arched, or even crooked. The typical gravity dam is straight, although many
designers curve the axis upstream to gain added stability through arch action.
One hundred years ago, the typical gravity dam was constructed of masonry. Large
stone blocks were shaped and fitted into the structure, and the joints filled with
cement and sand mortar. The materials for concrete gravity dams evolved gradually
into mass concrete. When dams constructed in this way became too expensive, in
comparison with earthfill and rockfill dams, a new construction method evolved for
concrete gravity dams, which placed and compacted concrete materials using earthfill
construction techniques, resulting in the term roller compacted concrete.
2.2. STRUCTURAL FEATURES
2.2.1. LAYOUT
The general layout of a gravity dam is shown in figure 2.1. The dam body is divided
by transverse contraction joints in to blocks each of which carries its load to the
foundation without any transfer of the load from or to adjacent vertical elements. The
block length between two adjacent contraction joints is usually in the range of 15...18
m. The joints are designed to avoid extensive random cracking of mass concrete that
can be induced by shrinkage and thermal contraction. The large amount of heat that is
generated during the concrete hardening leads to a significant change from the
maximum temperature to the final stable temperature inducing large volume changes
with consequent random cracking.
Properly designed contraction joints constitute only one provision for the control of
cracks. Other provisions are as follows:
- The construction of blocks by pouring the concrete in shallow vertical lifts,
preferably not more than 2 m high in large dams;
- The use of low cement content, with a low rate of heat generation;
- Precooling of aggregates and of the mixing water;
- Allowance of sufficient time between the constructions of vertical lifts to
permit a large loss of heat from the surface;
The horizontal line that is located in the middle of the dam crest and connects the two
dam abutments is the dam axis. The dam axis is straight or only slightly curved in
plane.
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The maximum cross section (upstream-downstream) through the dam body is called
the dam profile. The shape of the dam profile is determined by the prescribed loading
conditions, the shear resistance of the foundation rock and the height of the maximum
section.
Fig. 2.1. General layout of a gravity dam:
a. plan view; b. longitudinal and transverse cross sections:
1-dam axis; 2-nonoverflow block; 3-overflow block; 4-lifts; 5-contraction joint; 6-
dam crest; 7-spillway; 8-bottom outlet; 9-stilling basin; 10-ground line; 11-
foundation contour; 12-upstream face; 13-downstream face; 14-dam heel; 15- dam
toe; 16-foundation surface; 17-inspection gallery; 18-grouting and drainage
gallery; 19-grout curtain; 20-drainage drillings.
Several dam profiles, corresponding to representative gravity dams, are shown in
figure 2.2. The upstream face of a gravity dam is usually made vertical or slightly
inclined towards upstream to concentrate the concrete weight at the upstream face
where it acts to overcome the effects of the reservoir water load. The downstream face
usually have a uniform slope that is determined by both stress and stability
requirements at the base. The ratio between the dam basis B and the dam height H
(k=B/H) is in the range of 0.75 ... 0.85.
A batter may be used on the lower part of the upstream face to increase the thickness
at the base to improve the sliding safety of the blocks. If a batter is used, stresses and
stability should be checked where the batter intersects the vertical upstream face.
The crest thickness is dictated by roadway or other access requirements. Its value is
usually in the range of 5.00 to 10.00 m. When additional crest thickness is used the
downstream face should be vertical from the downstream edge of the crest to an
intersection with the sloping downstream face.
In most of the cases several blocks of a gravity dam are designed as overflow or
spillway section. The overflow profile is inscribed in the nonoverflow section. The
curves describing the spillway crest and the junction of the slope with the energy
dissipater are designed to meet the hydraulic requirements.
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Fig. 2.2. Gravity dam profiles
The entire area to be occupied by the base of the gravity dam is excavated to firm
material capable of withstanding the loads imposed by the dam. Generally, a
foundation surface appears as horizontal in the transverse (upstream-downstream)
direction. However, where an increased resistance to sliding is desired, the surface can
be sloped, upward from heel to toe of the dam.
If the canyon profile for a dam site is relatively narrow with steep sloping walls, each
vertical section of the dam, from the center towards the abutments is shorter in height
than the preceding one. Consequently section closer to the abutments will be deflected
less by the reservoir load. A sharp break in the excavated profile of the canyon will
result in an abrupt in the height of the dam. The effect of the irregularity of the
foundation rock causes a marked change in stresses in both the dam and foundation
and in stability conditions. For this reason, the foundation is shaped so that a
uniformly varying profile is obtained along the longitudinal contour, free of sharp
offsets or breaks.
In order to establish an effective barrier to seepage under the dam and to consolidate
the foundation rock the foundation treatment requires rock grouting. A grout mix,
basically consisting in water and cement, is injected in holes drilled into the rock
foundation.
Grouting operations may be performed from the surface of the excavated foundation,
from the top of concrete placements for the dam, from galleries within the dam and
from tunnels driven into the abutments. The preliminary low-pressure shallow
consolidation grouting is followed by high-pressure, deep curtain grouting.
LONGYANGXIA
21
Although a well-executed grouting program may materially reduce the amount of
seepage, some means are provided to intercept the water that percolates through and
around the grout curtain. Drainage is usually accomplished by drilling one or more
lines of holes downstream from the high - pressure grout curtain. As a general rule,
hole depths vary from 20% to 40% of the reservoir depth and 35% to 75% of the deep
curtain grouting depth. Drain holes are drilled from foundation and drainage galleries
within the dam, or from the downstream face of the dam if no gallery is provided.
Several examples of gravity dams are shown on the following figures. At the time of
its completion in 1942, Friant Dam (figure 2.3) was the fourth largest concrete dam
in the world. The dam is a concrete gravity structure with a structural height of 97 m
and a crest 1060 m long. 128 mm diameter drainage holes were drilled into the
foundation rock. In addition, the foundation was grouted by a cement grout curtain
under the upstream toe.
Fig. 2.3. Friant dam
Shasta Dam (figure 2.4) is a curved concrete gravity structure. The dam has a crest
length of 1054 m, a maximum height of 184 m, and a maximum base thickness of 269
m. The downstream face of the dam has a slope of 0.8 horizontal to 1 vertical, and the
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upstream face is vertical except for the portion falling below El. 720.0, which slopes
upstream at o.5 horizontal to 1 vertical.
Fig. 2.4. Shasta dam
The dam, while curved in plan to accommodate the configuration of the site, was
designed as a gravity structure throughout, resisting the pressure of the reservoir by its
sheer mass. Necessity of passing a major portion of the flood flow over the
downstream face of the dam led to the design of the world's highest man-made
waterfall.
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Izvorul Muntelui dam (Figure 2.5) holds the height record for gravity dams in
Romania. The dam has a crest length of 453 m, a maximum height of 127 m, and a
maximum base thickness of 119 m. The upstream face of the dam is inclined towards
upstream presenting two slopes while the downstream face has a more uniform slope
of 0.681 horizontal to 1 vertical, on the average. The dam body is divided into 30
blocks of 15 m wide, out of which four are overflowing blocks located in the central
area.
Two types of concrete were used, according to a concrete zoning concept: (1) face and
foundation concrete, with a cement content of 270 kg/m3 and (2) inner concrete with a
cement content of 175 kg/m3. The drainage system of the dam comprises the drains in
the dam body that collects the infiltrated water through 30 cm diameter porous pipes
and 15 m deep drilling holes in foundation, arranged on three successive rows from
downstream of the grout curtain to the dam toe.
Fig.2.5. Izvorul Muntelui Dam:
1- concrete block; 2- spillway; 3- bottom outlet; 4- gate chamber; 5- access shaft to
the gate chamber; 6- stilling basin; 7- road at the dam crest; 8- inspection galleries; 9-
grout curtain; 10- drainage galleries; 11- lateral wall.
MAIN CROSS SECTION
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2.2.2 FOUNDATION TREATMENT
Excavation – As it was mentioned before, the entire area to be occupied by the base
of the gravity dam should be excavated to firm material capable of withstanding the
loads imposed to the dam, reservoir, and appurtenant structures. Very often the
exploratory drilling or final excavation uncovers faults, seams, or shattered or inferior
rock extending to such depths that it is impracticable to attempt to clear such areas out
entirely. These conditions require special treatment in the form of removing the weak
material and backfilling the resulting excavations with concrete. This procedure of
reinforcing and stabilizing such weak zones is frequently called "dental treatment"
Over excavation to achieve symmetry on a nonsymmetrical site is not recommended.
Sharp breaks in the excavation profile should be avoided. Thrust blocks may be used
to establish an artificial abutment where a natural one does not exist, but not to
provide symmetry.
Foundation Grouting - The principal objectives of foundation grouting continue to
be consolidation (under low pressures) and establishment of an effective barrier to
seepage under and around the dam (under high pressures). Spacing, length and
orientation of grout holes, and the procedure to be followed in grouting a foundation
are dependent on the height of the structure and the geologic characteristics of the
foundation.
Consolidation grouting - Low pressure grouting to fill voids, fracture zones, and
cracks at and below the surface of the excavated foundation is accomplished by
drilling and grouting relatively shallow holes. For structures over 30 m in height, a
preliminary consolidation grout program will call for lines of holes parallel to the axis
of the dam extending from heel to toe, and spaced about 3 to 6 m apart. Holes with a
minimum diameter of 45 mm are staggered on alternate lines to provide better
coverage of the area. The depth varies from 10 to 15 m depending on local conditions
and to some extent on the height of the dam. Such a program is carried out using the
principal of split spacing. Drilling is usually accomplished from the excavated
surface, although in some cases drilling and grouting to consolidate steep abutments
has been accomplished from the tops of concrete placements in the dam to prevent
"slabbing" of the rock. Water-cement ratios for grout mixes may vary widely
depending on the permeability of the foundation rock. Starting water-cement ratios
usually range from 8:1 to 5:1 by volume. An admixture such as sand or clay may be
added if large voids are encountered.
Curtain Grouting - Construction of a deep grout curtain near the heel on the dam to
control seepage is accomplished by drilling deep holes and grouting them using
higher pressure. To permit application of high pressure without causing displacement
in the rock or loss of grout through surface cracks, this grouting procedure is carried
out subsequent to consolidation grouting and after some of the concrete has been
placed. Usually, grouting will be accomplished from galleries within the dam from
tunnels driven into the abutments especially for this purpose.
The alignment of holes should be such the base of the grout curtain will be located the
vertical projection of the hell of the dam. If drilled from a gallery that is some distance
25
from the upstream face, the holes may incline as much as 150 upstream from the plane
of the axis. If the gallery is near the upstream face, the holes will be nearly vertical.
The usual procedure will be first to drill and grout holes approximately 10 to 12 m
apart, or as far apart as necessary to prevent grout from one hole leaking into another
drilled but ungrouted hole. Drilling and grouting of additional intermediate holes,
splitting the spaces between completed holes, will continue until the desired spacing is
reached or until the amount of grout accepted by the last group of intermediate holes
indicates no further grouting is necessary. During the progress of the grouting, local
conditions may determine the actual or final depth of grouting.
The depth of holes depends on the characteristics of the foundation rock. For hard,
dense, relatively tight rock, the depth may be only 30 to 40 percent of the head, but
for rock with more permeable zones, the depth may reach 70 to 100 percent of the
head. The spacing of holes may be only 3 m or less. Foundations usually increase in
density and tightness of seams at greater depth.
Two general methods of grouting are used that permit higher pressures in lower
zones: descending stage grouting and ascending stage grouting. Descending stage
grouting consists of drilling a hole to a limited depth or to its intersection with an
open seam, grouting to that depth, cleaning out the hole after the grout has taken its
initial set, and then drilling and grouting next stage. Ascending stage grouting consists
of drilling a hole to its final depth and grouting the deepest high-pressure stage first by
use of a packer that is seated the top of this stage. After grouting this stage, the grout
pipe is raised so that the packer is at the top of the next stage, which is subsequently
grouted using somewhat lower pressure. This staged process is repeated, working
upward until the hole is completely grouted. Ascending stage grouting is becoming
more generally used, as it reduces the chances for displacement of the foundation
rock, gives better control as to the zones of injection, and expedites drilling.
Foundation Drainage - The purpose of drainage is to collect water that passes
through and around the grout curtain and to prevent the build up of high hydrostatic
pressures at the base of the dam and in the abutments. Usually one or more lines of 75
to 100 mm holes are drilled downstream of the grout curtain. Spacing, depth and
orientation are all influenced by foundation conditions. The holes are usually spaced 3
to 5 m on center. As a general rule, the depth varies from 20 to 40 percent of the
reservoir depth and 35 to 75 percent of the depth of the high-pressure grout curtain.
Drain holes should be drilled after all foundation grouting has been completed in the
area. They can be drilled from foundation and drainage galleries within the dam, or
from the downstream face of the dam if no gallery is provided.
In some instances where the stability of a rock foundation may be beneficiated by
reducing the hydrostatic pressure along planes of potentially unstable rock masses,
drainage holes have been introduced to alleviate this condition. A collection system
for drainages should be designed so that flows can be gathered and removed from the
area.
26
2.2.3. JOINTS
Cracking in concrete dams is undesirable because cracking in random locations can
destroy the monolithic nature of the structure, thereby impairing its serviceability and
loading to an early deterioration of the concrete. Cracking will occur when tensile
stresses are developed which exceed the tensile strength of the concrete. These tensile
stresses may occur because of imposed loads on the structure, but more often occur
because of restraint against volumetric change. The largest volumetric change in mass
concrete results from change in temperature and the cracking tendencies occur as a
result.
Joints placed in mass concrete are designed cracks, located where they can be
controlled and treated to minimize any undesirable effects. Two principal types of
joints are used in concrete dams: contraction and construction joints.
Contraction joints - In order to control the formation of cracks in mass concrete
dams, the current practice is to construct the dam in blocks separated by transverse
contraction joints. These contraction joints are vertical and extend from the
foundation to the top of the dam and are continuous from the upstream face to the
downstream face.
The location and spacing of transverse contraction joints should be governed by the
physical features of the dam site, results of temperature studies, placement methods
and the probable concrete mixing plant capacity. For average conditions a spacing of
15 m has proved to be satisfactory. In dams where pozzolan and retarders are used,
spacing up to 18 m have been acceptable.
A typical disposition of contraction joints is shown in Figure 2.6.
Fig. 2.6. Contraction joints:
a. Metal water stop; b. Plastic water stop:
1-copper strip ; 2-copper strip Z; 3- drainage shaft; 4-concrete; 5-PVC strip; 6-
bituminous mastic; 7-pipe for regenerating steam; 8- inspection shaft
27
The water stop provided by the metal or plastic seal is located at 1 to 1.5 m from the
upstream face. Stainless steel or copper strips were extensively used in the past. The
metal strip thickness is in the range of 2 to 3 mm, the width is between 0.75 and 1.5 m
and the length is some 3… 4 m. The strips are welded on site during the dam erection.
The wave placed within the joint surface (sometimes in a bituminous mastic box) may
have the shape of ,V, M or Z (figure 2.7).
Fig. 2.7. Metal water stops:
a. simple; b. shape; c. polygonal shape; d. Z shape
The plastic strips, usually PVC, are more common in the present. Such seals are 3 to 6
mm thick by 30 to 40 cm long, with a 1.5 cm radius bulb at each end and a cored 2 cm
radius bulb at the intersection of the joint (Figure 2.8). The plastic strips are provided
at much longer length, over 10 m, and are easily welded during the construction.
Fig. 2.8. Plastic PVC water stops:
a. strip types; b. capability of strips to withstand relative movements; c. joining
elements:
1- adjacent concrete blocks; 2- concrete blocks separated by bituminous mastic
Contraction joints should be constructed so that no bond exists between the concrete
blocks separated by the joint. However, in the American practice vertical keys are
sometimes provided in transverse joints. The keys are used primarily to provide
increased shearing resistance between locks. When the joints and keys are grouted a
monolithic structure is created which has greater rigidity and stability because of the
transfer of load from one block to another through the keys.
28
Drainage shafts are placed downstream of the water stops. The shaft section may have
circular or square shape with a radius / side length of 0.8 to 1.2 m. From the drainage
shaft towards the downstream face the joint is free draining.
Construction joints - Mass concrete is usually placed in 1.5 or 2 m lifts separated by
construction joints. The integrity of a concrete structure is dependent to a large extent
on the proper preparation of construction joints before placing fresh concrete upon the
construction joint surfaces. Bond is desired between the old and new concretes. Each
successive layer must be placed while the next lower layer is still plastic. The
vibrators must penetrate through each layer and revibrate the concrete in the upper
portion of the underlying layer to obtain a dense monolithic concrete throughout the
lift. Such a procedure will also prevent cold joints within the placement lift.
All laitance and inferior surface concrete must be removed from the old surface with
air and water jets and wet sandblasting as necessary. All surfaces should be washed
thoroughly prior to placing the new concrete, but should be surface dry at the time
they are covered with the fresh concrete. Generally a layer of concrete a few
centimetres thick with a finer particle size or a mortar layer is placed prior to
resuming mass concreting.
Rock surfaces to be covered with concrete must be sound and free of loose material
and should also be saturated, but surface dry, when covered with fresh concrete or
mortar. Mortar should be placed only on those rock surfaces that are highly porous or
are horizontal or nearly horizontal absorptive surfaces.
2.2.4. GALLERIES AND DRAINAGE SYSTEMS WITHIN THE DAM BODY
Drainage is provided primarily to relieve uplift pressure. Transverse joints are drained
by vertical shafts. In the body of the dam the inspection galleries provide additional
relief.
The galleries located within the dam body can be horizontal or inclined, following the
foundation contour along the longitudinal profile of the dam. The galleries are
provided for:
- Drainage collection of seepage water that percolates through the upstream
face of the dam or through the foundation;
- Accommodation of drilling and grouting works for the foundation treatment;
- Direct access in the dam body for regular inspections of the concrete
behavior, rate of cracking and joints performance (water tightness and drainage
control);
- Reading the monitoring parameters collected by the monitoring devices
embedded into the dam body;
- Access to the gate or valve chambers to operate the hydro mechanical and
electric equipment of the spillways and bottom outlets.
The galleries are usually provided close to the upstream face of the dam at distances
that vary from 5 to 10 m. A general rule establishes a minimum thickness between the
upstream face and the gallery of 1/10 of the water depth at the gallery elevation. An
interval of 20 ... 30 m is provided between the horizontal galleries along the dam
height foundation drainage.
29
The dimensions of the inspection galleries are limited to 1.20 m width and 2.00 m
height in order to avoid stress concentration. For the same reason their shapes are
rounded (fig. 2.9). The grouting and drainage galleries located in the vicinity of the
foundation have larger dimensions required to accommodate the drilling equipment.
The contours of galleries and shafts are reinforced in order to avoid concrete cracking.
Fig. 2.9. Typical cross sections of inspection and grouting galleries:
1- collecting trench; 2 – concrete fill
2.2.5. MASS CONCRETE FOR DAMS
a. General
The structural quality of concrete is closely related to the structural quality of
aggregate of which it is composed, to the cement type and its characteristics, to the
admixtures incorporated and to the water quality. Thorough and comprehensive series
of tests of all ingredients alone and also the proposed mixes is mandatory for large
dams.
b. Concrete ingredients
Aggregates for use in concrete should be of good quality and reasonably well graded.
When good quality natural sand and coarse aggregate is available, use of crushed sand
and/or coarse aggregate is generally limited to that needed to make up deficiencies in
the natural materials. In these instances, crushing is usually restricted to crushing of
oversize materials and/or the excess of any of the individual sizes of coarse aggregate.
Where little or no natural coarse aggregate is available in a deposit, it may be
necessary to use crushed coarse aggregate from a good quality quarry rock.
An ideal particle size curve is established, which enabled a mix to be produced with
the least possible cement content, while ensuring a good workability. Workability
requirements do not vary much, since the concrete mix is carried with buckets and
compacted in layers with vibrating needles.
Another design consideration is the type of cement to be used. Limitations on the heat
of hydration of this cement are specified when determined necessary to minimize
cracking in the concrete structure. Further limitation on the heat of hydration, if more
INSPECTION GALLERIES
GROUTING GALLERY
30
stringent control of heat is needed, can be obtained by providing cement of 70 calories
per gram at 7 days or 80 calories per gram at 28 days, or both. To reduce the heat of
hydration, special cement was selected in some cases.
Other methods of heat reduction include use of lower cement contents, inclusion of a
pozzolan as part of the cementitious material, use of a pipe cooling system, and use of
a specified maximum placing temperature of the concrete. An ideal particle size curve
can be established, which enables a mix to be produced with the least possible cement
content, while ensuring a good workability.
Admixtures are incorporated into the mix design. Admixtures have varying effects on
concretes, and should be employed only after a thorough evaluation of their effects.
Most commonly used admixtures are accelerators; air-entraining agents; water
reducing, set-controlling admixtures (WRA) and pozzolans.
Air-entraining agents should be used to increase the durability of the concrete,
especially if the structure will be exposed to cycles of freezing and thawing. Use of
such agents will expedited the placing of concrete under difficult conditions, such as
for large concrete placements in hot weather.
Good quality pozzolans can be used as a replacement for cement in the concrete
without sacrificing later-age strength. Pozzolan is generally less expensive than
cement and will, as previously indicated aid in reducing heat of hydration.
The water used in the concrete mix should be reasonably free of silt, organic matter,
alkali, salts, and other impurities.
c. Placing and curing
As it was shown in the previous section, mass concrete is placed in 1.5 or 2.0 m lifts
and each of these lifts is made up of 30- to 50 cm layers. Each successive layer must
be placed while the next lower layer is still plastic. The vibrators must penetrate
through each layer and revibrate the concrete in the upper portion of the underlying
layer to obtain a dense monolithic concrete throughout the lift. Bond is desired
between the old and new concretes. Generally a layer of concrete a few centimetres
thick with a finer particle size or a mortar layer is placed prior to resuming mass
concreting.
Thickness of lifts, time interval between lifts, height differentials between blocks, and
seasonal limitations on placing of concrete are main factors that control the concreting
of the dam.
Owing to hydration of the cement, a temperature rise will take place in the concrete
after placement. After the peak temperature is reached, the temperature will decline
depending upon the thickness of section, the exposure conditions, the rate and amount
of continued heat of hydration.
A considerable portion of the total heat of hydration in a placement lift can be lost
through the top exposed surface before the next lift is placed. Shallow lifts and longer
delays between placement lifts will result in the minimum temperature rise in the
31
concrete under these conditions. The minimum elapsed time between placing of
successive lifts in any one block is usually restricted to 72 hours, but temperature
studies should be made to relate heat loss or heat gain to the placement lifts.
From a temperature standpoint, an even temperature distribution throughout the
structure will be obtained when all blocks in the dam are placed in a uniform and
continuous manner. This even temperature distribution is desirable because of the
subsequent uniform pattern of contraction joint openings. Extreme temperature
gradients on the exposed sides of blocks will also be lessened when each lift is
exposed for a minimum length of time.
Minimizing the overall height differential between the highest and lowest blocks in
the dam will cause construction of the dam to progress uniformly up from the bottom
of the canyon. In practice, the maximum height differential between adjacent blocks is
usually 7.5 m when 1.5 m lifts are used or 8 m when 2 m lifts are used. The maximum
differential between the highest block in the dam and the lowest block is usually
limited to 12 ….16 m.
Curing of concrete is very important if high quality is to be obtained. The full
effectiveness of water curing requires that it be a continuous, not intermittent,
operation. Protection of the newly placed concrete against freezing is important.
When freezing temperatures may occur, enclosures and surface insulation should also
be required. One of the most important factors associated with protection of concrete
is advance preparation for the placement of concrete in cold weather.
d. Control testing during construction
Control testing is carried out at regular intervals as concreting progresses. They
comprise both testing during the fabrication process (with aggregates control and
fresh concrete testing), and testing on hardened concrete, based on samples and cores
taken from the placed concrete. Among the properties to be measured are the
compressive strength, the tensile strength, as well as various characteristics such as
density, and dynamic and static moduli of elasticity.
Specific tests are carried out every 300 to 500-600 m3
of placed concrete, or as a
function of the number of lifts to be concreted per day/per team, and thus as a
function of the dam's dimensions.
The test results (together with their variability) are compiled for each concrete type.
The variability of the results makes it possible to assess the safety margin with respect
to the effective stresses in the structure. If necessary, the cement content is adapted to
correct the mechanical strength. In this process, testing of the aggregates, the fresh
concrete and the seven-day compressive tests are of the utmost importance so that any
possible defect or decrease in production quality can be discovered as soon as
possible.
In dam construction, compressive strength has been the parameter most often monitored on
hardened concrete. Testing is usually; carried out in a site laboratory after 7, 28, 90 and
365 days. Some samples are tested after they have been kept for a longer period of time.
32
On average, strength increases by approximately 1 N/mm2
for every additional 10 kg/m3 of
cement content, which confirms the linear relationship between the water – cement (W/C)
ratio and strength, assuming constant water content (thus constant consistency):
,/6072)90( CWc in N/mm2
e. Cracking
Concrete cracking is a very complex process. On the one hand it is related to the
properties of the concrete itself, and on the other to the geometry of the structure or
of parts of the structure. It is necessary to distinguish the origin of the cracks and
their propagation.
It is known that the origin of the cracks is micro cracking caused by the prevented
shrinkage of the cement paste in the concrete mass. Temperature and moisture
gradients then induce microscopic cracks. During concrete placement, temperature
gradients develop in massive elements. These induce cracks if adequate preventive
measures are not taken. This type of cracking occurs within days, or sometimes
weeks, after the concrete has been placed. In general, these are surface cracks, which
often propagate in a vertical plane.
The volumetric changes of concern are those caused by the temperature drop from the
peak temperature, occurring shortly after placement, to the final stable temperature of
the structure. A degree of control over the peak temperature can be attained by
limiting the placing temperature of the fresh concrete and by minimizing the
temperature rise after placement. The placing temperature can be varied, within limits,
by precooling measures that lower the temperatures of one or more of the ingredients
of the mix before batching.
Precooling of aggregates and the use of low-heat cements, reduced cement, and
pozzolans are normally adopted as temperature control measures for gravity dams
containing no longitudinal joints.
Concrete loses some of the mixing water after removal of the framework. A water content
gradient then develops. If the resulting shrinkage is excessive, cracking can be
expected. In massive elements, desiccation can also create a state of stress that may lead to
internal cracks of random orientation.
Cracking during normal operation can have various causes: unfavourable geometry,
poorly executed construction joints, temperature distributions within the dam at the end of
construction, at closure time, or during impounding, and so on. Concrete cracking often
begins during the construction phase, and then develops.
f. Creep and shrinkage
As dams age, and in particular dams with annual operating cycles, one can often
observe year after year an increase in the maximum and minimum displacements,
both at full and low water levels. Such a trend in the annual maximum and minimum
deformations can reach several centimetres and is often still noticeable after several
years of operation.
33
Shrinkage, as one usually understands it, corresponds to a volume loss due to the
evaporation of the water not chemically bonded (drying shrinkage). It partly depends
on the concrete temperature, but is mostly related to the moisture gradient that exists
between the core of the structure and its surface.
Creep is a long-term deformation of concrete under constant loads. Concrete is a
visco-elastic material, which means that mechanical loading leads to both a quasi-
instantaneous deformation and a deferred deformation (creep). Creep develops quite
quickly at the beginning and then slows down. It keeps affecting the structure for
several tens of years after loading. Younger concrete undergoes a much stronger
specific creep than older concrete. After 15 or 20 years, creep-induced deformations
are in the order of two to four times larger than instantaneous deformations.
The respective influences of shrinkage and creep on a dam are not easy to distinguish.
Their combined effects are usually manifested by a contraction of the structure. Such
contraction has fewer consequences on gravity dams than on thinner structures like
arch or buttress dams. On such structures, the compressive stresses are higher and
shrinkage occurs on the particularly stressed superficial zones.
2.3. STRUCTURAL ANALYSIS
2.3.1. INTRODUCTION
Under reliably specific conditions the analysis methods available permit an accurate
assessment of the complete behavior of the dam and its foundation. The modern
computational tools can be involved to provide a reasonable answer for most
problems encountered. However some traditional methods of analysis of concrete
dams, which have been used with success in the post, remain in current use.
A simple two dimensional linear static analysis of a concrete gravity structure is based
intrinsically on the assumption that the shear resistance is uniformly distributed across
the potential sliding surface and that the normal stresses on that surface vary linearly
from upstream to downstream. An analysis of the same structure using linear static
finite element method will demonstrate significant stress concentrations at the heel
(tension) and at the toe (compression) of the dam. With the adoption of the "no
tension" criterion the finite element method will lead to a more conservative design.
Consequently, any method of the analysis has to be directly related to the basic
criteria.
Stress analyses of gravity dams fall into two classifications-those analyses based on
trapezoidal law (or gravity method) and those based on the finite element method.
Both methods are based on the assumption that a straight gravity dam is comprised of
a number of vertical elements of unit length, each of which carries its load to the
foundation without any transfer of the load from or to adjacent vertical elements.
Specific assumptions are made for each method and will be presented in the
corresponding sections.
An adequate assessment of sliding stability must account for the basic structural
behavior, the mechanism of transmitting compressive and shearing loads to the
34
foundation, the reaction of the foundation to such loads, and the secondary effects of
the foundation behavior on the structure. Sliding stability of concrete gravity dams
can be adequately assessed by using a limit equilibrium approach.
2.3.2. LOADS
Dead Load
The magnitude of dead load is considered equal to the weight of concrete plus
appurtenances such as gates and bridges. For preliminary design the unit weight of
concrete ( b ) is assumed to be 24 kN/m3. For final design the unit weight of concrete
should be determined by laboratory tests.
Reservoir and Tailwater
The hydrostatic pressure at any point on the dam faces is equal to the hydraulic head
at that point (h) times the unit weight of water ( = 10 kN/m3):
hp (2.1)
For the reservoir water load the normal design elevation is the highest elevation that
water is normally stored. Maximum design reservoir elevation is the highest
anticipated water surface elevation that occurs in conjunction with the routing of the
inflow design flood through the reservoir. For preliminary design the maximum
reservoir level can be assumed to be at the crest level.
The tailwater elevation should be the minimum that can be expected to occur with a
particular reservoir elevation.
In the case of a triangular profile as in Figure 2.10,a the water load is divided in
vertical and horizontal components:
Fig. 2.10. Reservoir and tailwater loads:
a. water pressure on faces; b. actual pressure at the upstream heel:
1- linear distribution; 2- reduced pressure
35
- horizontal upstream (reservoir) load:
20
2
1HP (2.2)
- horizontal downstream (tailwater) load:
2'0
2
1hP (2.3)
- vertical upstream load:
21
2
1HPv (2.4)
- vertical downstream load:
2'
2
1hPv (2.5)
where 1 is the upstream face slope ( 1 - Horizontal: 1 vertical) and is the
downstream face slope ( 1 - Horizontal: 1 Vertical).
If the dam is deeply embedded into foundation rock (Fig. 2.10,b) the hydrostatic
pressure may decrease under the rock levels. The m coefficient (m<1) depends on the
rock characteristics and the concrete-rock contact. In the engineering practice the
pressure reduction is neglected in spite of existing field data that support the pressure
diagram correction.
Uplift
Hydrostatic pressure from reservoir water and tailwater act on the dam and occur
within the dam and foundation as internal pressures in the pores, cracks, joints and
seams. The component of internal pressure acting to reduce the vertical compressive
stresses in the concrete on a horizontal section through the dam or at its base is
referred to as uplift. Internal hydrostatic pressures and uplift should be used for
analyses of the foundation, the dam body and overall stability of the dam at its contact
with the foundation.
In the hypothetical case of a perfect homogeneous dam without joints and drains the
uplift distribution on a horizontal section of the dam is assumed to vary linearly from
full hydrostatic head at the upstream face to zero or tailwater pressure at the
downstream face. The same distribution of uplift pressures is assumed on dam
foundation contour (Fig. 2.11). When drains are provided in the dam body the internal
pressure should be modified in accordance with the size, location and spacing of the
drains.
The internal pressure distribution through the foundation is dependent on rock
porosity, jointing and faulting and to a large extent on the grout curtain effects, and
the drainage system. Determination of the internal pressures can be made from flow
nets computed by numerical methods, modeling the effects of drainage and grouting
curtains. The numerical model has to include the jointing, faulting, variable
permeability and other geologic features.
36
Fig. 2.11 Theoretical distribution of uplift on foundation area
For preliminary design purposes some conventional uplift distributions are assumed
as illustrated by Figure 2.12. The uplift diagram is made from a straight - line drop
from reservoir level at the heel of the dam to a fraction of the difference in head
between reservoir and tail water along the line of drains and then another straight-line
drop to tailwater at the downstream toe. The value of that fraction is in the range of
0.25 to 0.50.
Fig.2.12. Uplift assumptions – tail water
If there is no tailwater, the downstream end of the uplift diagram is zero at the
downstream toe. The pressure is assumed to act over the entire foundation area
(Figure 2.13).
Maximum tail water
37
Fig. 2.13. Uplift distribution – no tail water
The reduction is based on observations on existing dams. Figure 2.14 showing the
uplift pressure gradients measured at Hiwassee dam renders evident that the actual
pressures at the drains fall well below the present design assumptions.
Fig. 2.14. Uplift pressures at the base of Hiwassee dam
In some European countries the uplift distribution for preliminary design is assumed
to vary linearly from a fraction m (m<1) of the headwater pressure at the dam heel to
the tailwater pressure at the downstream toe (Figure 2.15).
38
Fig. 2.15. Uplift distribution – simplified linear diagram:
a. with tail water; b. without tail water
The uplift force on the dam foundation is:
with tailwater BhHmhU2
1 (2.6)
without tailwater BHmU2
1 (2.7)
The m coefficient is called the uplift reduction coefficient or uplift coefficient.
Conservative values for uplift coefficient are in the range of 0.70...0.80. The current
practice recommends different m values according to the dam height and the rock
foundation characteristics. For large dams provided with grout curtains and drainage
wells the m values are defined by the foundation rock types:
m = 0.75 - stratified and fissured rocks;
m = 0.67 - slightly fissured rocks;
m = 0.50 - sound, homogeneous rock
In the design criteria it is suggested that the safety of large dams should not depend on
the proper functioning of grout curtains and drains. It must be remembered that large
dams may be in existence for hundreds of years. Drains have been known to clog.
Dams should still have a large margin of safety if they do. A conservative assumption
regarding the uplift distribution provides this reserve.
Silt pressure
In some reservoir finely divided silt or clay is deposited in substantially horizontal
layers against the upstream face of the dam. These deposits are produced by flows of
muddy water along the bottom of the reservoir and are to be distinguished from the
deltas of silt and sand that form in the upstream end of the reservoir. It is usually
assumed that the material is under complete saturation and is completely fluid.
39
Horizontal silt pressure is equivalent to that of a fluid weighing 14 kN/m3. Vertical silt
pressure is determined as if silt were a soil having a wet unit weight of 19.2 kN/m3,
the magnitude of pressure varying directly with depth.
More precise calculations can be made by determining the horizontal component of
the silt load from the Rankine formula, neglecting cohesion:
sin1
sin1
2
2ss
silth
P (2.8)
where s is the unit weight of the silt;
sh is the silt depth;
is the internal angle of friction of silt material.
Ice load
Ice pressure is created by thermal expansion of the ice. The pressure values are
dependent on the temperature rise of the ice, the thickness of the ice sheet, the
coefficient of expansion, the elastic modulus and the strength of the ice.
A significant factor is the rate of temperature rise. If this rate is reduced the plastic
deformation of ice attenuates the pressures acting on the dam face. In several
European countries the ice pressure is evaluated by using Royen's relationship:
3 2119 tg
n
tgtghgPice kN/m (2.9)
where hg is the ice thickness (m);
tg is the maximum temperature rise of ice sheet during n hours.
The ice temperature rise tg is evaluated in terms of air temperature rise in the same
time interval at ( tg = 0.35 at ).
Not all dams are subjected to ice pressure and based on the above factors an
allowance for ice pressure may be decided. An acceptable estimate of ice load to be
expected on the face of a structure may be taken in terms of the ice depth:
Ice depth (m) 0.5 0.7 1.0 1.20 1.50
Ice load (kN per linear m) 70 100 150 200 280
Ice load may be also created by the wind rag of floating ice. For large dams this ice
load is negligible. However, for thin, flexible structural element and especially for
gates the dynamic effect of floating ice can be important.
40
Temperature
Seasonal temperature changes of air and reservoir water propagate within the dam
concrete only in the first 5...6 m from the faces. The daily air temperature variation
propagates in a very thin concrete layer (20...30 cm) from the dam face. Comparing
with the very large concrete mass of the dam the affected zones are to small to induce
significant volumetric changes in the dam. Even if some volumetric changes are
larger, the contraction joints allow free deformation and the horizontal thrust is
negligible.
However, secondary stresses can occur at the faces of the dam and around openings
(drainage galleries, valve chambers) due to temperature differentials. These
temperature differentials are caused by differences in the temperature of the concrete
surfaces due to ambient air and temperature variation, solar radiation and air
movement in openings. These secondary stresses may produce cracks that could lead
to progressive deterioration.
Wave pressure
The upper portions of the dam are subject to the wave action, that induces additional
water pressures. The wave pressure depends on the dimensions of the wave (heights
and lengths) that in their turn depend on the extent of the water surface and the
velocity of the wind, among other factors.
For a gravity dam with a vertical or slightly inclined upstream face (see Figure 2.16)
the wave pressure load may be calculated as:
Fig. 2.16. Wave pressure:
a. pressure distribution; b. wave characteristics:
1- dam; 2- normal water level; 3- increased water surface
41
20
2
12
2
1HaHhhHPwave (2.10)
where:
h2 is the wave height;
0h is the average heightening of water level during the wind action;
a is wave pressure at the dam heel.
The wavelength and the wave height 2h are usually evaluated on the basis of
empirical formulas in terms of wind velocity (v) and the "fetch" or straight length of
water subject to wind action (F). The increased height of water surface 0h is then
calculated in terms of wave characteristics:
2
2
2
)2( 2
0H
htch
h (2.11)
or in terms of primary parameters:
H
Fvh
460
10 (m) (2.12)
where H is the reservoir depth, is the wind velocity (km/h) and F is the fetch
(km).
The wave pressure at the dam heel is approximated as
2
2
2
Hhc
ha for shallow reservoirs
0a for deep reservoirs
The wave pressure is a significant load for small dams with dam height less than 20 m
where its value may reach up to 12...15% of the water load. For very high dams (dam
height larger than 100 m) the wave load is much lower but is still a 2.5...4% of the
water load.
Seismic Loads
The problem of the earthquake response analysis of concrete dams is the subject of a
distinct chapter of this book. Under this section the earthquake forces are treated
simply as static forces to be combined with the hydrostatic pressure and gravity loads.
In representing the effects of ground motion - transverse to the axis of the dam - by
static lateral forces the dynamic response of the dam-water-foundation rock system is
neglected. Two types of static forces are included i.e. forces associated with the mass
of the dam and water pressures in addition to the hydrostatic pressure.
42
The earthquake intensity is characterized by the earthquake acceleration or by seismic
coefficient that is the ratio between the acceleration (aE) and the gravity a=aE /g.
Most dams in seismically active regions have been designed for an acceleration of
one-tenth gravity, or a = 0.1. According to different national standards, the seismic
coefficient depends on the seismicity of the site and ranges between 0.05 and 0.14.
The intensity of the inertia force associated to the mass of the dam is found from the
equation:
Gaag
GC Eg (2.13)
where gC is the earthquake force and G is the weight of the dam body (Figure 2.17).
The inertia force gC may by assumed acting through the center of gravity of the dam
or block in a downstream direction for horizontal acceleration and in an upward
direction for vertical acceleration.
The increased water pressure due to the inertia of the water in the reservoir can be
represented by a diagram of the form presented in figure 2.17.
Fig.2.17. Earthquake forces – static approach;
Increased water pressure represented by: 1- an ellipse; 2- a parabola
According to Westergaard, whose solutions are most frequently applied, the true
equation of the increased water pressure may be expressed by an ellipse or by a
parabola without appreciable error. The resulting equations are:
- for parabola equivalence:
HzCap pc (2.14)
43
3
2
6
/
10
75.71
8170mN
T
H
C p (2.15)
2
3
2HCaC pa (2.16)
- for ellipse equivalence:
zHzCap ec 2 (2.17)
)/(
10
75.71
6540 3
2
26
mN
T
H
Ce (2.18)
2
4HCaC ea (2.19)
where:
cp is the additional unit water pressure;
H = dam height or the depth of water acting on the dam;
z = current vertical coordinate;
pC and eC are factors depending on the height of the dam (H) and the
earthquake period (T);
aC = the additional total water pressure.
For medium dam heights the pC and eC factors may be approximated as pC =
0.830 and eC = 0.660.
Fig.2.18. Reduction coefficient K in terms of upstream slope 1
If the upstream face is inclined the additional water pressure normal to the inclined
face is lower than the one acting on a vertical face:
zHCaKp pc (2.20)
44
where K is a reduction coefficient that depends on the upstream face slope 1 (see
figure 2.18).
2.3.3. STRESS ANALYSIS - TRAPEZOIDAL LAW
Assumptions
As it was mentioned at the beginning of this section, the stress analysis based on
trapezoidal law (or gravity method) is based on the assumption that a straight gravity
dam is comprised of a number of vertical elements of unit length, each of which
carries its load to the foundation without any transfer of the load from or to adjacent
vertical elements. Specific assumptions are made for this method:
(1) The concrete in the dam is a homogeneous, isotropic, and uniformly elastic
material.
(2) There are no differential movements, which occur at the dam site due to
water loads on the reservoir walls and floors.
(3) All loads are carried by the gravity action of vertical, parallel-side
cantilevers, which receive no support from the adjacent elements on either side.
(4) Unit vertical pressures, or normal stresses on horizontal planes, vary
uniformly as a straight line from the upstream face to the downstream face.
(5) Horizontal shear stresses have a parabolic variation across horizontal
planes from the upstream face to the downstream face of the dam.
Vertical stresses - triangular profile
Only the more conventional analysis for a vertical section having the width of 1 m is
considered in this section. A simplified triangular profile is considered. The active
loads are the reservoir hydrostatic pressure, the dead load and the uplift (Figure 2.19).
The internal pressure (uplift) distribution, both within the dam body and through the
dam-foundation contour, is assumed to vary linearly from a fraction m of the head
water pressure to zero at the downstream end of the horizontal section.
Fig.2.19. Loading system - simplified triangular profile
45
For a horizontal section located at the depth z the vertical normal stresses at the
upstream and downstream faces are computed by the eccentric compressive formula:
W
M
A
Vupdw
(2.21)
where:
V is the algebraic summation of all active vertical forces;
M - the overturning moment taking into consideration all the
forces that act on the section;
A - area of the section;
W - modulus of strength.
The loads and their moment arms referred to the center of the gravity of the section
are (see figure 2.19):
- Dead load of the downstream prism:
2
2
1zG b arm:
6)3( 1
z
- Dead load of the upstream prism:
2
112
1zG b arm:
6)3( 1
z
- Horizontal reservoir load:
20
2
1zP arm:
3
z
- Vertical reservoir load:
21
2
1zPv arm:
6)3( 1
z
- Uplift (internal pressure) force:
21 )(
2
1zmU arm:
6)( 1
z
The resultant vertical force is:
2
1112
1zmUPGGV bv (2.22)
The resultant moment acting on the center of the section is:
46
32111
21
2 2312
1zmM b (2.23)
The section area is zA 1 and the corresponding area modulus is
221
6
1zW .
By replacing the above-evaluated terms in the Equation 2.21 the vertical normal
stresses up
at the upstream heel and dw at the downstream toe can be evaluated by
the formula:
zm
m
b
b
up
dw
}23
2
1
2
111
2
1
2
11
2
12
1 (2.24)
For the empty reservoir case 0 and the normal vertical stresses are:
zz bdwbup
1
1
1
(2.25)
Analyzing the normal stress formulas one can notice that:
- under both hypotheses - full and empty reservoir - the stresses depend
linearly on the depth z;
- maximum normal vertical stresses act on the upstream heel for empty
reservoir condition and on the downstream toe of the dam for full reservoir condition,
where z = H.
For a dam with a vertical upstream face the vertical normal stresses are:
- full reservoir:
zzm dwbup 22)( (2.26)
- empty reservoir:
zbup 0dw (2.27)
In the case of a real dam - with crest thickness, batter on the lower part, variable
downstream slope etc. the same general formula (2.21) has to be applied. The section
characteristics A, Wup and Wdw are properly evaluated. According to the specific
situation other significant loads can be included in the analysis. The uplift pressure
may have any conventional distribution (see figures 2.12 to 2.15).
In important structures, it may be desirable to determine the intensities and directions
of the principal and maximum shearing stresses at various points throughout the dam
section. The usual procedure in analyzing these stresses is to divide the section into
elementary prisms and consider each prism to be held in equilibrium by the stresses
47
acting on it. By starting with the vertical normal stresses acting on the upper and
lower surfaces of each elementary prism, it is possible to determine be successive
integration the vertical and horizontal shearing stresses intensities, the horizontal
normal stresses, and the first and second principal stress.
Principal and shearing stresses at the dam faces
Once again the conventional triangular profile is considered (figure 2.20). The
upstream and downstream face directions are directions of principal stress since the
shearing stress is zero along them. The directions normal to the faces are also
directions of principal stress.
Fig. 2.20. Principal stresses at the dam faces
To evaluate the principal stresses the first step is to separate from the dam face
triangular elements shown in figure 2.20. Each element is then assumed to be held in
equilibrium by the normal and shearing stresses:
upstream triangle: 12
112 sincospz (2.28)
downstream triangle: 22 sinz (2.29)
The principal stresses may be computed readily from the equilibrium equations as:
upstream: 21
211
2
121 1
sinpctgp z
z (2.30)
p2
downstream: 01
2
122 1
sinz
z (2.31)
The principal shearing stress:
21max2
1
48
has the values:
upstream: 2max 1
2
1pz (2.32)
downstream: 2max 1
2
1z (2.33)
Based on the above relationships it is important to note that:
- the principal stresses at the upstream face may become tensile stress when 21
211 pz ; in order to avoid the concrete cracking a more gentle slope of the
face is required in such cases;
- the maximum principal stress develop at the downstream face; at the
downstream toe, where z = H, the stress value is up to 2.5 times larger than the
maximum hydrostatic pressure;
- a change of the downstream face slope near the dam toe is recommendable in
order to reduce the maximum compressive stresses (figure 2.21);
Fig. 2.21. Local curvature of the downstream slope
- the local curvature of the downstream face near the dam toe is beneficial
since the principal shearing stresses (Equation 2.33) may reach quite large values.
Mention should be made that larger shearing stresses are allowable provided these are
not in the presence of tension.
2.3.4. STRESS ANALYSIS - FINITE ELEMENT METHOD
The structural behavior of high gravity dams, as determined by field measurements,
leads to the conclusion that the classic trapezoidal law produces stress patterns, which
do not even remotely resemble those obtained from field measurements.
Figure 2.22, for example, shows a comparison of measured and calculated stresses on
the foundation of Hiwassee dam under both low and high reservoir levels. Figure 2.23
shows foundation pressures under the Shasta dam measured when reservoir was
nearly full. The maximum pressure was measured at a point close to the center of the
base. The sharp reduction in pressures near the downstream face indicates that about
the downstream third of the concrete is taking a relatively minor part of the load.
49
Fig. 2.22. Hiwassee dam – stresses on the foundation
Fig. 2.23. Foundation pressure measured for Shasta dam
50
It will be noted that the upstream half of the base takes a greater percentage of the
load than that evaluated by the trapezoidal distribution. It will also be noted that the
maximum stress do not occur at the downstream toe and that there may be tension
instead of compression at the upstream heel.
The finite element method is an important advance in stress analysis of dams. By this
method the dam and its foundation are divided into elementary, contiguous finite
elements, and the elastic properties of each part of the dam – foundation system are
properly specified. It is not the object of this section to present into details the method.
Some general considerations are made in the context of gravity dam analysis.
Assumptions regarding loading conditions, initial stress, etc., have to be considered
before an analysis is carried out. In addition, after the results become available some
criteria concerning their interpretation will be needed.
The foundations of the dam are an integral part of the structure, and their
deformability can be included in the analysis without difficulty. As the stresses caused
by the dam within the foundations "dissipate" rapidly it is possible to use larger
elements where stress gradients are less significant. .
Initial stresses due to weight and various kinds of tectonic action exist within the
foundation rock prior to the construction of the dam. It is a general rule that these
stresses are estimated (or computed) before the interconnection with the dam. This
means that no gravity loads within the foundation should be applied to the analysis of
the dam-foundation complex. The initial gravity, tectonic, and pore-water-pressure
stresses are obviously simply superposed on the additional effects of dam stresses.
In the analysis it is important to know at least the approximate elasticity constants of
the rock material. With the finite-element process no difficulty arises in dealing with
nonhomogeneity or anisotropy, as will be.
In the dam itself it is often accurate enough to consider the gravity as if it were
applied externally to the completed, weightless structure. This assumption is
manifestly not true, and for special cases the step-by-step construction process can be
followed in the finite-element analysis. The approximation of applying gravity to the
whole structure gives results, which do not differ by a large amount from those of the
more exact process.
The finite element method may be used for evaluating the piezometric levels resulting
from the flow through the dam body and the underlying rock. The basis of these
calculations is the Darcy law. Anisotropic permeability resulting from the orientation
of the discontinuities can be taken into account. Variations in permeability induced by
the foundation treatment – grouting curtain and drainage system – can be easily
modeled.
Temperature effects on stresses are treated easily in the general formulation as simply
one of the load systems. The two types of temperature distribution which arise (1)
from external causes such as seasonal cycles and (2) from heat of hydration present
somewhat different problems. In the first case a reasonably elastic behavior of the
concrete can be assumed without serious error. The second acts on the concrete during
51
its early life when creep effects are most serious. While again the solution of such
creep problem is possible by the finite-element method, it is subject to certain
uncertainties and indeed.
It is usually no more expensive to obtain separate solutions for each load and obtain
totals by automatic addition. The separate effects can thus be studied individually or
in sum. All programs should be capable of computing the principal stress system
acting at various points of the structure. It is these stresses, which will finally decide
whether suitable safety is ensured, and decisions on modification of the design will be
taken on that basis.
One of the basic criteria usually introduced is that no tensile stress should be present
in the final structure. Certainly this must apply in the rock, which is usually fissured,
and probably it is desirable to extend this to the concrete mass, where cracking could
have occurred by thermal or shrinkage action. However, in elastic stress analysis it is
almost impossible to design a dam structure with no tension in any part. The criterion
must therefore be modified. A reasonable approach is to consider the criterion as
applicable after a limited amount of cracking has occurred
While the elastic stress analysis gives a good picture of working stresses and makes it
possible to estimate the least factor of safety against failure, the true failure load can
only be obtained by the introduction of plastic nonlinearities into the analysis. Also,
the introduction of cracks into finite-element analysis presents little difficulty.
In order to demonstrate the power of the finite element analysis in the field of dam
safety evaluation an example is presented in the followings. A complete stress and
seepage analysis has been performed for Eder dam in Germany to verify the
effectiveness of the rehabilitation measures.
The Eder dam is a gravity dam with a total height of 48 m, relatively thin (figure
2.24). Achieving stability was possible either by restricting the water level, or by
taking other steps to improve the dam condition. Because of economic considerations
a solution involving the anchoring of the dam to the rock by installing permanent
anchors was given preference.
To verify the stability calculations several two-dimensional FE analyses were carried
out. The finite element discretization includes a 300 m-long and 159 m-high section
from the foundation, as well as the 48 m-high dam body (figure 2.24,b). Isotropic
behaviour in the elastic range was assumed for the dam body (E=7500 MPa) and for
the rock foundation (E=5000 MPa). The finite element mesh has 2757 isoparametric
elements, each with eight nodes, and 2881 nodal points. The fine meshed modelling
of the dam on the upstream and downstream sides can be seen. The object of this is to
calculate as accurately as possible the stresses in the area with large stress gradients.
The same discretization was used for the seepage analysis as well as for the stress
analysis. According to the results of the field tests the foundation rock was divided
into three zones with respect to permeability. The permeability of the grout curtain
zone was assumed as one order of magnitude lower than the average rock
permeability.
52
Fig. 2.24. Eder dam finite element analysis:
a. dam cross section; b. finite element mesh
The equipotential lines resulting from the seepage flow analysis are shown in figure
2.25. The draining effect of the inspection gallery and the effectiveness of the grout
curtain are rendered evident. The uplift pressure distribution along the dam foundation
a. MAIN CROSS SECTION
b. DISCRETIZATION
53
contact show that downstream of the grout curtain the pressures are 40% of the
hydrostatic pressure, thus confirming the assumptions used in stability analysis.
Fig. 2.25. Seepage analysis results
The seepage forces from the above-presented calculation, together with the loads from
the self-weight and anchors produced the principal stress distribution shown in figure
2.26. Because of the vertical tensile stresses that cannot coop with the actual strength
of the bedding rock, horizontal cracks occur at the heel of the dam on the upstream
side. Mention should be made that the stresses calculated by the classic trapezoidal
law led to the conclusion that this zone experiences compression. However, the area
covered by the horizontal cracks is small, and because they do not reach the injection
zone the watertightness of the grout curtain is not affected.
UPLIFT PRESSURES ON FUNDATION
EQUIPOTENTIALS
Analysis results
Measured values
Grout curtain
54
Fig. 2.26. Principal stresses under full reservoir hypothesis.
2.3.5. SLIDING STABILITY
Assumptions
An adequate assessment of sliding stability must account for the basic structural
behavior, the mechanism of transmitting compressive and shearing loads to the
foundation, the reaction of the foundation to such loads, and the secondary effects of
the foundation behavior on the structure.
Sliding stability of concrete gravity dams can be adequately assessed by using a limit
equilibrium approach. Assumptions and simplifications are listed below:
- A two dimensional analysis is accepted involving a unit length of the block;
- Only force equilibrium is satisfied. Moment equilibrium is not used;
- Considerations regarding displacements are excluded from the limit
equilibrium approach;
- Analyses are based on assumed plane failure surface defined by the dam-
foundation contour. The calculated factor of safety will be realistic only if the
assumed failure mechanism is kinematically possible;
- A linear relationship is assumed between the resisting shearing force and the
normal force acting along the failure surface.
- Shear strength is a combination of internal friction that varies with the
normal compressive stress and cohesive strength.
Sliding stability evaluation based on friction coefficient
The sliding of a gravity dam along its foundation contour takes place when the total
horizontal force H overpass the resisting force that can be mobilized at the contact.
55
The maximum resisting force can be assumed that is given by the product between the
total vertical load V acting normal to the foundation and a so called "concrete-rock
friction coefficient" f. Sliding stability condition is:
H < f V (2.34)
This condition can be expressed in terms of the Factor of Safety (FS) as:
FS H = f V (2.35)
The concrete-rock friction coefficient includes both the cohesion and friction effects.
The in situ tests performed in order to evaluate the shear strength at the concrete-rock
contact define the dependence between the shear stress along the block-rock
foundation contour and the normal vertical stress acting on the same contour. The
same field tests allow for relating the shear strength to the shear displacement along
the sliding contour. The test results can be processed assuming the Mohr-Coulomb
failure criterion:
tannc (2.36)
and thus the mobilized shear strength parameters c ( ) and tan ( ) are defined. That
is, for an allowable shear displacement one can evaluate the available cohesion c
and the available internal friction tan .
The relationship 2.34 corresponding to the limit equilibrium ( H = f V ) divided by
the foundation area becomes nf . Comparing this expression to the Equation
2.36 one can relate the concrete-rock friction coefficient to the available shear
strength parameters:
tann
cf (2.37)
For large dams, where the normal vertical stress n acting on the foundation contour
is rather large, the cohesion term nc / is neglected. For preliminary calculations the
concrete-rock friction coefficient is assumed to be:
f = 0.65 ... 0.70 for sound eruptive rocks
f = 0.50 ... 0.65 for sedimentary rocks
Corresponding to this simplifying assumption the required factor of safety is
moderate: FS = 1.15 ... 1.30 for normal static loading conditions and FS = 1.00 ... 1.05
for seismic loading conditions. FS is selected in terms of the class of importance of
the dam.
Sliding stability evaluation based on cohesion and friction
Although, generally, the foundation surface appears as horizontal in the transverse
(upstream-downstream) direction the actual irregularities of the foundation rock cause
a marked apparent cohesion. The cohesion term of the shearing strength is no longer
negligible. The sliding stability condition is:
56
AcVHFS tan (2.38)
where A is the foundation area.
Following this approach, the minimum required factor of safety is FS = 2.0 for normal
static loading conditions and FS = 1.3 for seismic loading condition. Mention should
be made that in the past the minimum required factor of safety for static loading
conditions was 4. The primary reasons for use of this conservative factor of safety
were the uncertainty in determining rock shear strength parameters and the peak shear
strength from in situ tests. In the last decades the methods of testing have substantially
improved and much better definition of mobilized cohesion and friction are now
possible.
Multiple - plane failure surface
When the dam structure is significantly embedded and some weak planes are
encountered in the foundation rock an additional sliding stability analysis is required.
The potential failure surface has to be defined based on the stratification, location and
orientation of the discontinuities and the configuration of the dam foundation.
Most frequently the failure surface is defined by two weak planes (Figure 2.27). The
assumed slide mass is divided in two wedges. The factor of safety FS is obtained from
the equations:
2
1
0
2
1
tan
tancos1
iii
iiiiii
i
i
VP
UVAcn
FS (2.39)
where
i
iiFSn
i 2tan1
tantan1
1
(2.40)
ic - cohesion on the sliding contour (segment) i;
iU - uplift force acting under the wedge i ;
iA - area (length) of the segment i;
iV - all applied vertical forces (body - dam and rock - and surcharge)
acting on the wedge i;
i - angle between the inclined plane (segment) i and the horizontal
( 0 for upslope sliding and 0 for downslope sliding);
i - angle of internal friction along the segment i.
57
Fig. 2.27. Multiple planes sliding mechanism
Equation 2.39 is implicit in FS since n is a function of FS. Therefore, the
mathematical solution of Equation 2.39 requires an iteration procedure. An initial
estimate of FS is inserted into the n term and a first FS is calculated. The calculated
FS is then inserted into the n term and the process is repeated until the calculated FS
converges with the inserted FS.
Mention should be made that Equation 2.39 is similar to the generalized method of
slices but in order to develop a simple analytic technique the vertical side forces due
to impending motion of the wedges between slices were assumed to be zero.
Therefore, although the equation satisfies complete horizontal static equilibrium,
complete vertical equilibrium is in general not satisfied.
Constructive measures
In order to increase the sliding stability of the dam some additional constructive
measures are provided that cannot be quantified. Besides the consolidation grouting
and the excavation to the firm rock the foundation contour itself may significantly
contribute to an improved stability (figure 2.28).
Fig. 2.28. Foundation contours:
a. upstream heel groin; b. irregularities along the foundation; c. inclined steps
58
Figure 2.28,a shows the effect induced by the upstream heel groin on the shear stress
distribution. Several irregularities along the foundation contour (Figure 2.28,b) create
a more even shear stress distribution and contribute to stability. If the foundation
contour is excavated following a pattern of inclined steps (Figure 2.28,c) the resultant
force under full reservoir condition is almost perpendicular to the steps thus reducing
the tangential component that induces sliding.
The beneficial effect of the upward sloped foundation, from heel to toe of the dam,
may be noticed in Figure 2.29.
Fig. 2.29. Forces acting on an inclined foundation
If is the angle of sloping, then the sliding stability condition may be expressed as:
NfTFS (2.41)
that is similar to the Equation 2.35. Since:
sincos VHT (2.42)
sincos HVN (2.43)
the actual factor of safety:
sin1
cos
sincos
H
H
FSf
fFSFS (2.44)
is increased in comparison to the factor of safety HFS of a dam with horizontal
foundation contour.
2.4. DESIGN OF GRAVITY DAM PROFILES
Design criteria
Assuming that the common profile has a triangular shape the design has to determine
the upstream and downstream slopes of the dam faces. Two main criteria are used:
59
First criterion. Under full reservoir condition the vertical normal stress at the dam
heel has to be a compressive stress. It is assumed that the dam-foundation joint is
incapable of resisting tensile stresses that may cause a slight opening of the joint.
Such an opening at the upstream heel is objectionable as it may admit full reservoir
pressure over the entire area not in compression with a further opening of the joint.
The progressive extension of the joint may be sufficient to cause failure. According to
the simplified trapezoidal law the criterion is written as:
0W
M
A
Vup (2.45)
where the notations are the same as for Equation 2.21.
Second criterion. The total frictional resistance to sliding on the foundation surface
must exceed by a safe margin the total horizontal force at the foundation level in order
to withstand the tendency to slide:
HVf (2.46)
where the notations are the same as for Equation 2.34.
The condition 2.46 may become the Equation HVf if the concrete-rock
friction coefficient f is properly corrected such as to include the cohesion and friction
effects and also the reduction corresponding to the required factor of safety.
Additional criteria are used in the design process. Among them are:
- Tension shall not exist in any joint of the dam under any condition of
loading;
- The ultimate shearing strength of any joint must exceed the total horizontal
force above the joint for all condition of loading;
- The principal compressive stresses in the dam and the foundation shall not
exceed certain allowable values.
Once the shape of the dam profile has been determined in accordance with the two
main criteria careful attention must be given to the additional criteria that can affect
the details of the design.
Dams with inclined upstream face
Assuming the load combination shown in figure 2.30: dead load, water pressure and
uplift, the two main criteria (Equations 2.45 and 2.46) may be written as:
Solving the system an equation on 1 is obtained:
(2.47)
(2.48)
60
Once the 1 value is determined the downstream slope can be determined from
Equation 2.48.
Fig. 2.30. Design of dams with inclined upstream face:
a. load combination; b. slopes variation in terms of coefficients f and m
Based on a parametric study the variation of the upstream and downstream slopes in
terms of concrete- rock friction coefficient f and uplift coefficient m is presented in
Figure 2.30. The upstream slope is strongly dependent on the uplift value, while the
downstream slope is more significantly defined by the friction coefficient.
If the dam is located in a seismic area the load combination includes the seismic
forces Ca and Cg as it is shown in figure 2.31:
Fig.2.31. Load condition and slope variation – seismic loads included:
a. loads; b. slope variation in terms of earthquake intensity
(2.49)
61
The design criteria (Equations 2.45 and 2.46) are written as:
where mb
i
b .
The equation in 1 becomes:
The 1 value is determined from the above Equation and then the downstream slope
is determined from Equation 2.51. The variation of the dam slopes in terms of the
seismic coefficient a (that depends on earthquake intensity) is shown in figure 2.31.
One can notice that the upstream slope becomes gentler as the earthquake intensity
increases while the downstream slope is practically constant.
Dams with vertical upstream face
The dam profile is defined by only one parameter, the downstream face slope . The
loading conditions for the two combinations: normal loads and extreme loads are
presented in figure 2.32.
Fig. 2.32. Load conditions for designing the profile with the vertical upstream face:
a. normal loads; b. extreme loads
(2.50)
(2.51)
(2.52)
62
Assuming the normal load combination, without earthquake loads, the first design
criterion – upstream compressive stress- leads to the Equation:
mb
(2.53)
The second criterion – sliding stability- is expressed by:
)( mf b
(2.54)
The actual slope value is selected as the maximum value given by the two equations.
If the seismic loads are included the two equations are:
The slope selection is made by the same procedure.
Dams with upstream batter
In order to define the profile of a dam with an upstream batter one has to determine
three parameters (Figure 2.33): downstream slope , the height of the batter and the
slope of the batter o.
Fig.2.33. Profile definition and notations:
a. profile parameters and loads; b. additional design criterion
(2.55)
(2.56)
63
Two conditions are given by the main design criteria:
- compressive stress at the upstream heel:
The two equations are solved for o that in its turn depends on :
In order to define the profile parameters an additional criterion is introduced, that are
the limiting the tensile stresses in the section x-x from figure 2.33,b. If allowable
tensile stress is ta then the condition is written as:
ta
GR
H
MM
22
6
1
0 (2.60)
where:
MR is the moment corresponding to the foundation reactions along the batter
extension;
MGo is the moment due to the dead load of the batter zone.
The final form of the condition 2.60 is:
ta
b HH
)33()(
0
2
03
00
22
0 (2.61)
Since an explicit form of the equations is not available a multiple step design is
required. In the first step a certain value for is assumed. From Equation 2.59 results
the o slope, and then from Equation 2.58 results the downstream slope . In the
second step the profile parameters are introduced in inequality 2.60. If that is satisfied
with a rational margin of safety then the profile is defined. If it is not, a new value for
is proposed. By a trial and error process the final shape of the profile is established.
BIBLIOGRAPHY
Davis, C.,V., Sorensen, E.,K. Handbook of applied hydraulics. McGraw-Hill, 1969.
Popovici, A. Water storage dams. (in Romanian), Bucharest, 1992.
Priscu, R. Hydraulic structures. (in Romanian) , Bucharest, 1974.
- sliding stability:
(2.57)
(2.58)
(2.59)
64
Raphael, J.,M. Concrete gravity dams. Development of Dam Engineering in the
United States. Kolgaard, E.,B., Chadwick, W.,L. editors, Pergamon Press, 1988.
Romanian National Committee on Large Dams. Dams in Romania, Bucharest 2000.
Swiss Committee on Dams. Concrete of Swiss dams: Experiences and Synthesis,
September 2000.
Stematiu, D. Finite element analysis of hydraulic structures. (in Romanian).
Bucharest, 1988.
USBR. Design of gravity dams, Denver, 1976.
US Corps of Engineers. Sliding stability for concrete structures. ETL 1110-2-256,
June, 1981.
65
3. BUTTRESS DAMS
3.1. INTRODUCTION
The buttress dams are a derivation from the massive gravity type with the introduction
of intermediate spaces (Figure 3.1). These spaces allow water seepage through
foundation and dam body to discharge not only downstream, but also side and
upwards into them, thus greatly reducing the uplift pressures. Theoretically, the total
elimination of the uplift forces would permit a reduction of a gravity dam's mass by
40% without reducing its stability. On the other hand the intermediate spaces facilitate
the dissipation of the heat produced during the hardening of the concrete, so the
elaborate cooling measures are seldom needed during the construction of a buttress
dam.
However, the actual reduction of the uplift pressures proved considerably smaller
because the intermediate spaces had to be closed upstream with slabs, arches or a
thickening of the buttress heads to make them contiguous. The saving in costs is even
more modest due to the fact that a buttress dam requires more formwork for the more
complicated shape and higher cement content for a slimmer structure.
Fig.3.1. Derivation of the buttress dam types from the massive gravity dam
Given the absence of uplift, more substantial savings are possible by inclining the
upstream face and thus mobilizing the vertical water load on it for sliding stability.
Also the eccentricity of the resultant force is greatly improved, since it moves from
the downstream third of the base or horizontal sections in the case of vertical
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upstream face to almost their center in the case of a 1H: 1V upstream face inclination.
Correspondingly, the vertical stresses are almost uniform over the section, although
several times larger. Except for high dams, this is welcome because it permits a better
utilization of the strength of the construction material.
3.2. BUTTRESS DAM TYPES
Buttress dams represent that class of structures having a component that retains the
reservoir and is supported by a series of buttresses. Three major types of buttress
dams exist:
- flat slab and buttress;
- multiple arch;
- massive head buttress.
The flat slab and buttress dam is a concrete structure comprising a flat reinforced
concrete slab inclined in the downstream direction that retains water and transmits
loads from the reservoir and slab to buttresses and thence to the foundation (Figure
3.2). The slab can be simply supported at the buttress (Ambursen type), made
continuous with the buttress or suspended from corbels cantilevered from the
upstream side of the buttresses. The buttresses usually are reinforced members
although in some cases where the member is relatively massive, reinforcement has
either been minimized or omitted entirely.
Fig.3.2. A typical flat slab and buttress dam:
a. cross sections; b. slab connection with the upstream end of the buttresses:
1- construction joint; 2- struts between buttresses; 3- plinth; 4- bituminous mastic
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The multiple arch dam is a concrete structure that comprises a series of concrete
arches, semicircular or segmental in plan, whose thrust from the reservoir and dead
load is carried out by buttresses and thence to the foundation (Figure 3.3). The arches
are usually inclined in the downstream direction and are designed with reinforcement.
They are usually supported by, and constructed integrally with, equally spaced,
triangularly shaped buttresses.
Fig.3.3. A typical multiple arch dam
The massive head, buttress dam is a structure comprised of heavy counterforts having
their upstream ends enlarged into a bulb or mushroom to full span width (Figure 3.4).
Fig. 3.4. A typical massive head, buttress dam:
a. cross sections; b. rounded heads: buttress enlargement; 2- contraction joint; 3-
water stop
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F.A. Noetzli proposed the original design in 1925. The rounded head transmitted the
water load to the buttress in compression. Each buttress is an independent entity and is
separated from its neighbor by a contraction joint. Inserting singular or multiple
waterstops at the upstream side of the joint ensures watertightness. The expanded
upstream end of the counterfort may have a variety of shapes that approximate the
mushroom head. Usually this approximation is made with a series of straight lines that
results in a faceted configuration or diamond head.
An alternative to the massive head buttress dam proposed by Noetzli is the hollow
gravity dam, promoted by Italian engineers and standardized by C. Marcello (Figure
3.5). Contraction joints are provided for at only every second intermediate space,
resulting in a shaped buttresses.
Fig. 3.5. Typical buttress, hollow gravity – type dam:
1- drainage pipe
Marcello’s double-buttress alternative, as well as the Noetzli’s single buttress design
became less important for economic reasons, the rise of labor cost in relation to the
prices of materials and the ensuing mechanization working strongly against them.
Nevertheless, the largest hydropower plant ever built so far, namely the 12,600 MW
Itaipu scheme, has a double-buttress main dam with an unprecedented height of 196
m.
3.3. FLAT SLAB AND BUTTRESS DAM – STRUCTURAL FEATURES
The structural features of a flat slab and buttress dam are presented on the basis of an
outstanding example that is La Prele Dam designed and constructed in USA during
the period 1906 to 1908 (Figure 3.6).
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The dam, which is 42 m high and 99 m long at its crest, consists of a reinforced
concrete slab supported by 17 reinforced concrete buttresses. Two 100 mm diameter
steel pipes serve to regulate irrigation releases. A low-flow outlet consisting of one
steel pipes is used for releases to maintain minimum streamflow. The new spillway,
which replaced an overflow crest spillway, consists of a side channel located in
natural rock which discharges through a left abutment tunnel about 75 m downstream.
The flab slab is inclined approximately 400 from the horizontal and is supported by 17
buttresses at center-to center spacing of 5.50 m. The face slab varies from 1.50 m
thick at the base to 35 cm thick at the top.
Fig. 3.6. La Prele dam: cross section and plan view
PLAN VIEW
TRASHRACK
JOINTS IN DECK SLAB
CREST
NWL
DRAINAGE
SLIDE GATE
EXISTING SLAB
SUPLEMENTAL SLAB
CROSS SECTION
70
The slab deck was made up of independent slabs between each pair of buttresses.
Each buttress was provided with a double-grooved tongue in which the slab fits. This
groove was then painted with waterproofing consisting of successive coats of asphalt
primer, waterproof paint, felt and asphalt, after which the concrete slab was placed. A
small V-groove was left where the top of the slab meets the top of the tongue, and this
was finally filled with pitch as a last precaution against water entering the joint.
Struts are provided between buttresses. Cutoff walls are provided at the upstream and
downstream ends of the base slab.
In 1971 inspection showed that about 20 percent of the original face slab thickness
had eroded away. Rehabilitation included: (1) construction of a new face slab
over the existing slab, (2) grouting the abutments and foundation underneath the dam
in the river channel area, (3) installation of rock bolts to tie the structure to the
foundation, and (4) construction of a new side channel spillway in the left abutment.
The early popularity of the flat and buttress dam was enhanced by the large savings in
materials in conjunction with cheap skilled labor available at the time. Analysis of the
concrete slab was straightforward and followed the principles of reinforced concrete
design, treating the slab as a simply supported component free to expand or contract
in the direction parallel to the dam axis (Figure 3.7). Loads were imposed and tested
for shear and moment, a slab thickness determined, and reinforcement computed
accordingly.
Fig.3.7. Types of interfaces between slab and buttresses
Early designers considered the buttress component of flat slab and buttress dams as
cantilever beams of variable cross section. The dimensions of the "beam" had to be
sufficient to avoid tension at the upstream face of the member. For higher
structures, buckling became a concern. This concern was mitigated by treating the
buttress as a bearing wall with the minimum thickness governed by column criteria.
Additional strength against buckling was gained by including struts between
71
buttresses, by pilasters or flanges constructed along the width of the buttress, or by
diaphragm walls between buttresses.
As buttress design evolved, the cantilever beam approach was supplanted by
designing these members as columns. Those features were included in the buttresses
to facilitate these design assumptions (Figure 3.8). The buttresses were divided by
contraction joints into independent "columns". Keys were included along the
contraction joint to interlock each column segment to its neighbor. Although not
completely acting as independent columns, the approach more closely approximates
theory. Other advantages of the contraction joints include better control of cracks in
the buttress due to temperature and shrinkage, reduction in reinforcement steel, and
facilitation of construction.
Fig. 3.8. Layout of contraction joints in buttress
Flat slab and buttress dams also had their disadvantages. These disadvantages
included (1) a height limitation due to increased thickness of slab and the amount of
required reinforcement when compared to other types of concrete buttress dams, (2) a
need for exceptional quality control during construction, because the relatively thin
structural components are subject to deterioration, and (3) the rapidly escalating cost
of labour and materials from 1955 onwards. Moreover, early structures have required
extensive maintenance and repairs after being in service a relatively short time. In
many instances, the durability of buttress dams in extreme climatic conditions was
being questioned.
3.4. MULTIPLE ARCH DAM – STRUCTURAL FEATURES
The structural features of a multiple-arch dam are presented on the basis of two
examples. The first one is a common thin structure. The second one is a multiple
domes structure supported by massive buttresses.
Gem Lake Dam is a thin reinforced concrete dam with a height of 34 m (Figure 3.9),
with concrete arches varying in normal thickness from 30 cm at the top to 1.10 m at
the deepest point. The buttresses vary in thickness from 0,60 m at the top to 1.40 m at
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the deepest point. The buttress counterforts are 1.50 m wide at their tops and 3.60 m
wide at the deepest point. Double struts between buttresses have a cross section of 30
cm by 45 cm.
The upstream faces of all of the arches are covered with one more layers of gunite of
varying thickness and extent where the arches have been extensively modified or
repaired. A so-called concrete "gravity section" was placed against the intrados of
each arch up to an elevation of 15 m above the foundation ground. This massive
support of the arches was judged necessary because of disintegration of the arch
concrete due to a combination of freeze-thaw action and leaching.
Fig. 3.9. Gem Lake dam
73
In 1966, the extrados of all arches were refaced with an average of about three inches
of gunite, reinforced with heavy wire mesh. A polysulphide rubber coating was then
applied to the surface for additional protection.
Coolidge Dam consists of three egg-shaped domes supported by two massive
intermediate buttresses and the canyon walls (Figure 3.10). The dam has a structural
height of 76.2 m, a hydraulic height of 70 m, and a crest length of 280 m.
Appurtenances to the dam include two uncontrolled spillways with super elevated
chutes, an outlet works consisting of two conduits located partially in the buttress, and
a power plant located in the central dome between the two buttresses.
Fig. 3.10. Coolidge dam
CROSS SECTION
74
The domes are 1.30 m thick at the crest and have a maximum thickness of 8.20 m at
the foundation. The span of the domes from center to center of the buttresses is 60 m.
Buttress thickness ranges from a minimum of 7.90 m to a maximum of 19.60 m. The
buttresses are unreinforced except for the area near the spring line of the domes; the
domes are heavily reinforced. Two inclined contraction joints were built in each
buttress to facilitate contraction and expansion of the concrete during temperature
changes. The joints are approximately parallel to the trajectories of the minimum
principal stress.
Seepage control is afforded by a continuous double line grout curtain, which extends
beneath the structure and the spillway weir sections. Each line consists of holes 6.50
m deep on 3-m centers, staggered to produce an effective 1.70 m center-to-center
spacing along the curtain.
Flooding and seismic events have been recorded since construction of the dam, but no
significant damage has occurred to the dam structure.
Multiple-arch dams evolved at approximately the same time as the slab and buttress
dam, but at a much slower rate. Unlike the articulated Ambursen dam, multiple arches
are continuous, monolithic structures where loss of an important structure component
could lead to loss of the entire dam. For this reason, these structures normally require
a better foundation than the Ambursen type.
The arches are oriented normal to the upstream faces of the buttresses. However, due
to the inclination of the arch, the water load is not distributed uniformly from crown
to abutment, since the crown is always at a higher elevation than the corresponding
abutments.
Use of the theory of elasticity could adjust for this effect by allowing for increased
arch thickness at the arch abutment or modifying the circular shape to some other
geometric shape to some other geometric shape to achieve the same purpose.
The design for the buttresses of multiple arch dams essentially was identical to that
developed for the flat slab and buttress dam. A major innovation, initially proposed by
Noetzli was the hollow or double walled buttress. This concept featured a buttress
comprising two relatively thin walls with the interior faces of the walls stiffened by
reinforced concrete diaphragm elements. A substantial savings in concrete, and
reduction of uplift forces made for an overall cost savings. Utilization of the double-
wall buttress had a further advantage in eliminating or minimizing the need for
exterior struts between buttresses.
3.5. MASSIVE HEAD BUTTRESS DAM– STRUCTURAL FEATURES
The structural features of massive head buttress dam are presented on the basis of
several examples. The first one is Gura Raului dam built in Romania between 1973
and 1980 (Figure 3.11). The dam has a total height of 73.50 m, a crest length of 330
m, and a concrete volume of 300,500 m3.
The dam structure is divided into 22 blocks of 15 m wide. The buttresses have a
variable thickness, from 4.50 m at the dam crest to 8.0 m at the base. Also a gradual
75
thickening was provided from buttress head to the downstream face. In order to
increase the economics of the dam the upstream face slope is very large (0.57
Horizontal to 1 Vertical), to allow that a part of the sliding stability required block
weight to be replaced by the vertical water pressure on the upstream face. Inclined
construction joints, parallel to the downstream face are provided into each buttress.
Fig.3.11. Gura Raului dam
Water- tightening of the joints between the buttresses was achieved by means of a 1.5
mm thick cooper strip doubled by a PVC strip. Foundation water tightening was
achieved by a grout curtain consisting in 2 rows of grouted drillings at 1.5 m span,
with a depth of 45 m for the upstream row and 40 m for the downstream row.
Drainage underneath of the buttress heads was provided by 30 m deep drillings, two
for each block. Drainage of the rock mass is achieved by two groups of horizontal
drillings on each abutment.
The concrete in the dam was zoned, by using 240 kg cement / m 3 of concrete in the
buttress heads and a 200 kg cement / m 3 of concrete the buttresses. In order to avoid
PLAN VIEW
CROSS SECTIONS
76
cracking during the warm seasons the aggregates and the cement were cooled, the
concrete temperature at placing not exceeding 16o C.
Ben Metir dam was built in Tunisia between 1954 and 1955. The dam, with a
structural height of 71 m, has several specific constructive measures imposed by a
weak foundation rock (Figure 3.12). The current buttress presents a 14 m wide head
and a 4 m thick buttress slab. Near the foundation line the buttresses are enlarged and
become interconnected thus reducing the vertical stress transferred to the ground.
Fig. 3.12. Ben Metir dam:
a. cross section; b. contraction joint; c. buttress foundation:
1- grouting gallery; 2- drainage gallery; 3- reinforced concrete bulb;
4- bituminous mastic; 5- drainage shaft
Sliding stability of the dam was ensured by the weight of the water on the
significantly inclined upstream face and by sloping the foundation, upward from heel
to toe of the dam up to 15 % in the central zone. Due to the continuous concrete cover
of the foundation an extensive drainage system was provided by means of drainage
galleries and drainage drillings.
Figure 3.13 shows the most representative diamond-head buttress dams built
according to the modern concept. For each dam the profile and the characteristic
vertical and horizontal sections are presented. Some basic features are:
- the upstream and the downstream slopes are very similar;
- on the average, the ratio between the base width and the dam height is in
the range of 0.9 and 1.1;
- the head width varies between 14 and 18 m.
The hollowness coefficient , defined as the ratio between the total hollow spaces and
the block width, is in the range of 1/2 to 2/3. In other words, depending upon the
allowable stresses, somewhere between two-thirds and three-quarters of the volume of
77
a gravity dam is required as a counterweight to overcome overturning and shear-
friction forces.
For many dams the buttresses are provided with contraction joints parallel to the
downstream slope in order to avoid the concrete cracking induced by temperature
variation. Contiguous foundation pad is created by enlargement of the buttresses when
the foundation rock is weak.
Fig. 3.13. Representative diamond-head buttress dams
Ancipa dam is a hollow gravity dam having features typical of those dams that have
been designed and constructed principally by Italian engineers (Figure 3.14). The dam
was built during 1949 to 1952 period in Sicily. The maximum dam height is 112 m
and the 253 m wide valley is dammed by 9 blocks of 22 m wide each. The upstream
and downstream face slopes are each 4.5 horizontal to 10 vertical. The base width at
the foundation level is 0.9 of the dam height. This compares with base widths varying
between 0.75 and 0.80 of the height as commonly used for gravity dams.
78
The 7.0 m-wide internal cavity creates two buttresses, each having a maximum
thickness of 5.0 m. To increase lateral stability, flared sections at both the upstream
and downstream faces join these buttresses. The stabilizing effect of the vertical load,
introduced by providing a sloping upstream face, more than compensates for the loss
of weight that results from coring the monoliths.
The design concept eliminates the redundant concrete, provides massive unreinforced-
concrete sections, and has adequate lateral bracing for the buttresses.
Fig. 3.14. Ancipa dam:
a. plan view; b. characteristic sections:
1- massive concrete wing; 2- contraction joint; 3- drainage gallery
3.6. MASSIVE HEAD BUTTRESS DAMS– DESIGN
The design criteria used for gravity dams may also be applied to the buttress dam
type. The forces acting on a buttress dam are normally the weight of the concrete, the
reservoir water pressure, uplift pressure (pore pressure for other horizontal section
except foundation), earthquake effects and ice thrust. Mention should be made that
uplift pressure is assumed as decreasing linearly from a value equal to that resulting
from full head at the upstream face to one-tenth (or zero) of this pressure at the
downstream end of the buttress head. Pore pressures are assumed to have the same
distribution as those assumed for the uplift pressures.
79
For stress calculation the trapezoidal law can be applied, without substantial error, to
dams in the medium height range. In cases involving significant differences between
the elastic properties of the concrete and foundation materials a more exact analysis
by using the finite element method is required.
For current sliding stability analysis the shear strength is a combination of internal
friction that varies with the normal compressive stress and cohesive strength.
However, in order to simplify the preliminary design equations, the ultimate
resistance of the dam to sliding is considered as equal to the product of the total
normal force multiplied by the coefficient of static friction.
Under these simplifying assumptions the triangular profile of the dam is defined by
the upstream slope 1 and by the downstream slope . The hollowness coefficient is
previously selected based on the engineering practice, taking into account the
foundation strength. By applying as design criteria the conditions of zero vertical
stress at the dam heel and the sliding stability along the dam foundation contour the
numerical parametric calculations lead to the diagram in Figure 3.15.
Fig. 3.15. Design diagrams for a buttress dam:
a. loading conditions; b. face slopes
The upstream face slope is strongly dependent on the hollowness coefficient and
on the static friction coefficient f. The downstream slope is defined by the
upstream slope and by the static friction coefficient.
As it was mentioned before, the trapezoidal law on which the above diagrams are
based is not appropriate in cases involving significant differences between the
elastic properties of the concrete and foundation materials. In order to evaluate
how far the “conventional” linear assumption of the trapezoidal law can err, a
finite element analysis of a massive head buttress dam is reproduced, after
Zienkievicz, in the followings.
Figure 3.16 shows the dam section, its foundation in which various
inhomogeneities exist, and the division into finite elements. The heterogeneous
foundation region is subject to plane strain conditions while the dam itself is
considered as a plane stress structure of variable thickness.
80
Fig. 3.16,a. Dam cross sections
Fig.3.16,b. Finite element discretization of the dam-foundation system
Figure 3.17 shows the actual vertical stress distribution in two horizontal sections. For
the section B-B located ad mid-height of the dam the finite element stresses are not far
from the linear distribution corresponding to the trapezoidal law. A complete different
situation is encountered in section A-A near the foundation. Due to the weak intrusion
of altered grit under the buttress downstream toe the rock deformability is much larger
and the concrete stresses are reduced. The linear distribution of the vertical stresses is
no longer valid.
81
Fig. 3.17. Distribution of vertical stresses due to gravity and water pressure
3.7. MASSIVE HEAD BUTTRESS DAM– ECONOMY
The economic merits of the buttress dams have been systematically analysed by C.
Marcello. The main factor rendered evident was the concrete saving that corresponds
to a massive head buttress dam and to a hollow gravity dam respectively, as compared
to a gravity dam. The percentage saving is shown in Figure 3.18.
Fig. 3.18. Concrete savings in terms of the valley shape and the dam height
Savings
82
Three shapes were considered for the dammed valley: triangular, trapezoidal and
rectangular. Based on the diagrams in Figure 3.18 one can notice that:
- regardless the buttress dam type the concrete saving increases as the valley
opens;
- hollow gravity dams are more economic than the massive head buttress
dams;
- the concrete saving becomes significant when the dam height is higher
than 35 m;
- for dams higher than 70 - 80 m the concrete saving is constant 30 % on the
average.
However, the saving in costs is more modest due to the fact that a buttress dam
requires more formwork for the more complicated shape and higher cement content
for a slimmer structure. Further reduction of the cost saving is due to the difficulties in
dam concreting induced by the reduced concreting area in the slimmer zones of the
buttresses. According to Italian practice the actual cost reduction per cubic meter of
concrete in the replaced gravity dam was several percentages.
BIBLIOGRAPHY
Constantinescu, Al., Stematiu, D., Hapau-Petcu, S. Staged implementation of the
remedial works program for Poiana Uzului buttress dam. Transactions of 21
Congress on Large Dams, Q82, R20, June, 2003.
Davis, C.,V., Sorensen, E.,K. Handbook of applied hydraulics. McGraw-Hill, 1969.
ICOLD Bulletin 88. Rock foundation for dams. 1993.
Legas, J. Concrete buttress dams. Development of dam engineering in the United
States. Kolgaard, E.,B., Chadwick, W.,L. editors, Pergamon Press, 1988.
Popovici,A. Water storage dams. (in Romanian), Bucharest, 1992.
Priscu, R. Hydraulic structures. (in Romanian) , Bucharest, 1974.
Romanian National Committee on Large Dams. Dams in Romania, Bucharest 2000.
Schnitter, N. A history of dams – the useful pyramids. A.A.Balkema, 1994.
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