In this article we will discuss about:- 1. Design of Gravity Dams 2. Galleries in Gravity Dams 3. Joints 4. Elementary Profile 5. Foundation Treatment 6. Supply Sluices 7. Modes of Failure 8. Advantages 9. Disadvantages.
Contents:
- Design of Gravity Dams
- Galleries in Gravity Dams
- Joints in Gravity Dams
- Elementary Profile of a Gravity Dam
- Foundation Treatment of the Gravity Dams
- Supply Sluices in Gravity Dams
- Modes of Failure of Gravity Dams
- Advantages of Gravity Dams
- Disadvantages of Gravity Dams
1. Design of Gravity Dams:
It is not possible to adopt elementary profile as such, because of certain practical requirements. The preliminary design of gravity dams is done by two dimensional gravity method by considering the dam as being made of a number of cantilevers of unit length and acting independently of adjacent cantilevers.
(a) Effect of Top Width Added at the Apex of Triangular Profile:
ABC is an elementary profile of the dam. Let a be the top width added at the apex. The effect of this added top width is that the resultant of the dam section would shift slightly towards U/S side when reservoir is empty. Let AE1 and AE2 be the inner and outer-third point lines respectively.
Let NI be the vertical line passing through the C.G. of the added triangular concrete ADK. Let NI and AE1 lines intersect at point H. For all the dam sections lying below point H or section FHG the resultant would be shifted towards the U/S face of the line AE1. This shift in resultant causes development of tension at the toe when reservoir is empty. Hence to avoid the possibilities of tension at toe when dam is empty, some batter has to be provided to U/S face below the plane FHG.
The depth (h’) of plane FHG can be found out as follows:
c is the uplift pressure intensity coefficient. Thus upto height h’ no batter in the U/S face is required, but for larger depths U/S face has to be battered.
Now, let us consider the case when reservoir is full of water. The vertical line NJ cuts the outer-third point line AE2 at point j. Hence resultants of all the dam section lying below the plane JK are again shifted to the U/S side. To bring the resultant back to the outer third point line, the slopes of D/S force have to be flattered. Figure 13.13 shows the effect of top width of various sizes.
From diagram it can be easily seen that with increase in the size of the top width, the
batter of U/S face of the dam is increased while that of D/S face decreased. The total effect of addition of masonry at the top actually causes reduction in overall volume of the masonry of the dam rather than increasing it.
The most economical top width of the gravity dam is about 14 per cent of the height of the dam. In case of low dams increased top width may be provided from practical considerations such as provision of roadway on the top etc.
(b) Multiple Step Method of Design of Gravity Dam:
In this case, the total dam height is divided into various zones with the help of various horizontal sections. Each zone, starting from top of the dam, is deigned in such a way that all the stability requirement for it is fully satisfied. The total height may be divided into seven zones as shown in Fig. 13.14. Brief descriptions of conditions for each zone are given one by one.
Zone I:
This is the top most rectangular part of the dam lying above the full reservoir level. The height of this zone is controlled by the free board requirements and thickness is fixed on the basis of practical considerations. If ice is likely to deposit at the surface of the reservoir, the thickness and height of this zone is fixed on the basis of sliding of the zone due to ice pressure.
Zone II:
This is the zone which has both of its faces vertical. The position of bottom of this zone (c.c.) is fixed, such that the resultant passes through the outer third point of the plane c.c.
Zone III:
In this zone U/S face is maintained vertical, whereas D/S face is given the slope. The position of the bottom of this zone (d.d.) is fixed in such a way that the resultant for reservoir full and empty conditions, pass through the outer middle third point and inner middle third point respectively.
Zone IV:
In this zone U/S face of the dam is also battered like D/S face but batter of U/S face with vertical is very small. The position of the bottom of the zone (e.e.) is fixed in such a way that the maximum stress developed at toe for the condition when reservoir is full, reach the allowable limit of the stress for the material. The height of the dam above the bottom of zone IV (e.e.) is the height of the low dam.
Zone V:
D/S slope is further flattened in this zone so that the maximum pressure at D/S toe remains within the working stress under reservoir full condition. The resultant for reservoir full, remains well within middle third point of the base of this zone. For the reservoir empty condition, the resultant cuts the U/S middle third point of the base of this zone in section ff and stress at heel reached the permissible limit.
Zone VI:
In this zone, the resultant lines for both the conditions of reservoir, full and empty, well within the middle third points of the base of this zone, maximum stresses developed at toe for reservoir full condition and at heel for reservoir empty condition reach the maximum permissible value.
Zone VII:
At the bottom of this zone the maximum compression at the D/S toe exceeds the permissible limit. This zone is generally eliminated by revising the design of the dam. If change in design is not possible, then this zone is made from superior materials so that it may sustain the increased stresses developed at toe and heel.
(c) Single Step Method for Design of High Dams:
We have seen in multiple step method of design of the dam that upto bottom of zone IV, the dam is low gravity dam. But if we go beyond the height of low dam, U/S slope has very steep slope whereas D/S slope has convex shape outwards as shown in Fig. 13.16. Convexity outwards is not allowed. This convexity is avoided by designing the dam as a single block but conforming to the conditions laid down in zone VI. The shape of the high dam designed according to single step method is shown in Fig. 13.16.
In this method the U/S face of the dam is maintained vertical for some depth which may be determined as given in Fig. 13.12 (a). Below this section, both U/S and D/S faces are given such slopes that for both the conditions of reservoir full and empty, the stresses at toe and heel at all the sections reach their maximum values. This condition can be accomplished by performing several trials at all the sections. After having done this the dam is checked again for stability requirements for reservoir full and empty both, about the base of the dam.
Figure 13.16 shows super-position of dam section, designed according to single step method over that designed according to multi-step method. It is very clear that cubic content of the dam designed by multi-step method in economical. Dam designed by multi-step method is fully stressed at all the heights lying below the height of the low dam. But in case of dam, designed according to single step, the section is under-stressed everywhere except at the base.
From the discussions done until now, following inferences can be easily drawn:
1. Low dams should be designed by multi-step method as they prove economical.
2. High dams beyond zone VI should be designed by single step method so as to avoid convex curvature on the D/S face.
3. It may be economical to eliminate the zones V and VI by using more superior materials in the lower part of the dam, as in that case, permissible compressive stress will be more and hence higher stresses can be sustained by the dam.
But all these forces seldom act simultaneously on the dam. There are some combinations of the loads that may act simultaneously. Design of the dam should be based on the most adverse combination of “probable load condition”.
USBR has recommended two load combinations:
1. Standard Load Combinations:
Under this heading three possible combinations are given.
(i) Horizontal water pressure, at normal reservoir level + ice pressure + silt pressure + normal uplift pressure.
But this combination is adopted where ice pressure is considerable.
(ii) Horizontal water pressure at normal reservoir level + earthquake pressure + silt pressure + normal uplift pressure.
(iii) Horizontal water pressure at H.F.L. + silt pressure + normal uplift pressure.
2. Extreme Load Combination:
Maximum flood water elevation + silt pressure + extreme uplift with all the drains choked.
While designing the dam, whatever load combination might have been considered, the design must be checked for reservoir empty condition also. This condition is primarily important for testing stresses inside the dam and around the openings provided in the body of the dam.
2. Galleries in Gravity Dams
:
Galleries have to be left in the gravity dams during their construction. The size of the galleries depends upon the purpose, they have to perform. The galleries may be aligned both along the axis and across the axis of the dam. They are provided at all the levels of the dam.
All the galleries are given some longitudinal slope and small channels along both the edges of the galleries are formed. Seeping water through the dam section is collected by the channels running along the galleries. Since channels have longitudinal slope, the collected water in channels keeps on flowing automatically and is collected at some central place from where it is discharged into the D/S side of the dam.
Galleries are constructed to perform the following functions:
1. It may be cement concrete or masonary dam; some water definitely seeps through the joints and pores of the dam. This seeping water, if not intercepted, would create internal stresses in the dam and may cause its failure. Galleries intercept the seeping water and relieve the dam from interval stresses.
2. They form a measure to reach each and every part of the dam.
3. They are used for dissipation of heat, developed by setting action of the cement concrete during construction of the dam.
4. They are used for plugging the longitudinal joints of the dam, after the dam has been completed.
5. They are used to carry out drilling and grouting of the dam or the foundations.
6. They are used to study the behaviour of the dam after completion.
7. They are used for fitting mechanical equipment like pumps etc. in them.
8. Galleries are also essential for operation of sluice gates, outlet gates etc.
Shape of the gallery is generally rectangular but it may be oval shaped also. Side channels on both the sides of the gallery are provided. .
Shafts:
Dams are also provided with shafts. Shaft is a vertical opening in the dam. Shafts connect galleries at various levels. Shafts are generally provided with lifts so as to conduct effective inspection of the dam and also to facilitate quick approach anywhere in the dam. They are sometimes used to measure the deflections of the dam also.
3. Joints in Gravity Dams:
The joints that are necessarily provided in the dam may be classified under two heads:
1. Construction Joints:
The concreting of the dam is not done at a stretch but in stages. Each stage of the concreting is known as lift. Lift is nothing but thickness of a horizontal layer of concreting laid once. In concrete dams the thickness of each layer or in other words the lift, is kept about 1.5 m.
The horizontal joint between two successive lifts is known as construction joint. The lift or thickness of each concreting layer is decided so that cooling of the concrete, while setting, may be effectively accomplished by natural as well as artificial agencies. Thickness of lower most layer of concreting is kept half i.e. about 0.75 m. Modern techniques of treatment of surface before laying the new layer of concrete has almost eliminated the necessities of providing keys or water stops in the construction joints.
2. Contraction Joints:
The main purpose of providing contraction joints is to avoid development of shrinkage cracks in the dam due to changes in the temperature. Shrinkage cracking of the concrete can be controlled to some extent by properly controlling the temperature and adopting proper methods of curing. But provision of contraction joints in mass works like dams is invariably essential. Construction joints may further be classified as transverse contraction joints and longitudinal contraction joints.
(i) Transverse Contraction Joints:
Direction of the joints is at right angles to the axis of the dam. The spacing of these joints depends on factors like topographical features, location of the dam, type of cement, climatic conditions, but the general practice is to restrict spacing to about 15 m or the height of the dam whichever is small.
These joints extend throughout the height of the dam. To insure proper contact or connection between adjacent parts so that stresses are properly transmitted, the joints are either filled by grouting or by leaving a slot which is filled later when shrinking ceases. The joints may not be grouted and rendered water tight by introducing water stops or key ways in the joints.
(ii) Longitudinal Contraction Joint:
These joints are provided along the direction of the axis of the dam. These joints are considered objectionable from safety point of view as they may coincide very closely with the planes of maximum shear. Longitudinal joints do not run continuously and they are staggered in plan as shown in Fig. 13.19.
However they are continuous in vertical direction. They are laid between two adjacent transverse joints. The spacing of these joints is also limited to about 15 m. These joints are provided with key ways so as to transmit the principal stresses. Spacing of key ways vertically is 1.5 m or one key way is to be provided in each lift.
Keys:
It is a device, with the help of which shearing stresses from one block are transferred to the adjacent block. The provision of keys is essential for longitudinal joints but optional for transverse joints. The adjoining surfaces of each block are given such a shape that they together with transfer of stresses, cause effective interlocking also. Key ways may be of several shapes such as triangular, trapezoidal or trough shaped.
Water Stops:
The main job of water stops is to prevent leakage from the dam. They may be made of copper, steel, sheet, lead or of natural rubbers and plastics. Metal water stops are provided only in the case of non-yielding foundations. Rubber water stops are used in case the foundation is of yielding type. Drainage wells filled with asphalt are also sometimes used along with along water bars. Water bars are also a type of water stops.
4. Elementary Profile of a Gravity Dam:
If a gravity dam is subjected to horizontal pressure due to water along with its own weight, the elementary profile of the dam would be a right angled triangle. The thickness of the dam at the level of water surface will be zero as there is no hydrostatic pressure to be resisted.
The thickness at base would be maximum as there will be maximum hydrostatic pressure to be resisted by the dam. As the variation in hydrostatic pressure from water level to the bottom, is linear; variation in elementary profile from top to the dam to its bottom would also be linear.
Elementary profile of the low dam is shown in Fig. 13.8 (a). The triangular elementary profile also provides the maximum possible stabilizing force against overturning without causing tension in the base when reservoir is empty. This is because in this case weight of the dam acts at b/3 from the U/S vertical face.
Should there be any other triangular profile other than rt. angled, the stability of the dam is further increased but tension would develop at the toe when reservoir is empty.
Elementary profile of the dam is also sometimes known as theoretical profile of the dam.
Following forces are considered as acting on the dam while determining the elementary profile:
(i) Weight of the Dam (W):
(W) = 1/2 bHpw. It acts vertically downwards and acts at C.G. of the dam.
(ii) Water Pressure (P):
P = 1/2 wH2
Force P is horizontal and acts at H/3 from the bottom of the profile.
(iii) Uplift Pressure (U):
Uplift pressure acts vertically upwards. Its direct effect is that it reduces the gravity effect or load of the dam.
In all the three expression given above:
b = Base width of the dam.
H = Height of the elementary profile.
r = Specific density of the dam material.
ω = Unit weight or density of water.
C = Uplift pressure intensity coefficient.
U = Uplift pressure.
P = Horizontal water pressure.
W = Weight of the dam as a whole.
Base Width of Elementary Profile:
The base width of elementary profile is to be determined for following conditions.
1. Stress Basis:
We know that for no tension to develop the resultant should pass through the inner middle third point, when reservoir is empty and through outer middle third point when reservoir in full of water. Take moments of all the forces acting on the profile about the outer middle third point, and equate it to zero.
If uplift pressure is not considered c = 0 and hence b = 
2. Stability on Sliding Basis:
In order to prevent sliding of the dam, the horizontal force causing sliding should be either equal to or less than the frictional resistance opposing the sliding of the dam. Critical condition occurs when horizontal force (p) is equal to the frictional resistance.
The value of b should be adopted greater than the values obtained on stress basis and sliding basis.
Stresses Developed in Elementary Profile:
Maximum and minimum normal stresses in an elementary profile of the dam are given by –
At heel normal stress is zero and as such principal and shear stresses will also be zero.
When Reservoir is Empty:
In this case, the only force acting on the elementary profile is its weight. This weight acts at inner middle third point of the base. There will be no uplift pressure as reservoir is empty.
Maximum normal stress at heel = 2W / b.
Minimum normal stress at toe = 0.
Practical Profile of a Gravity Dam:
The elementary profile cannot be adopted as such. Some modifications have to be incorporated, to make it adaptable in practice.
Modifications in elementary profile are necessitated due to following reasons:
1. Some free board is essential whereas elementary profile does not provide any free board.
2. Road way is generally provided at the top of the dam. This necessitates quite thick top of the dam, whereas elementary profile does not provide any thickness at the top.
3. Additional load due to extra height provided for free board and also due thick top of the dam, induces some additional stress in the dam section. Some extra darn section has to be provided at the base of the dam along the U/S face to counter act such additional stresses. The amount of free board usually provided is 1.5 hw where hw is the height of waves in metres between through and crest. Minimum top width of the dam should be about one-seventh the
Maximum principal stress at the toe is given by –
pmax = ωH (P-C + 1)
In this formula variable element is only H the height of the dam. The value Pmax should not exceed the allowable stress (pa) for the material of which dam 01 its foundation is made.
While determining the limiting height of the dam, uplift is generally not considered.
If height of the dam exceeds the value given by expression
, the value of maximum compressive stress would exceed the safe limit of the stress for the material and dam would fail if measures for lowering the value of maximum compressive stress are not taken. Now low dams and high dams can be easily differentiated. If the height of the dam is equal to or less than height as given by equation
, the dam is called a low gravity dam.
In case of low dams, the value of maximum compressive stress, at the most, reaches the safe allowable stress for the material. If the height of the dam is more than that, given by the equation 
, it is known as high gravity dam. For high dams, the U/S and D/S faces will have to be given extra slopes below the limiting height required for low dams so as to bring the excessive compressive stress within safe limits of the stress. Elementary profiles for low and high gravity dams are shown in Fig. 13.8.
Profile of High Masonry Gravity Dam:
Mr. G. Molesworth gave the following formulae for fixing the profile of a high gravity dam, made of masonry. These formulae are applicable for masonry gravity dams only.
Where x = D/S offset from the vertical line also known as axis of the dam at a depth y below the maximum reservoir level.
Z = U/S offset from the vertical line at a depth y metres.
b1 = Base width of the dam at h/4 below the full reservoir level.
a = Thickness of the dam at the full reservoir level. It is taken as 0.4 b1.
pa = Allowable compressive stress for masonry in t/m2, the value of which may vary between 77 to 110 t/m2.
5. Foundation Treatment of the Gravity Dams:
The foundation of the gravity dam should be hard, strong, durable and impervious. Imperviousness of foundation is very important as uplift pressure depends greatly upon the seepage. Uplift pressure is increased when seepage is more. Hence to render the foundation water proof or impervious, it has to be suitably treated.
All the loose overlying soil from the site is removed and solid rocky foundation is reached. The rocky foundation should also be excavated for some depth so that the proposed dam fits in the rock. This aspect will prevent the sliding of the dam over its foundation. A 3 cm thick layer of rich cement mortar should be laid on the excavated rocky foundation before concreting is done over it.
All the faults, seams, cavernous rocks, crushed zones etc., should be either made good or removed from the foundation site. In order to prevent seepage through foundation, trenches may be excavated near heel of the dam and filled with cement concrete. Holes are drilled covering whole of the foundation and filled with cement grout. If foundation is to be treated for large depths, the holes are also drilled for large depth. The holes are filled with cement grout in stages. Any other fault noticed in the foundation is rectified.
6
. Supply Sluices in Gravity Dams:
Some openings in the dam have to be provided so as to pass the excess flow D/S of the dam. These openings are known as outlet sluices or supply sluices. If water from the reservoir is to be released for irrigation purpose at a controlled rate, it is done with the help of these supply sluices.
All the supply sluices are fitted with gates which can be raised or lowered. The control on the gates is exercised from the top of the darn. The gates are fitted in the grooves formed at the sides of the openings in the dam.
When gates are lowered they stop flow of water and when raised they again start discharging water D/S. Sluices may be provided at more than one depth. By this, water can be drawn from different elevations or depths. Supply sluices are also sometimes used to scour out the silt deposited in the vicinity of the U/S of the dam.
7. Modes of Failure of Gravity Dams
:
A gravity dam can fail due to the following reasons:
1. Overturning of the Dam:
If the resultant of all the possible forces (internal as well as external) acting on the dam cuts the base of the dam downstream of the Toe, the darn would overturn unless it can resist tensile stresses. To safeguard the dam against overturning, the resultant of the forces should never be allowed to go down stream of the Toe.
If resultant is maintained within the body of the dam, there will be no overturning. All the forces acting on the dam cause moments. Some of the forces help maintain stability of the dam, while others try to disturb the stability. The moments of the forces, helping dam to maintain its stability are known as resisting moments (Mr).
The moments of the forces that try to disturb the stability of the dam are known as overturning moments (M0). The moments of all the forces are generally taken about the Toe of the dam. Till Mr ≤ M0 there will be no overturning. As soon as M0 exceeds Mr over-turn of the dam would take place.
Factor of safety (F.S.) against overturning can be found out as follows:
F.S. = Resisting moment / Overturning moment = M0 / Mr
The value of F.S. against overturning should not be less than 1.5.
2. Sliding of the Dam:
In this mode of failure, the dam fails in sliding. The dam as a whole slides over its foundation or one part of the dam may slide over the part of the dam itself, lying below it. This failure occurs when the horizontal forces causing sliding are more than the resistance available to it, at that level.
The resistance against sliding may be due to friction alone or it may be due to combination of friction and shear strength of the joint. Shear strength develops at the base if benched foundation is provided. At other joints the shear strength is developed by laying joints carefully so as to obtain good bond. Interlocking of stone blocks in stone masonry also helps increase shear strength.
In case of low masonry dams shear strength is not taken into account. In that case factor of safety against sliding is obtained by dividing net vertical forces by net horizontal forces and multiplying the resultant by coefficient of friction μ.
Where μ = Coefficient of friction.
Σ (V-U) = Net vertical force.
ΣH = Sum of the horizontal forces causing sliding
The value of coefficient of friction varies from 0.65 to 0.75. The value of F.S. should always be greater than one.
In case of large high dams, the shear strength of the joint should also be considered along with static coefficient of friction. In this case factor of safety is known as shear friction factor (S.F.F.)
From safety point of view, the value of shear friction factor (S.F.F.) should lie between 4 and 5.
3. Crushing or Compression Failure:
If the compressive stress developed anywhere in the dam exceeds the safe permissible limit, the dam may fail by crushing of the dam itself or of foundation. The maximum compressive stress can develop at toe when reservoir is full of water. If reservoir is empty the maximum compressive stress is likely to develop at the heel of the dam.
The magnitude of maximum compressive and minimum compressive stresses can be found out by using following equation:
Where pn = Value normal stress.
V = Total vertical force.
B = Width of the dam base at level of consideration.
e = Eccentricity of resultant force R from the centre of the base.
H = Total horizontal force.
R = Resultant force.
Plus sign is used to evaluate the amount of maximum compressive stress which will occur at Toe of the dam when reservoir is full and at heel when reservoir is empty.
Hence to safeguard the dam against failure due to compression or crushing, the value of maximum compressive stress i.e. to exceed the allowable, compressive stress 
should be allowed to exceed the allowable, compressive stress (f) for the foundation material.
Hence 
When eccentricity e becomes equal to b/6 we get maximum compressive stresses as 2V / b
4. Failure due to Development of Tension:
Negative sign of this stress indicates that nature of this stress is tensile rather than compressive. Hence as soon as e exceeds b/6 tension is developed in the dam and dam fails by opening of the joints, as concrete and masonry are almost nil in tension.
When reservoir is full of water, tension is likely to develop at heel and when reservoir is empty tension is likely to develop at Toe of the dam. In other words it can be stated that until resultant of the forces lies within the middle third width of the base tension cannot develop anywhere in the dam.
In the case of gravity dams, having moderate height, no tension is allowed to be developed anywhere. However in case of very high dams, a small tensile stress may be permitted to be developed, but only for short durations during heaving floods or earthquakes.
Once tensile cracks develop at heel, the dam cannot be rendered safe. Due to tension cracks, uplift pressure gets increased and consequently net vertical downward force is reduced. This causes further shifting of the resultant towards the Toe and this leads to further lengthening of the cracks.
Due to lengthening of the cracks, effective width of base is further reduced and compressive stress at toe further increases. Ultimately compressive stress at toe increases to such an extent that dam fails by crushing at Toe.
8. Advantages of Gravity Dams:
There are some advantages of concrete dams described as following:
1. Maintenance cost of gravity dams is very small.
2. Spill ways can be installed in the dam itself and no separate site for them is required.
3. They can be constructed for very large heights.
4. Ice and other outer effects do not affect the stability of the dam.
5. Water is not lost by seepage.
6. Outlet sluices may be installed in the dam.
7. At valleys where side slopes are very steep, only this dam is found as the most suitable choice.
8. This dam gives pre-warning before failure. If timely measures are taken, the dam may even be made safe.
9. Disadvantages of Gravity Dams:
There are some disadvantages of gravity dams as below:
1. They are very costly.
2. They require very skilled labour for construction.
3. They have to be continuously cured during construction.
4. Large calculation work is involved in their design.
5. They require solid hard foundation.
6. The height of the dam cannot be increased later.