## Designs and Construction of Gravity dam

**STRUCTURE (PARTS) OF A GRAVITY DAM**

**Toe:**Portion of structure in contact with ground or river-bed at downstream side.**Abutment:**Sides of the valley on which the structure of the dam rest.**Galleries:**Small rooms like structure left within the dam for checking operations.**Spillways**: It is the arrangement near the top to release the excess water of the reservoir to downstream side.**Sluice way**: An opening in the dam near the ground level, which is used to clear the silt accumulation in the reservoir side.**Crest**: The top of the dam structure. These may in some cases be used for providing a roadway or walkway over the dam.**Parapet walls**: Low Protective walls on either side of the roadway or walkway on the crest.**Heel**: Portion of structure in contact with ground or river-bed at upstream side.**Spillway**: It is the arrangement made (kind of passage) near the top of structure for the passage of surplus/ excessive water from the reservoir.**Abutments**: The valley slopes on either side of the dam wall to which the left & right end of dam are fixed to.**Gallery**: Level or gently sloping tunnel like passage (small room like space) at transverse or longitudinal within the dam with drain on floor for seepage water. These are generally provided for having space for drilling grout holes and drainage holes. These may also be used to accommodate the instrumentation for studying the performance of dam.**Free board**: The space between the highest level of water in the reservoir and the top of the structure.**Dead Storage level**: Level of permanent storage below which the water will not be withdrawn.**Diversion Tunnel**: Tunnel constructed to divert or change the direction of water to bypass the dam construction site. The hydraulic structures are built while the river flows through the diversion tunnel.

### Force acting on a Dam structure

In the design of a dam, the first step is the determination of various forces which acts on the structure and study their nature. Depending upon the situation, the dam is subjected to the following forces:

1. Water pressure

2. Earthquake forces

3. Silt pressure

4. Wave pressure

5. Ice pressure

6. Self weight of the dam.

The forces are considered to act per unit length of the dam. For perfect and most accurate design, the effect of all the forces should be investigated. Out of these forces, most common and important forces are water pressure and self weight of the dam.

**1. Water Pressure**

Water pressure may be subdivided into the following two categories:

**I) External water pressure:**

It is the pressure of water on the upstream face of the dam. In this, there are two cases:

(i) Upstream face of the dam is vertical and there is no water on the downstream side of the dam. The total pressure is in horizontal direction and acts on the upstream face at a height H/3 from the bottom. The pressure diagram is triangular and the total pressure is given by

P_{1 }= wh^{2}/2

Where w is the specific weight of water. Usually, it is taken as unity.

H is the height upto which water is stored in m.

(ii) Upstream face with batter and there is no water on the downstream side

Here in addition to the horizontal water pressure **P _{1}** as in the previous case, there is vertical pressure of the water. It is due to the water column resting on the upstream sloping side. The vertical pressure

**P**acts on the length ‘b’ portion of the base. This vertical pressure is given by

_{2}P_{2} = (b x h_{2 }x w) + (0.5b x h_{1} x w )

Pressure** P _{2}** acts through the centre of gravity of the water column resting on the sloping upstream face.

If there is water standing on the downstream side of the dam, pressure may be calculated similarly. The water pressure on the downstream face actually stabilizes the dam. Hence as an additional factor of safety, it may be neglected.

**II) Water pressure below the base of the dam or Uplift pressure**

When the water is stored on the upstream side of a dam there exists a head of water equal to the height upto which the water is stored. This water enters the pores and fissures of the foundation material under pressure. It also enters the joint between the dam and the foundation at the base and the pores of the dam itself. This water then seeps through and tries to emerge out on the downstream end. The seeping water creates the hydraulic gradient between the upstream and downstream side of the dam. This hydraulic gradient causes vertical upward pressure. The upward pressure is known as uplift. Uplift reduces the effective weight of the structure and consequently, the restoring force is reduced. It is essential to study the nature of uplift and also some methods will have to be devised to reduce the uplift pressure value.

With reference to figure, uplift pressure is given by

**P _{u = (wH x B)/2}**

Where ** P _{u}** is the uplift pressure, B is the base width of the dam and H is the height upto which water is stored.

This total uplift acts at **B/3 **from the heel or upstream end of the dam. Uplift is generally reduced by providing drainage pipes or holes in the dam section. Self weight of the dam is the only largest force which stabilizes the structure. The total weight of the dam is supposed to act through the centre of gravity of the dam section in vertically downward direction. Naturally when specific weight of the material of construction is high, restoring force will be more. Construction material is so chosen that the density of the material is about 2.045 gram per cubic meter.

**2. Earthquake Forces**

The effect of earthquake is equivalent to an acceleration to the foundation of the dam in the direction in which the wave is travelling at the moment. Earthquake wave may move in any direction and for design purposes, it is resolved into the vertical and horizontal directions. On an average, a value of 0.1 to 0.15g (where g = acceleration due to gravity) is generally sufficient for high dams in seismic zones. In extremely seismic regions and in conservative designs, even a value of 0.3g may sometimes by adopted.

Vertical acceleration reduces the unit weight of the dam material and that of water is to **(1- k _{v})** times the original unit weight, where

**k**is the value of g accounted against earthquake forces, i.e. 0.1 when 0.1g is accounted for earthquake forces. The horizontal acceleration acting towards the reservoir causes a momentary increase in water pressure and the foundation and dam accelerate towards the reservoir and the water resists the movement owing to its inertia. The extra pressure exerted by this process is known as hydrodynamic pressure.

_{v}**3. Silt Pressure**

If h is the height of silt deposited, then the forces exerted by this silt in addition to the external water pressure, can be represented by Rankine formula

acting at **h/3** from the base.

Where,

k_{a} = Coefficient of active earth pressure of silt =

= angle of internal friction of soil, cohesion neglected.

= submerged unit weight of silt material.

h = height of silt deposited.

**4. Wave Pressure**

Waves are generated on the surface of the reservoir by the blowing winds, which exert a pressure on the downstream side. Wave pressure depends upon wave height which is given by the equation

for F < 32 km, and

for F > 32 km

Where **h _{w}** is the height of water from the top of crest to bottom of trough in meters.

V – wind velocity in km/hour

F – fetch or straight length of water expanse in km.

The maximum pressure intensity due to wave action may be given by **P _{w} = 2.4γ_{w}h_{w}** and acts at

**h**meters above the still water surface.

_{w}/2The pressure distribution may be assumed to be triangular of height **5h _{w}/3** as shown in the figure.

Hence total force due to wave action acting at 3**h _{w}/8** above the reservoir surface and given by

**5. Ice Pressure**

The ice which may be formed on the water surface of the reservoir in cold countries may sometimes melt and expand. The dam face is subjected to the thrust and exerted by the expanding ice. This force acts linearly along the length of the dam and at the reservoir level. The magnitude of this force varies from 250 to 1500 kN/sq.m depending upon the temperature variations. On an average, a value of 500 kN/sq.m may be taken under ordinary circumstances.

**6. Weight of dam**

The weight of dam and its foundation is a major resisting force. In two dimensional analysis of dam, unit length is considered.

**The stability of a dam can be analysed in the following steps:**

i. Consider unit length of the dam.

ii. Work out the magnitude and dimensions of all the vertical forces acting on the dam and their algebraic sum, i.e. ?V.

iii. Similarly work out all the horizontal forces and their algebraic sum i.e. ?H.

iv. Determine the lever arm of all these forces above the toe.

v. Determine the moments of these forces about the toe and find the algebraic sum of all those moments, i.e. ?M.

vi. Find out the location of the resulting force by determining its distance from the toe.

vii. Find out the eccentricity (e) of the resultant (R) using

It must be less than **b/6** in order to ensure that no tension is developed anywhere in the dam.

viii. Determine the vertical stresses at the toe and heel using

ix. Determine the maximum normal stresses.

x. Determine the factor of safety against overturning as equal to

xi. Determine the factor of safety against sliding using

Sliding factor =

Shear friction factor (S.F.F)

=

### Causes of failure of a Gravity Dam

Failure of gravity dam occurs due to overturning, sliding, tension and compression. A gravity dam is designed in such a way that it resists all external forces acting on the dam like water pressure, wind pressure, wave pressure, ice pressure, uplift pressure by its own self-weight. Gravity dams are constructed from masonry or concrete. However, concrete gravity dams are preferred these days and mostly constructed.The advantage of gravity dam is that its structure is most durable and solid and requires very less maintenance.

**A gravity dam may fail in following modes:**

- Overturning of dam about the toe
- Sliding – shear failure of gravity dam
- Compression – by crushing of the gravity dam
- Tension – by development of tensile forces which results in the crack in gravity dam.

**Overturning Failure of Gravity Dam**

The ratio of the resisting moments about toe to the overturning moments about toe is called the factor of safety against overturning. Its value generally varies between 2 and 3.

Factor of safety against overturning is given by

FOS = sum of overturning moments/ sum of resisting moments

**Fig : sum of external horizontal forces greater than vertical self-weight of dam (overacting, sliding occurs)**

### Sliding Failure of Gravity Dam

**Factor of safety against sliding can be given based on**

- Frictional resistance
- Frictional resistance and shear strength of the dam

**Factor of safety based on frictional resistance:**

### Gravity Dam Failure due to Tension Cracks

Masonry and concrete are weak in tension. Thus masonry and concrete gravity dams are usually designed in such a way that no tension is developed anywhere. If these dams are subjected to tensile stresses, materials may develop tension cracks. Thus the dam loses contact with the bottom foundation due to this crack and becomes ineffective and fails. Hence, the effective width B of the dam base will be reduced. This will increase pmax at the toe. Hence, a tension crack by itself does not fail the structure, but it leads to the failure of the structure by producing excessive compressive stresses.

For high gravity dams, certain amount of tension is permitted under severest loading conditions in order to achieve economy in design. This is permitted because the worst condition of loads may occur only momentarily and may not occur frequently.

### Gravity Dam Failure due to Compression

A gravity dam may fail by the failure of its material, i.e. the compressive stresses produced may exceed the allowable stresses, and the dam material may get crushed.

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