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
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 (figure 1).
The total pressure is in horizontal direction and acts on the upstream face at a height from the bottom. The pressure diagram is triangular and the total pressure is given by
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 (figure 2).
Here in addition to the horizontal water pressure 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 acts on the length ‘b’ portion of the base. This vertical pressure is given by
Pressure 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 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 3, uplift pressure is given by
Where 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 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 times the original unit weight, where 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.
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 from the base.
= 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 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
and acts at meters above the still water surface.
The pressure distribution may be assumed to be triangular of height as shown in figure 4.
Hence total force due to wave action
= acting at above the reservoir surface.
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.