Forces Acting on Gravity Dam and Their Magnitude and Line of Action.

What is Gravity Dam

A Gravity Dam has been defined as a structure which is designed in such a way that its own weight resist the external forces and this type of structure is most durable and solid. It requires less maintenance and it can be constructed with masonry or concrete.

External Forces Acting on Gravity Dam

• Water Pressure.
• Uplift Pressure.
• Earthquake Forces.
• Silt Pressure.
• Wave Pressure.
• Ice Pressure.
• Weight of Dam.

1. Water Pressure :

Water Pressure is one of the mass major external forces acting on gravity dam. The horizontal water pressure exerted by the water stored on upstream side of dam can be collected from hydrostatic pressure distribution.

2. Uplift Pressure :

Water seeping through the pores and fissures of the foundation material and water seeping through the dam of the body and there to the bottom through the joints between the body of the dam and its foundation at the base, exerts an uplift pressure on the base of the dam.

This kind of uplift pressure virtually reduces the downward weight of the body of the dam and hence acts against the dam stability. It is assumed that uplift pressure are not affected by the earthquake forces.

It can be controlled by constructing weight of walls under the upstream face by constructing drainage channel between the dam and its foundation and by pressure grouting the foundation.

3. Earthquake forces :

An Earthquake produces waves which are capable of shaking the dam in every possible direction. The effect of Earthquake is equivalent to imparting an acceleration to the foundations of the dam in the direction in which the wave is travelling at the moment. Acceleration can be splitted into 2 components :

• Horizontal Acceleration (αh) = Kh×g
• Vertical Acceleration (αv) = K×g

The values of these acceleration are generally expressed as % of acceleration due to gravity (g) i.e α = 0.19 or 0.29. The value of alpha (α) depends upon 5 seismic zones in which the dam lies.

Effect of Vertical Acceleration (αv)

Vertical acceleration may be downward or upward. When it acts in upward direction, the foundation of the dam will be lifted upward and becomes closer to the body of the dam and thus effective weight of the dam will increase and the developed stress will be greater. While the acceleration is acting downward the foundation shall try to move downward from along the body of the dam, thus reducing the effective weight and the stability of the dam. This kind of acceleration will therefore exert an inertia force as follows :

∴ inertia force = mass × acceleration
= (w/g)× αv

∴ Net effective weight of dam = W – (w/g) (αv)
= W – (w/g) (Kvg)
= W (1-Kv)

Effect of Horizontal Acceleration (αh)

It causes following 2 forces :

•  Hydrodynamic pressure.
• Horizontal inertia force.

4. Silt Pressure :

If ‘h’ is the height of silt deposited, then force exerted by the silt in addition to external water pressure can be represented by Rankine’s formula,

Psilt= ½ γsub h² Ka and it acts at h/3 from base.

where, Ka    = 1-sinΦ/1+sinΦ.
γsub = submerged unit weight of silt material.
h      = height of silt deposited.

If the upstream face is inclined, the vertical weight of the silt which is supported on the slope will also acts as a vertical force. As per USBR, the total horizontal force will be 1.8h² kn/m and vertical force will be 4.6h² kn/m.

5. Wave Pressure :

Waves are generated on the surface of the reservoir by the blowing winds, which can cause a pressure towards the downstream side wave pressure and it depends upon the wave height. Wave height may be given by the following equation,

hw = 0.032 √vf + 0.763 – 0.271 f¾,  for f<32.

where, hw = height of water from top of crest to bottom of trough in meters.
v = wind velocity in km/h.
f =  fetch or straight length of water expanse in km.

The maximum pressure intensity due to wave action may be given by,

Pw = 2.4 γw hw and acts at hw/2 meter above the silt water surface.

The pressure distance is assumed to be triangular of height 5hw/3. Hence the total force due to wave action,                  Pw = ½ (2.4 γw hw) 5/3hw
= 2 γw h²w
= 2×9.81 h²w  kn/m
= 19.62 h²w.
This force acts at a distance 3/8 hw above the reservoir surface.

6. 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 then has to resist force 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- 1500 kn/m².

7. Weight of the Dam :

The weight of the dam body and its foundation is the major resisting force. In two dimensional analysis of the gravity dam, unit length of the dam is considered. The c/s then can be divided into rectangles and triangles. The resultant of all these downward forces will represent the total weight of dam acting the center of gravity of the dam.