# Irrigation Engineering Questions and Answers – Gravity Dam Design – Typical Cross-section

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This set of Advanced Irrigation Engineering Questions and Answers focuses on “Gravity Dam Design – Typical Cross-section”.

1. The vertical component of the earthquake wave which produces adverse effects on the stability of a dam when is acting in ____________________
a) upward direction
b) downward direction
c) both upward and downward direction
d) any direction

Explanation: When the vertical acceleration is acting downward the foundation try to move downward away from the dam body. This reduces the effective weight and the stability of the dam. It is the worst case for design.

2. The horizontal component of an earthquake wave producing instability in a dam is the one which acts __________________
a) towards the reservoir
b) towards the dam
c) away from the reservoir
d) away from the dam

Explanation: Hydrodynamic pressure and horizontal inertia force are caused by the horizontal acceleration of an earthquake wave acting towards the reservoir. As the foundation and dam accelerate towards the reservoir there is an increase in the water pressure which is resisted by water, the extra pressure is hydrodynamic pressure.

3. The vertical downward earthquake acceleration av = 0.1g acting on a gravity dam will ________________________
a) increase the resisting weight of the dam by 10%
b) decrease the resisting weight of the dam by 10%
c) increase the uplift by 10%
d) decrease the uplift by 10%

Explanation: The net effective weight of the dam is given as W [1 – Kv] and vertical acceleration av = Kv.g = 0.1.g i.e 10%
where W is the total weight of the dam and Kv is the fraction of gravity adopted for vertical acceleration.
This is considered as the worst case for design as the foundation tries to move downward away from the dam body when there is downward vertical acceleration. This reduces the effective weight and the stability of the dam.

4. A gravity dam is subjected to hydrodynamic pressure caused by __________
a) the rising waves of the reservoir when a flood wave enters into it
b) the rising waves in the reservoir due to high winds
c) the increase in water pressure momentarily caused by the horizontal earthquake acting towards the reservoir
d) the increase in water pressure momentarily caused by the horizontal earthquake acting towards the dam

Explanation: Hydrodynamic pressure is the extra pressure exerted when the horizontal acceleration of an earthquake wave is acting towards the reservoir. As the foundation and dam accelerate towards the reservoir there is an increase in the water pressure which is nothing but hydrostatic pressure acting at a height of 3H/4π above the base. Mathematically, this value is given by Von-Karman equation.

5. In a concrete gravity dam with a vertical upstream face the stabilising force is provided by the ___________________
a) weight of the dam
b) the water supported against the upstream slope
c) uplift pressure
d) water pressure at the tail end

Explanation: The major resisting force is the weight of the dam body and its foundation. A unit length of the dam is considered in the 2D analysis of a gravity dam. The resultant of all the downward forces will represent the total weight of the dam acting on it.

6. What is the value of horizontal destabilizing force caused by the formation of waves in a storage reservoir having a fetch of 52 km due to high wind of 172 km/h?
a) 30 KN
b) 60 KN
c) 130 KN
d) 180 KN

Explanation: When F > 32 km, the wave height is given by hw = 0.032 (V.F)1/2
hw = 0.032 (172 x 52)1/2 = 3.02 m
The force caused by waves is given by the equation – Pw = 19.62 hw2 KN/m run of the dam
Pw = 19.62 x 3.022 = 179.69 KN.

7. Calculate the value of free-board that should be provided for a reservoir having a wind velocity of 92 km/h and it extends up to 18 km upstream.
a) 1.2 m
b) 1.6 m
c) 2.25 m
d) 2.5 m

Explanation: When F < 32 km, the wave height is given by – Hw = 0.032(V.F)1/2 + 0.763 – 0.271 F1/4
Hw = 0.032(92 x 18)1/2 + 0.763 – 0.271 (18)1/4 = 1.5 m
Free board is generally provided equal to 1.5 Hw = 1.5 x 1.5 = 2.25 m.

8. The upward acceleration of dam due to seismic activity will ________________________
a) increase the base pressure
b) decrease the base pressure
c) not affect the effective weight of the dam
d) increase the horizontal dynamic force

Explanation: Vertical acceleration can be resolved in two parts i.e. upward vertical accelerations and downward vertical accelerations. The effective weight of the dam increases when there is an upward vertical acceleration as it brings the foundation closer to the dam. In downward acceleration, the effective weight reduces and is considered as the worst design case.

9. What is the average value of acceleration that is sufficient for high dams in seismic zones?
a) 0.1g to 0.15g
b) 0.05g to 0.1g
c) 0.3gs
d) 0.15g (where g is the acceleration due to gravity)

Explanation: An average value of acceleration equal to 0.1 to 0.15 g is sufficient for high dams in seismic zones and for areas not subjected to extreme earthquake ah = 0.1 g and av = 0.05 g may be used. These forces are neglected in areas of no earthquake or very less earthquake.

10. What is Von Karman’s formula for hydrodynamic force (Pe)?
a) Pe = 0.726 pe H
b) Pe = 0.424 pe H
c) Pe = 0.555 pe H
d) Pe = 0.555.Kh. Yw H2

Explanation: According to Von-Karman, the hydrodynamic force is given by –
Pe = 0.555. Kh. ϒw H2 where, ϒw is the unit weight of water, H is the depth of water and Kh is a fraction of gravity adapted for horizontal acceleration which acts at the height of 4H/3π above the base. In addition to this, an inertia force is also produced by the horizontal acceleration into the body of the dam.

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