This set of Irrigation Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Gravity Method”.

1. When the reservoir is empty, the single force acting on it is the self-weight of the dam which acts at a distance of ____________

a) B/2 from the heel

b) B/6 from the heel

c) B/3 from the heel

d) B/4 from the heel

View Answer

Explanation: The only single force on the dam when the reservoir is empty is the self-weight of the dam acting at a distance of B/3 from the heel. It provides maximum possible stabilizing moment about the toe without causing tension.

2. When the reservoir is empty, the maximum vertical stress equal to ________________

a) At heel = 2W/B and at toe = 0

b) At heel = 0 and at toe = 2W/B

c) At heel = toe = zero

d) At heel = toe = 2W/B

View Answer

Explanation: The vertical stress distribution at the base when the reservoir is empty is given as –

P

_{max/min}= V/B [1 + 6e/B] and V/B [1 – 6e/B] where e = B/6 and V = total vertical force = weight W

P

_{max}= 2W/B and P

_{min}= 0.

The maximum vertical stress at the heel is equal to 2W/B and at the toe is zero.

3. The two-dimensional stability analysis of gravity dams proves better for U-shaped valleys than for V-shaped valleys.

a) True

b) False

View Answer

Explanation: The transverse joints in the dam body are generally not grouted in U-shaped valleys but are keyed together in V-shaped valleys. In V-shaped valleys, the entire length of the dam acts monolithically as a single body. The assumption that the dam is considered to made up of a number of cantilevers of unit width each may involve errors here.

4. Calculate the value of minimum base width for an elementary triangular concrete gravity dam supporting 72 m height of reservoir water and full uplift? (Take specific gravity of concrete as 2.4 and coefficient of friction as 0.7)

a) 36.28 m

b) 39.77 m

c) 51.5 m

d) 73.5 m

View Answer

Explanation: Using formula –

Case 1: B = H / (S

_{c}– c)

^{1/2}(For full uplift c = 1 and specific gravity of concrete = 2.4 )

= 72/ (2.4 – 1)

^{1/2}= 60.85 m

Case 2: B = H/μ (S – 1) where μ = coefficient of friction taken as 0.7

B = 72 / 0.7 x 1.4 = 73.46 m

The highest among the two base width value is to be selected i.e. B = 73.46 m.

5. For usual values of permissible compressive stress and specific gravity of concrete, a high concrete gravity is the one whose height exceeds ______________

a) 48 m

b) 70 m

c) 88 m

d) 98 m

View Answer

Explanation: The limiting height is – H

_{max}= f / (S

_{c}+ 1) ϒ

_{w}Permissible strength of concrete = 3000 KN/m

^{2}, S

_{c}= specific gravity of concrete = 2.4

H

_{max}= 3000/[(2.4 + 1) x 9.81] = 89.9 m.

6. For triangular dam section of height H for just no tension under the action of water pressure, self-weight and uplift pressure, the minimum base width required is _____________

a) H / (S-1)

b) H / S^{1/2}

c) H / (S – 1)^{-1}

d) H / (S-1)^{1/2}

View Answer

Explanation: The minimum base width (B) of a gravity dam having an elementary profile –

B = H / (S – 1)

^{-1}where S is specific gravity of concrete and H is the height of water.

If uplift is not considered – B = H/S

^{1/2}.

7. If the eccentricity of the resultant falls outside the middle third, the ultimate failure of the dam occurs by ______________

a) tension

b) crushing

c) sliding

d) overturning

View Answer

Explanation: When eccentricity is greater than B/6 (eccentricity falls outside the middle third), tension may develop. When tension prevails, cracks develop near the heel and uplift pressure distribution increases reducing the net salinizing force.

8. What is the value of eccentricity for no tension condition in the dam?

a) e < B/6

b) e > B/6

c) e > B/3

d) e < B/3

View Answer

Explanation: The resultant of all the forces i.e hydrostatic water pressure, uplift pressure and self-weight of the dam should always lie within the middle third of the base for no tension. When e < B/6, the value of stress intensity at toe and heel are positive i.e compression on both sides.

9. What is the formula for limiting height of a gravity dam?

a) H_{max} = f / (S_{c} + 1) γ_{w}

b) H_{max} = f / (S_{c} – 1) γ_{w}

c) H_{max} = f / (S_{c} + C) γ_{w}

d) H_{max} = f / (S_{c} – 1) γ_{w}

View Answer

Explanation: The critical height or limiting height of a dam having elementary profile is –

H

_{max}= f / (S

_{c}+ 1) γ

_{w}where f = allowable stress of the dam material, S

_{c}= Specific gravity of concrete and γ

_{w}= unit weight of water.

This limiting height draws a dividing line between a low gravity dam and a high gravity dam.

10. Calculate the top width of the dam if the height of water stored is 84m.

a) 5 m

b) 2.5 m

c) 5.55 m

d) 7.75 m

View Answer

Explanation: Bligh has given an empirical formula for finding out the thickness of the dam at top.

A = 0.522 H

^{1/2}= 0.522 x 84

^{1/2}= 5.05 m.

As per Creager, the economical top width has been found to be equal to 14% of the dam height without considering earthquake forces.

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