This set of Irrigation Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Gravity Dams – Stability”.
1. The factor of safety against overturning generally varies between ___________
a) 2 to 3
b) 1.5 to 2
c) 0.5 to 1.5
d) 1 to 2
Explanation: Factor of safety against overturning can be determined by the ratio of righting moments about the toe to the overturning moments about the toe. The value generally varies between 2 to 3.
2. What is the maximum permissible tensile stress for high concrete gravity dam under worst conditions?
a) 500 KN/m2
b) 500 kg/cm2
c) 5 kg/m2
d) 50 KN/m2
Explanation: The masonry and concrete gravity dams are usually designed in such a way that no tension is developed anywhere in the structure. The maximum permissible tensile stress for high gravity dams is taken as 500 KN/m2 under worst conditions. If subjected to such tensile stresses crack develops near the heel.
3. Which failure occurs when the net horizontal force above any plane in the dam or at the base of the dam exceeds the frictional resistance developed at that level?
d) BY development of tension
Explanation: Sliding should always be fully resisted. At any horizontal section of the dam, the factor of safety against sliding is –
FOS = u Ph / Pv where u = coefficient of friction, Ph = Sum of horizontal forces causing sliding and Pv = Algebraic sum of vertical forces.
4. Which failure occurs when the minimum stress exceeds the allowable compressive stress of the dam material?
d) By development of tension
Explanation: The compressive stress produced if exceeds the allowable stresses then the dam material may get crushed, a dam may fail by the failure of its own material. The allowable compressive stress of concrete is generally taken as 3000 KN/m2.
5. Tension cracks in the dam may sometimes lead to the failure of the structure by?
a) Sliding of the dam at the cracked section
b) Overturning about the toe
c) Crushing of concrete starting from the toe
d) Both overturning and crushing
Explanation: When tension prevails, cracks develop near the heel and uplift pressure increases, reducing the net salinizing force. This crack by itself does not fail the structure but it leads to failure of the structure by producing excessive compressive stresses.
6. The major principal stress at the toe of a gravity dam under full reservoir condition neglecting the tailwater effect is given by ____________________
b) Pv tanQ2
c) Pv secQ2
d) Pv sinQ2
Explanation: When there is no tailwater, the principal stress in such a case is Pv secQ2 where Pv is the intensity of vertical pressure. This value of principal stress should not be allowed to exceed the maximum allowable compressive stress of dam material.
7. Which of the following criteria has to be satisfied for no tension at any point on a gravity dam?
a) The resultant of all the forces must always pass through the mid-point of the base of the dam
b) The resultant force for all conditions of loading must pass through the middle third of the base
c) The resultant of all the forces must pass through the upstream extremity of the middle third of the base
d) The resultant of all the forces must pass through the downstream extremity of the middle third of the base
Explanation: The minimum vertical stress Pmin is equal to zero in order to ensure that no tension is developed anywhere. If Pmin = 0, e = B/6 i.e. the maximum value of eccentricity that can be permitted on either side of the center is equal to B/6. This concludes the fact that the resultant of all forces must lie within the middle third of the joint width.
8. The bottom portion of a concrete or a masonry gravity dam is usually stepped in order to _______
a) increase the overturning resistance of the dam
b) increase the shear strength
c) decrease the shear strength
d) increase the frictional resistance
Explanation: The foundation is stepped at the base to increase the shear strength at the base and at other joints and measures is taken to ensure a better bond between the dam and the rock foundation. By ensuring a better bond between the surfaces the shear strength of these joints should be made as good as possible.
9. The governing compressive stress in a concrete gravity dam which should not be allowed to exceed the permissible value of about 3000 KN/m2 while analyzing full reservoir case is ____________________
a) the vertical maximum stress at the toe
b) the major principal stress at toe
c) the shear stress at the toe
d) the principal stress at the heel
Explanation: In reservoir full case, the resultant is nearer to the toe and hence, maximum compressive stress is produced at the toe. The vertical direct stress distribution at the base is the sum of the direct stress and the bending stress and is given by the equation –
Pmax = V/B [1 + 6e/B] where V is the total vertical force, e is the eccentricity of the resultant force from the center of the base and B is the base width.
10. If the uplift increases and the net effective downward force reduces, the resultant will shift towards the toe.
Explanation: The resultant shifts towards the toe if the uplift increases and the net effective downward force reduces. This further increases the compressive stress at the toe and further lengthening the crack due to the development of tension. It finally leads to the failure of the toe by direct compression.
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