Test: Gravity Dams – Stability - Civil Engineering (CE) MCQ

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.

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.

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.

Sliding should always be fully resisted. At any horizontal section of the dam, the factor of safety against sliding is –
FOS = u P_h / P_v where u = coefficient of friction, P_h = Sum of horizontal forces causing sliding and P_v = Algebraic sum of vertical forces.

When there is no tailwater, the principal stress in such a case is P_v secQ² where P_v 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.

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.

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.

The minimum vertical stress P_min is equal to zero in order to ensure that no tension is developed anywhere. If P_min = 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.

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.

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 – P_max = 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.