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Overturning Factor of a Gravity Dam

Harddamsoverturningstability
A gravity dam has a rectangular cross-section 4 m wide and 7 m tall, with concrete weighing 24 kN/m3. Water stands 6 m deep against the vertical upstream face. Considering only the concrete weight and the hydrostatic thrust, and taking moments about the downstream toe, the factor of safety against overturning is most nearly:
  1. A1.3
  2. B2.5
  3. C3.8
  4. D5.2
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Answer: C. 3.8

Per metre of dam length, the hydrostatic resultant is F = ½γh² = ½(9.81)(6)² = 177 kN acting at h/3 = 2.0 m above the base, so the overturning moment is 177(2.0) = 353 kN·m. The concrete weight is W = 24(4)(7) = 672 kN acting at the section centroid, 2.0 m from the toe, giving a resisting moment of 672(2.0) = 1,344 kN·m. The factor of safety is 1,344/353 ≈ 3.8. Placing the hydrostatic resultant at mid-depth rather than at h/3 is the most common error.
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