The maximum permissible eccentricity for no tension at the base of a gravity dam is

Explanation:

An elementary profile of a gravity dam is shown:

Let the resultant pass through any point at a distance e from the centre of CB. Hence ‘e’ is the eccentricity.

The components of R are shown as above.

\(\therefore {{\rm{\sigma }}_{\rm{c}}} = \frac{{{{\rm{R}}_{\rm{v}}}}}{{{\rm{b}} \times 1}} - \frac{{\left( {{{\rm{R}}_{\rm{v}}} \times {\rm{e}}} \right) \times \left( {\frac{{\rm{b}}}{2}} \right)}}{{1 \times \frac{{{{\rm{b}}^3}}}{{12}}}}\;\)

For no tension at base,

σc ≥ 0

\( \Rightarrow \frac{{{{\rm{R}}_{\rm{v}}}}}{{{\rm{b}} \times 1}} \ge \frac{{\left( {{{\rm{R}}_{\rm{v}}} \times {\rm{e}}} \right)\left( {{\rm{b}}/2} \right)}}{{\left( {{{\rm{b}}^3}/12} \right)}}\)

⇒ e ≤ b/6

Hence when the resultant force lies in the middle-one-third region, there is no tension anywhere at the base of the elementary profile of a gravity dam.

Important Points

• Gravity dam is made of concrete or masonry and resists the water force using the weight of the dam only.
• An elementary profile of a gravity dam is a triangular section having zero width at water level and maximum base width where hydrostatic pressure is maximum
• The resultant force R mainly comprises the water force and weight of the dam.