For no tension to develop in gravity dam the eccentricity of the resultant force should be: (where b is the width of base)

Concept:

Maximum and minimum base pressures are given by the expression;

\(σ_{{max}/{min}}=({R_V\over B\times 1})(1\pm{6e\over B}) \)

Where Rv = vertical component of the resultant force, e = eccentricity, and B = base width of retaining wall.

\(σ_{max}=({R_V\over B\times 1})(1+{6e\over B}) \)

\(σ_{min}=({R_V\over B\times 1})(1-{6e\over B}) \)

For the 'no tension' condition,

σmin = 0

\(({R_V\over B\times 1})(1-{6e\over B}) =0\)

\(1-{6e\over B} =0\)

\(e={B\over 6}\)

• Shows the distribution of base pressures when the resultant falls within the middle third. For e = B/6, i.e., the resultant acting at one-third point, the minimum base pressure becomes equal to zero and the base pressure distribution becomes triangular.
• When the resultant falls outside the middle third, that is, for e > B/6, the minimum base pressure becomes negative or tensile. This condition must not be allowed to develop, since the soil is incapable of resisting tension. 

For no tension to develop in the gravity dam the eccentricity of the resultant force should be e < b/6. Hence option (3) is the correct answer.