Correct Answer - Option 3 : 27 kPa

**Concept:**

The relationship between cohesion and unconfined compression strength is given by,

\(c = \frac{{{q _u}}}{2}\)

\(Cohesion = \frac{{Unconfined\;compressive\;strength}}{2}\)

**Calculation:**

Given:

q_{u} = 54 kPa

\(\rm c = \frac{{{54}}}{2}=\rm 27~ kPa\)

The relationship between major and minor principle stress in** triaxial test** is given by

\({σ _{1}} = {σ _{3}}{\tan ^2}\left( {45^\circ + \frac{\phi }{2}} \right) + 2c\tan \left( {45^\circ + \frac{\phi }{2}} \right)\)

σ1 - Major principle stress

σ3 - Confining pressure

c - Cohesion of clay

In unconfined compression test confining pressure is zero ∴σ3 = 0

∴ \({σ _{1}} = 2c\tan \left( {45^\circ + \frac{\phi }{2}} \right)\)

For saturated clay ϕ =0

σ1 = 2 × c

σ1 becomes qu (unconfined compressive strength)

∴ \(c = \frac{{{q _u}}}{2}\)