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:
qu = 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)
∴ \(c = \frac{{{q _u}}}{2}\)