# Comprehension The unconfined compressive strength of a saturated clay sample is 54 kPa. The value of cohesion for the clay is

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The value of cohesion for the clay is
1. zero
2. 13.5 kPa
3. 27 kPa
4. 54 kPa

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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)

∴ $c = \frac{{{q _u}}}{2}$