Question

A cohesionless soil sample has showed an angle of internal friction 30$^\circ$ at failure corresponding to a cell pressure of 100 kPa. The deviator stress at failure is..........

• A. 300 kPa
• B. 200 kPa
• C. 100 kPa
• D. 60 kPa

Hint:

For cohesionless soils ($c = 0$), deviator stress at failure depends only on confining pressure and friction angle.

Answer 1

The Correct Option is B

Given:
Angle of internal friction, $\phi = 30^\circ$
Cell pressure = 100 kPa
Cohesionless soil implies $c = 0$
In a triaxial test for cohesionless soil, deviator stress at failure is given by:
$\sigma_d = \sigma_3 \cdot \left(\tan^2\left(45^\circ + \frac{\phi}{2}\right)\right)$
$= 100 \cdot \tan^2(60^\circ)$
$\tan(60^\circ) = \sqrt{3} \approx 1.732$
$\sigma_d = 100 \cdot (1.732)^2 = 100 \cdot 3 = 200$ kPa
Therefore, the deviator stress at failure is 200 kPa.