The GATE Grind

GATE 2025 CE (CE1) – Question 17

Geotechnical Engineering · Shear strength, Mohr circle, stress-strain characteristics, stress paths · 1 mark · Multiple choice

The results of a consolidated drained triaxial test on a normally consolidated clay are shown in the figure. The angle of internal friction is

A Mohr circle plotted with shear stress $\tau$ (kPa) against normal stress $\sigma$ (kPa). The circle cuts the $\sigma$ axis at 50 kPa and at 100 kPa.
  1. $\sin^{-1}\left(\frac{1}{2}\right)$
  2. $\sin^{-1}\left(\frac{1}{3}\right)$
  3. $\sin^{-1}\left(\frac{2}{3}\right)$
  4. $\sin^{-1}\left(\frac{3}{4}\right)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $\sin^{-1}\left(\frac{1}{3}\right)$

Explanation

The circle cuts the axis at the minor and major principal stresses $\sigma_3 = 50$ kPa and $\sigma_1 = 100$ kPa. A normally consolidated clay has no cohesion, so its failure envelope passes through the origin and is tangent to the circle. Then $\sin\phi = \frac{\sigma_1 - \sigma_3}{\sigma_1 + \sigma_3} = \frac{50}{150} = \frac{1}{3}$, and $\phi = \sin^{-1}\left(\frac{1}{3}\right)$.