If the angle of internal friction φ = 30° for a soil, the angle of the failure plane relative to the major principal plane in a triaxial test will be:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 30/10/2020 (Morning)
Detailed Explanation
On the Mohr diagram, the failure plane corresponds to the point where the Mohr circle touches the envelope. Geometry of that tangent point gives the angle between the failure plane and the major principal plane:
\[ 2\theta_f = 90^\circ + \phi \quad\Rightarrow\quad \theta_f = 45^\circ + \frac{\phi}{2} \]
\[ \theta_f = 45^\circ + \frac{30^\circ}{2} = 60^\circ \]
Why “60°” Is Correct
For φ = 30°, the failure plane makes 60° with the major principal plane (the horizontal plane in a triaxial test). Equivalently, it makes 30° with the direction of σ₁.
Why the Other Options Are Wrong
- A. 45°: 45° is the answer only when φ = 0 (pure clay, undrained).
- C. 30°: 30° is the angle between the failure plane and the direction of σ₁ (90° − 60°), not the angle with the major principal plane.
- D. 67.6°: 67.6° does not correspond to φ = 30°; it would need φ ≈ 45°.
Key Point
θf = 45° + φ/2 from the major principal plane.
Key Concepts for Students
- For φ = 0 clay: θf = 45°.
- Dense sand with φ = 40°: θf = 65°.
- The same angle appears in Rankine's passive and active wedge theory.
Practice more: this is question 26 in Shear Strength of Soils MCQs – Part 2. Try the whole set and check every answer instantly.