For a certain soil, the angle of internal friction is 30°. The coefficients of active and passive pressure, respectively, will be:
Try it first: pick an option, then read the explanation.
Correct answer: B. 0.33, 3
Asked in SSC JE 30/10/2020 (Evening)
Detailed Explanation
Use Rankine's formulas for a cohesionless soil with a level backfill.
\[ K_a = \frac{1 - \sin 30^\circ}{1 + \sin 30^\circ} = \frac{0.5}{1.5} = 0.33 \qquad K_p = \frac{1.5}{0.5} = 3 \]
Why “0.33, 3” Is Correct
With sin 30° = 0.5 the numbers are simple: Ka = 1/3 and Kp = 3. They multiply to 1, as they should.
| Coefficient | Formula (cohesionless soil) | φ = 30° |
|---|---|---|
| Active, Ka | (1 − sin φ)/(1 + sin φ) = tan²(45° − φ/2) | 1/3 ≈ 0.333 |
| At rest, K0 | μ/(1 − μ) (elastic) or ≈ 1 − sin φ (Jaky) | ≈ 0.5 |
| Passive, Kp | (1 + sin φ)/(1 − sin φ) = tan²(45° + φ/2) | 3 |
For Rankine's theory with a level backfill, Ka × Kp = 1 and Ka < K0 < Kp.
Why the Other Options Are Wrong
- A. 0.4, 1.2: 0.4 × 1.2 ≠ 1, and neither value matches φ = 30°.
- C. 0.6, 2.4: 0.6 and 2.4 do not follow from sin 30° = 0.5.
- D. 0.5, 0.8: Kp must be greater than 1; 0.8 is impossible.
Key Point
φ = 30°: Ka = 1/3, Kp = 3 — worth memorising.
Key Concepts for Students
- φ = 0: Ka = Kp = 1.
- φ = 36.87°: Ka = 1/4, Kp = 4.
- Ka falls and Kp rises as φ increases.
Practice more: this is question 10 in Earth Pressure and Retaining Wall MCQs – Part 1. Try the whole set and check every answer instantly.