The internal angle of friction of a soil is 30°. What is the active earth pressure coefficient for the soil mass?
Try it first: pick an option, then read the explanation.
Correct answer: C. 0.333
Asked in SSC JE 27/01/2018 (Morning) / SSC JE 24/01/2018 (Morning)
Detailed Explanation
Use Rankine's active coefficient for a cohesionless soil.
\[ K_a = \frac{1 - 0.5}{1 + 0.5} = \frac{1}{3} = 0.333 \]
Why “0.333” Is Correct
sin 30° = 0.5 gives Ka = 1/3 = 0.333.
| 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. 0.005: 0.005 is far too small; Ka for real soils is usually 0.2–0.5.
- B. 0.025: 0.025 is also far too small.
- D. 0.555: 0.555 is too large for φ = 30°.
Key Point
φ = 30° → Ka = 0.333.
Key Concepts for Students
- Same as Q321.
- Ka = tan²30° = 1/3.
- Active thrust = ½ × 0.333 × γH².
Practice more: this is question 18 in Earth Pressure and Retaining Wall MCQs – Part 2. Try the whole set and check every answer instantly.