The ratio Nc/Nq for a purely cohesive soil is ____ (Nc and Nq are Terzaghi's bearing capacity factors).
Try it first: pick an option, then read the explanation.
Asked in SSC JE 10/10/2023 (Evening)
Detailed Explanation
Terzaghi's equation for a strip footing is:
\[ q_u = cN_c + \gamma D_f N_q + \tfrac{1}{2}\gamma B N_\gamma \]
The factors depend only on φ. A purely cohesive soil (saturated clay, undrained) has φ = 0.
For \(\phi = 0\): \(N_c = 5.7,\ N_q = 1,\ N_\gamma = 0\).
\[ \frac{N_c}{N_q} = \frac{5.7}{1} = 5.7 \]
Why “5.7” Is Correct
With φ = 0, Nq becomes exactly 1 and Nc is 5.7 in Terzaghi's theory, so the ratio is 5.7.
| φ | Nc | Nq | Nγ |
|---|---|---|---|
| 0° | 5.7 | 1.0 | 0 |
| 10° | 9.6 | 2.7 | 1.2 |
| 20° | 17.7 | 7.4 | 5.0 |
| 30° | 37.2 | 22.5 | 19.7 |
Terzaghi's bearing capacity factors (general shear). They depend only on the angle of internal friction φ.
Why the Other Options Are Wrong
- B. 2.57: 2.57 is about half of 5.14, not a Terzaghi value.
- C. 5.14: 5.14 (= π + 2) is N_c for φ = 0 from Prandtl/Skempton, not Terzaghi.
- D. 2.85: 2.85 is half of 5.7 and has no meaning here.
Key Point
Terzaghi, φ = 0: Nc = 5.7, Nq = 1, Nγ = 0.
Key Concepts for Students
- Skempton's Nc for a strip footing on clay is 5.14, rising to 6.2 for square footings at the surface.
- For clay, net ultimate bearing capacity ≈ c·Nc.
- Nγ = 0 for φ = 0, so footing width does not change q_u for undrained clay.
Practice more: this is question 12 in Shallow and Deep Foundation MCQs – Part 1. Try the whole set and check every answer instantly.