A railway embankment of height 2 m was constructed at a Site A, having a clay layer 8 m thick with single drainage condition. A settlement of 5 cm was observed in one year, corresponding to 50% average degree of consolidation. It was found that at a neighboring Site B, the same type of clay exists but having a thickness of 16 m. How long will it take for 50% consolidation to occur and what will be the magnitude of settlement if an embankment of same magnitude as at Site A was to be constructed at site B? (Assume γ = 18 kN/m³)
- A8 years
- B6 years
- C4 yearsCorrect
- D2 years
Solution
Concept
Time factor and drainage path
Formula
t ∝ Hdr²
Step-by-step solution
1. For the same U (and cv), t ∝ Hdr². 2. Both sites have single drainage: Hdr = 8 m and 16 m. 3. tB = 1 × (16/8)² = 4 years. 4. The final settlement is proportional to the thickness (about double that at A).
Explanation
Doubling the drainage path increases the time four times.
Why the other options are wrong
2, 6 and 8 years do not follow the square law.
Shortcut
t ∝ H².
Common mistake
Taking t ∝ H.
Correct answer: C) 4 years