A normally consolidated clay layer settled by 20 mm when the effective stress was increased from 25 to 50 kN/m². What will be the settlement when the effective stress is increased from 50 to 100 kN/m²?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 11/12/2020 (Evening)
Detailed Explanation
For a normally consolidated clay, settlement is calculated from the compression index. Because the e – log σ′ line is straight, what matters is the ratio of final to initial effective stress, not the difference between them.
\[ \Delta H = \frac{C_c\,H}{1+e_0}\,\log_{10}\!\left(\frac{\sigma'_f}{\sigma'_0}\right) \quad\Rightarrow\quad \Delta H \propto \log_{10}\!\left(\frac{\sigma'_f}{\sigma'_0}\right) \]
\[ \frac{\Delta H_2}{\Delta H_1} = \frac{\log_{10}(100/50)}{\log_{10}(50/25)} = \frac{\log_{10} 2}{\log_{10} 2} = 1 \]
\[ \Delta H_2 = 20 \text{ mm} \]
Why “20 mm” Is Correct
The first increment doubles the stress (25 → 50) and the second also doubles it (50 → 100). On a log scale these are equal steps, so the clay settles by the same amount: 20 mm. (Strictly, H and e₀ are a little smaller for the second stage, but that change is ignored in exam problems.)
Why the Other Options Are Wrong
- A. 5 mm: 5 mm would mean the clay became four times stiffer; on a log scale the second step is the same size, not smaller.
- B. 40 mm: 40 mm comes from treating settlement as proportional to the stress increase (50 kN/m² is twice 25 kN/m²). Settlement depends on the log of the stress ratio, not on the difference.
- D. 10 mm: 10 mm would only follow if the stress ratio in the second stage were √2 instead of 2.
Key Point
For NC clays settlement depends on log(σ′f/σ′₀). Same stress ratio → same settlement.
Key Concepts for Students
- Each doubling of effective stress gives roughly the same settlement in a NC clay.
- For overconsolidated clays, use the recompression index Cr (much smaller than Cc) up to σ′c.
- Using mv instead: ΔH = mv·Δσ′·H, which is valid only for small stress ranges.
Practice more: this is question 8 in Soil Consolidation MCQs – Part 1. Try the whole set and check every answer instantly.