In a consolidation test, when the load is changed from 50 kN/m² to 100 kN/m², the void ratio changes from 0.80 to 0.60. The coefficient of compressibility will be:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 29/10/2020 (Morning)
Detailed Explanation
The coefficient of compressibility av measures how much the void ratio decreases for each unit increase in effective stress. It is the slope of the e – σ′ curve over the stress range considered.
\[ a_v = \frac{e_1 - e_2}{\sigma'_2 - \sigma'_1} \]
\[ a_v = \frac{0.80 - 0.60}{100 - 50} = \frac{0.20}{50} = 0.004\ \text{m}^2/\text{kN} \]
Why “0.004 m²/kN” Is Correct
The void ratio is dimensionless and the stress is in kN/m², so av has units of m²/kN. A drop of 0.20 in void ratio over a stress increase of 50 kN/m² gives 0.004 m²/kN.
Why the Other Options Are Wrong
- A. 0.003 m²/kN: 0.003 m²/kN would need a void ratio change of 0.15 over the same stress range.
- B. 0.002 m²/kN: 0.002 m²/kN is what you get by dividing by 100 (the final stress) instead of the stress increase of 50.
- D. 0.001 m²/kN: 0.001 m²/kN is four times too small.
Key Point
av = Δe/Δσ′ (m²/kN). mv = av/(1 + e₀). Here mv = 0.004/1.8 ≈ 0.0022 m²/kN.
Key Concepts for Students
- av is not constant: it decreases as the stress level increases because the e – σ′ curve flattens.
- Coefficient of volume compressibility mv = av/(1 + e₀) is used in ΔH = mv·Δσ′·H.
- Coefficient of consolidation cv = k/(mv·γw).
Practice more: this is question 10 in Soil Consolidation MCQs – Part 1. Try the whole set and check every answer instantly.