A coarse grained soil has a void ratio of 0.7 and specific gravity 2.7. Calculate the critical gradient at which quick condition will occur.
Try it first: pick an option, then read the explanation.
Asked in SSC JE 06/11/2024 (Morning)
Detailed Explanation
When water flows upward through a soil, the seepage force pushes the grains up while their submerged weight pulls them down. As the hydraulic gradient increases, the effective stress between grains falls. The gradient at which the effective stress becomes zero is called the critical hydraulic gradient. At that point a cohesionless soil loses all its strength and behaves like a liquid: this is the quick (boiling) condition.
Effective stress becomes zero when the upward seepage pressure equals the submerged unit weight:
\[ i_c\,\gamma_w = \gamma' = \frac{(G-1)\,\gamma_w}{1+e} \quad\Rightarrow\quad i_c = \frac{G-1}{1+e} \]
\[ i_c = \frac{2.7-1}{1+0.7} = \frac{1.7}{1.7} = 1.00 \]
Why “1.00” Is Correct
With G = 2.7 and e = 0.7 the numerator and denominator are both 1.7, so the critical gradient is exactly 1.0. This is also the commonly quoted typical value: for most sands ic is close to 1.
Why the Other Options Are Wrong
- A. 0.93: 0.93 does not come from (G − 1)/(1 + e) with these values; it would need a smaller G or larger e.
- C. 1.25: 1.25 is too high; it would require a much denser soil (lower e) or heavier solids.
- D. 0.97: 0.97 is close but not correct; the arithmetic here gives exactly 1.00.
Key Point
Critical gradient i_c = (G − 1)/(1 + e) = γ′/γw. Typical value ≈ 1.0 for sands.
Key Concepts for Students
- Quick sand is a hydraulic condition, not a type of sand; it can happen in any cohesionless soil under upward flow.
- Clays do not usually go quick because their cohesion keeps some strength even when effective stress is low.
- Factor of safety against piping/boiling = i_c ÷ exit gradient; designs usually require 3 to 4.
Practice more: this is question 3 in Soil Consolidation MCQs – Part 1. Try the whole set and check every answer instantly.