Question

If the \(D_{10}\) is the effective grain size, the coefficient of permeability of a soil is proportional to

• A. \(D_{10}\)
• B. \((D_{10})^2\)
• C. \((D_{10})^3\)
• D. \((D_{10})^{\frac{1}{2}}\)

Hint:

The coefficient of permeability \(k\) measures how easily water flows through a soil. It depends strongly on the size of the soil particles and the pore spaces between them.

Answer 1

The Correct Option is B

Concept:
The coefficient of permeability \(k\) measures how easily water flows through a soil. It depends strongly on the size of the soil particles and the pore spaces between them. The effective grain size \(D_{10}\) is the particle diameter such that 10% of the soil (by weight) is finer than it.

Step 1:
Allen Hazen, studying clean uniform sands, found experimentally that permeability is governed mainly by the smaller particles, which control the size of the flow channels.

Step 2:
Hazen's empirical relation is \(k = C\,(D_{10})^2\), where \(C\) is a constant and \(D_{10}\) is in cm. This shows that \(k\) varies as the square of the effective grain size, so a soil with twice the \(D_{10}\) is about four times more permeable.

Answer: Option (2) — \((D_{10})^2\).