The coefficient of compressibility of soil is the ratio of ______.

Asked in SSC JE 04/03/2017 (Morning)

Detailed Explanation

The coefficient of compressibility tells us how much a soil compresses for each unit of stress added. Compressibility is always ‘deformation per unit load’; stiffness (modulus) is the opposite, ‘load per unit deformation’.

\[ a_v = \frac{e_1 - e_2}{\sigma'_2 - \sigma'_1} = \frac{-\Delta e}{\Delta\sigma'} \qquad m_v = \frac{a_v}{1+e_0} = \frac{\text{volumetric strain}}{\Delta\sigma'} \]

Why “strain to stress” Is Correct

Change in void ratio is a measure of strain (deformation), and it is divided by the change in effective stress. So the coefficient of compressibility is a ratio of strain to stress. Its units (m²/kN) are the inverse of stress units, which confirms it is ‘per unit stress’.

e – σ′ curve on natural scales. The coefficient of compressibility a_v is the (negative) slope of this curve over the stress range considered: a_v = Δe / Δσ′. Because the curve flattens, a_v falls as stress rises.

Why the Other Options Are Wrong

A. stress to strain: Stress divided by strain is a modulus (stiffness), the inverse of compressibility. For a confined soil, 1/mv is the constrained modulus.
C. stress to settlement: Stress to settlement has units of stress per length and is not how av is defined.
D. rate of loading to that of settlement: Rates of loading and settlement are about time, which belongs to the coefficient of consolidation, not compressibility.

Key Point

Compressibility = strain per unit stress (av, mv in m²/kN). Modulus = stress per unit strain.

Key Concepts for Students

Strictly, av uses change in void ratio; mv uses volumetric strain. Both are ‘strain ÷ stress’.
mv is about 0.1–1.0 m²/MN for medium clays.
Constrained (oedometer) modulus D = 1/mv.

Practice more: this is question 17 in Soil Consolidation MCQs – Part 2. Try the whole set and check every answer instantly.