Consolidation MCQ with answer and solution

Concept

m_v is the change in volume per unit original volume per unit increase in effective stress.

Formula

m_v = a_v / (1 + e₀) = (-Δe / (1 + e₀)) × (1 / Δσ')

Step-by-step solution

1. Coefficient of compressibility: a_v = -Δe / Δσ'. 2. Volumetric strain = -Δe / (1 + e₀). 3. m_v = volumetric strain / Δσ' = (-Δe / (1 + e₀)) × (1 / Δσ'). 4. This matches option (A).

Explanation

m_v tells how much a soil's volume reduces per unit increase in effective stress. Volume strain is Δe divided by (1 + e₀), and this is then divided by Δσ'. So m_v = a_v / (1 + e₀).

Why the other options are wrong

B: has no Δe term, so it is not a volume change. C: uses (1 - e₀) and has no Δσ' term. D: uses (1 - e₀) instead of (1 + e₀).

Shortcut

m_v = a_v / (1 + e₀); remember 'plus e₀'.

Common mistake

Writing (1 - e₀) instead of (1 + e₀), or forgetting to divide by Δσ'.