Consolidation MCQ with answer and solution

Concept

Ultimate consolidation settlement is independent of the drainage conditions and depends solely on the applied stress increment and the compressibility of the soil layer.

Formula

S_c = H × (C_c / (1 + e₀)) × log10((σ₀' + δ_sigma') / σ₀')

Step-by-step solution

1. Identify that the total settlement depends on the thickness of the clay layer (H) and the applied stress increment. 2. Note that drainage layers affect the rate of consolidation (time factor and coefficient of consolidation), not the ultimate magnitude of settlement. 3. Since the applied stress and clay thickness remain unchanged, the total settlement remains 10 cm.

Explanation

Total primary consolidation settlement depends only on the magnitude of the applied stress, the thickness of the clay layer, and the compressibility characteristics (compression index, initial void ratio) of the soil. Introducing a drainage layer alters the rate of consolidation (time taken), but it does not change the total ultimate settlement.

Why the other options are wrong

A: Incorrectly assuming settlement is halved when drainage path is halved. C: Incorrectly assuming settlement doubles. D: Incorrectly assuming settlement is halved.

Shortcut

Drainage conditions only affect the rate of consolidation (time), not the magnitude of total settlement.

Common mistake

Mistaking rate of consolidation (time) with magnitude of settlement, thinking that more drainage paths reduce the total settlement amount.