Soil Consistency – Consistency Index (Ic) for a clayey soil Choose the correct expression in terms of LL (liquid limit), PL (plastic limit), PI (plasticity index), and w (natural water content).

Introduction / Context:
Consistency Index (Ic) indicates the relative consistency (firmness) of cohesive soils at their in-situ water content. It places the natural water content w within the Atterberg Limit range and is widely used to judge stiffness and likely behavior during excavation and foundation work.

Given Data / Assumptions:

• LL = Liquid limit, PL = Plastic limit, PI = LL − PL.
• w = natural (field) water content of the clay.
• Units are consistent (percent for all limits and w).

Concept / Approach:

Ic measures how far below the liquid limit the current water content lies, normalized by the plastic range. Thus Ic = (LL − w) / (LL − PL) = (LL − w) / PI. Values near 1 indicate dry, stiff conditions close to PL; values near 0 indicate very soft conditions near LL; negative values suggest w > LL.

Step-by-Step Solution:

Verification / Alternative check:

If w = PL → Ic = (LL − PL)/PI = 1 (stiff). If w = LL → Ic = 0 (very soft). These boundary checks confirm the formula's logic.

Why Other Options Are Wrong:

(b) is liquidity index (not Ic). (c) LL − PL is PI, not Ic. (d) 0.5 w is unrelated to Atterberg concepts.

Common Pitfalls:

Confusing consistency index with liquidity index, or mixing absolute and percentage units mid-calculation.

Final Answer:

Ic = (LL − w) / PI