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).
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AIc = (LL − w) / PI
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BIc = (w − PL) / PI
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CLL − PL
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DIc = 0.5 * w
Answer
Correct Answer: Ic = (LL − w) / PI
Explanation
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:
1) Compute PI = LL − PL.2) Subtract: LL − w.3) Form ratio: Ic = (LL − w) / PI.4) Interpret Ic: the larger the Ic, the stiffer (at same soil type).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