Consistency index I_c (Atterberg limits): I_c is defined as which of the following ratios for a cohesive soil at natural water content w_n?
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AI_c = (LL + w_n) / PI
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BI_c = (LL − w_n) / PI
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CI_c = (w_n − PL) / PI
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DI_c = (w_n + PL) / PI
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EI_c = (LL − PL) / w_n
Answer
Correct Answer: I_c = (LL − w_n) / PI
Explanation
Introduction / Context:The consistency index I_c indicates the relative consistency of a cohesive soil in the plastic range. It complements the liquidity index I_L and helps engineers infer the likely undrained behavior (stiff, soft) at the in-situ water content.
Given Data / Assumptions:
- Atterberg limits: LL (liquid limit), PL (plastic limit), PI = LL − PL.
- Natural water content w_n is known.
- Index applies to fine-grained soils.
Concept / Approach:
Definitions: liquidity index I_L = (w_n − PL)/PI and consistency index I_c = (LL − w_n)/PI. I_c close to 1 indicates a soil near the plastic limit (stiff), while I_c near 0 indicates a soil near the liquid limit (soft). Negative values imply w_n > LL (flowing).
Step-by-Step Solution:
Recall PI = LL − PL.Write I_c = (LL − w_n)/PI.Match with the provided options → choose (LL − w_n)/PI.Verification / Alternative check:
Check that I_c + I_L = 1, which is a useful consistency relation.
Why Other Options Are Wrong:
(a), (d) use addition incorrectly; (c) is the liquidity index; (e) is not a standard index definition.
Common Pitfalls:
Interchanging I_L and I_c; forgetting that PI must be positive and defined only if LL > PL.
Final Answer:
I_c = (LL − w_n) / PI