Plasticity index in Atterberg limits: The plasticity index (PI) of a fine-grained soil is defined as the numerical difference between which two consistency limits?
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ALiquid limit (LL) and plastic limit (PL)
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BPlastic limit (PL) and shrinkage limit (SL)
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CLiquid limit (LL) and shrinkage limit (SL)
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DNone of these
Answer
Correct Answer: Liquid limit (LL) and plastic limit (PL)
Explanation
Introduction / Context:The Atterberg limits quantify consistency changes of fine-grained soils with water content. The plasticity index is widely used for classification (USCS, AASHTO) and correlating engineering behavior such as compressibility and strength.
Given Data / Assumptions:
- Standard definitions: LL, PL, and SL are water contents defining transitions among liquid, plastic, semi-solid, and solid states.
- PI is a scalar difference expressed in percentage points (or decimal fraction if preferred).
Concept / Approach:PI measures the width of the plastic range: PI = LL − PL. A larger PI indicates greater plasticity and usually more clay-sized, active minerals. LL − SL or PL − SL are other indices (e.g., toughness index, shrinkage index) but are not the plasticity index itself.
Step-by-Step Solution:
State the definition: PI = LL − PL.Relate meaning: span of water content where soil can be molded without cracking or flow.Use PI along with LL on the plasticity chart to distinguish clays from silts.Conclude Option A is correct.Verification / Alternative check:USCS boundaries (A-line) use PI and LL; road specifications often set PI limits for subgrade materials.
Why Other Options Are Wrong:
- PL − SL defines a shrinkage index component, not PI.
- LL − SL is not the plastic range; it exceeds the true plastic window.
- “None of these” is incorrect because PI is clearly LL − PL.
Common Pitfalls:Confusing PI with liquidity index or consistency index; mixing percentage points with decimals without unit clarity.
Final Answer:Liquid limit (LL) and plastic limit (PL)