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?

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:

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)