Clay Consistency – Toughness index (It) of clayey soils Select the correct expression.

Introduction / Context:
The toughness index It measures the resistance of a clay to deformation near the plastic limit by relating plasticity to the rate of change of consistency. It is useful in differentiating clays of similar plasticity but different workability.

Given Data / Assumptions:

• Plasticity index PI = LL − PL.
• Flow index IF from the slope of the flow curve in the liquid limit test.
• All limits expressed in percentage terms consistently.

Concept / Approach:

Toughness index is defined as It = PI / IF. A higher It indicates a tougher clay exhibiting greater resistance to shearing near the plastic limit region.

Step-by-Step Solution:

Verification / Alternative check:

Comparing clays with equal PI but different IF demonstrates that lower IF (steeper consistency change) increases It, reflecting greater toughness.

Why Other Options Are Wrong:

Options (b), (c), and (d) mix unrelated indices; only PI/IF is the standard definition of toughness index.

Common Pitfalls:

Confusing toughness index with liquidity index or consistency index, or using inconsistent units for limits.

Final Answer:

Plasticity index / Flow index