Indices of consistency and strength: Identify the correct statements about flow index, plasticity index, shrinkage index, and toughness index for fine-grained soils.

Introduction / Context:

Atterberg-related indices quantify how fine-grained soils transition between liquid, plastic, semi-solid, and solid states. These indices not only aid in classification (such as the plasticity chart) but also correlate with engineering properties including compressibility and undrained shear strength.

Given Data / Assumptions:

• Standard definitions for Atterberg limits and derived indices are used.
• Laboratory determinations follow typical procedures (Casagrande/cone for LL and rolling threads for PL).

Concept / Approach:

Plasticity index (PI) = LL − PL. Shrinkage index (SI) = PL − SL. Flow index (If) is the slope of the flow curve in the liquid limit test; greater If implies larger reduction in strength with small reduction in water content. Toughness index (It) = PI / If, reflecting the material’s resistance to deformation near the plastic limit.

Step-by-Step Solution:

Verification / Alternative check:

Correlations such as liquidity index vs. undrained shear strength support the interpretation of flow index as reflecting sensitivity of strength to water content near LL.

Why Other Options Are Wrong:

• Options a–d are all correct; therefore “All the above” is the only comprehensive choice.

Common Pitfalls:

• Confusing shrinkage index with shrinkage limit alone; SI is a difference between PL and SL.
• Assuming flow index equals plasticity index; they measure different aspects.

Final Answer:

All the above