Atterberg limits interpretation — the liquidity index (LI) is defined as which percentage ratio of natural water content w, plastic limit PL, and plasticity index PI?

Introduction / Context:
Liquidity index LI situates a cohesive soil’s in-situ water content within its Atterberg limits. It is widely used for qualitative assessment of consistency, workability, and expected undrained strength. Values below zero indicate stiff to hard soils; values near one indicate very soft behavior approaching liquid limit.

Given Data / Assumptions:

• w is the natural water content in percent.
• PL is the plastic limit determined by roll thread test.
• PI is the plasticity index defined as PI = LL - PL, where LL is the liquid limit.

Concept / Approach:

The standard definition is LI (%) = (w - PL) / PI * 100. This normalizes the natural water content relative to the plastic range. If LI = 0, w equals PL; if LI = 1, w equals LL. Practitioners correlate LI with field behavior (e.g., hand vane shear) and with settlement potential under loading.

Step-by-Step Solution:

Verification / Alternative check:

The consistency index Ic is complementary: Ic = (LL - w) / PI. Note that LI + Ic = 1 when expressed as fractions, providing a cross-check between reported values.

Why Other Options Are Wrong:

Options reversing signs or adding PL do not reflect the definition. Using LL - w corresponds to Ic, not LI.

Common Pitfalls:

Mixing percentage and decimal forms; using disturbed samples with moisture loss before testing; misreporting PI due to inconsistent LL/PL determinations.

Final Answer:

natural water content minus plastic limit, divided by plasticity index