Indices from Atterberg limits: A soil has natural water content w = 30.5%, liquid limit LL = 42.5%, and plastic limit PL = 22.5%. What is the ratio (Liquidity index / Plasticity index)?

Introduction / Context:Atterberg limits quantify fine-grained soil consistency. The liquidity index I_L places the in-situ water content within the plastic range, while the plasticity index PI measures the width of that range. Their ratio helps compare state to plastic range width.

Given Data / Assumptions:

• w = 30.5%.
• LL = 42.5%.
• PL = 22.5%.
• Definitions: PI = LL − PL; I_L = (w − PL)/PI.

Concept / Approach:

Compute PI, then I_L, and finally the requested ratio I_L / PI. Keep units consistent (percent values are used as numbers in the formulae).

Step-by-Step Solution:

Verification / Alternative check:

Note that I_c = (LL − w)/PI = (42.5 − 30.5)/20 = 0.60, and I_c + I_L = 1.0, confirming internal consistency.

Why Other Options Are Wrong:

0.20 and 0.04 result from misplacing numerator/denominator; 0.50 and 2 contradict the computed I_L and PI values.

Common Pitfalls:

Confusing I_L with I_c; dividing by 100 unnecessarily; mixing percent and decimal forms inconsistently.

Final Answer:

0.02