Granular Soils – Name of the Void-Ratio–Based Measure (e_max, e, e_min) The quantity defined as (e_max − e) / (e_max − e_min), where e is the natural void ratio, is generally termed as:

Introduction / Context:
For sands and gravels, relative packing controls strength and stiffness. A widely used non-dimensional index compares the in-situ void ratio to the loosest and densest states achievable in the laboratory.

Given Data / Assumptions:

• e_max: void ratio in the loosest state.
• e_min: void ratio in the densest state.
• e: natural (in-situ or current) void ratio.

Concept / Approach:

The expression (e_max − e) / (e_max − e_min) is formally called the density index (also commonly known as relative density). It scales from 0 to 1 (or 0% to 100%) as the soil goes from very loose to very dense compared with laboratory bounds.

Step-by-Step Solution:

Verification / Alternative check:

Standards and textbooks use 'density index' and 'relative density' synonymously; 'degree of density' and 'relativity' are non-standard/confusing terms, and 'relative compaction' refers to Proctor-based compaction ratio for fines.

Why Other Options Are Wrong:

'Degree of density' and 'relativity' are imprecise or uncommon; 'all of the above' would wrongly include those; 'relative compaction' is a different concept tied to dry density and Proctor maximum.

Common Pitfalls:

Mixing up density index with compaction percentage; misusing e-based index for plastic clays where Atterberg limits are more relevant.

Final Answer:

Density index