The ratio of the difference between the void ratio of the soils in its loosest state and its natural void ratio to the difference between the void ratios in the loosest and fully dense state, is generally termed as..............

Detailed Explanation

This describes the standard definition of relative density (also called density index or degree of density), used to quantify how densely a cohesionless (granular) soil is packed relative to its loosest and densest possible states:

I_D = (e_max − e_natural) / (e_max − e_min)

Here, e_max corresponds to the soil's loosest possible state, and e_min corresponds to its densest (fully compacted) state. The numerator captures how far the natural (in-situ) void ratio is from the loosest extreme, while the denominator captures the full possible range between loosest and densest — so I_D = 0 at the loosest state and I_D = 1 (100%) at the densest state.

Since "degree of density," "relative density," and "density index" are simply different names for this same concept, the correct choice is (d) All options are correct.

Key Concepts for Students

• Relative density (density index), I_D = (e_max−e)/(e_max−e_min) — quantifies packing state on a 0-100% scale.
• I_D = 0% at the loosest possible state (e = e_max) and I_D = 100% at the densest possible state (e = e_min).
• This parameter is calculated specifically for cohesionless (granular) soils, since "loosest" and "densest" states are determined via standard loose-pouring and vibratory-compaction laboratory procedures applicable to sands and gravels.
• Degree of density, relative density, and density index are used interchangeably in textbooks and codes to refer to this exact same quantity.