What is the useful relationship in terms of void ratio, saturation, and specific gravity?

• A. e * S = w * G
• B. e + S = w / G
• C. G * w = e / S
• D. S / e = G * w

Answer: (A)

The relationship e * S = w * G is derived from the definitions and interconnections between void ratio (e), degree of saturation (S), water content (w), and specific gravity (G).

In the context of soil mechanics, the void ratio represents the ratio of the volume of voids to the volume of solids in a soil sample, while the degree of saturation indicates the extent to which the voids are filled with water. Specific gravity is a measure of the density of soil solids relative to the density of water. The water content expresses the amount of water in the soil relative to the solids.

This relationship highlights how the degree of saturation (S) influences the void ratio (e) and integrates the specific gravity (G) and water content (w) into a cohesive formula. By multiplying the void ratio (e) by the degree of saturation (S), you effectively relate these parameters to the weight of water (w) scaled by the specific gravity (G), which ties them into an essential equation in soil mechanics.

This equation serves practical applications in geotechnical engineering, allowing engineers and soil scientists to understand and predict the behavior of soils under different moisture conditions, which is critical for construction and foundation design.