Compute degree of saturation S: A natural soil has water content w = 15%, specific gravity Gs = 2.50, and void ratio e = 0.5. What is the degree of saturation?

Introduction / Context:

The degree of saturation S quantifies how much of the void space is filled with water. It is a key parameter for evaluating compressibility, permeability, and strength. With water content, specific gravity, and void ratio known, S can be computed from standard mass–volume relationships used in soil mechanics.

Given Data / Assumptions:

• w = 15% = 0.15.
• Gs = 2.50.
• e = 0.5.
• rho_w is taken as 1.0 in consistent units so it cancels in ratios.

Concept / Approach:

The relationship among w, S, e, and Gs is: w = (S * e) / Gs. Rearranging gives S = (w * Gs) / e. This comes from equating the mass of water to the mass of solids times water content and expressing void volume in terms of e.

Step-by-Step Solution:

Verification / Alternative check:

Check bounds: S must lie between 0% and 100%. The computed 75% is physically reasonable for a natural deposit at modest moisture content.

Why Other Options Are Wrong:

• 50% and 60% underestimate S for the given w, e, and Gs.
• 80% is higher than the computed value.
• 40% is far too low.

Common Pitfalls:

• Mistaking porosity n for void ratio e in the formula; the correct relation uses e.
• Forgetting to convert percent water content to a decimal before substitution.

Final Answer:

75%