Degree of saturation from w, G, and e: If the water content of a soil is 40% (w = 0.40), the specific gravity of solids G = 2.70, and the void ratio e = 1.35, compute the degree of saturation Sr.

Introduction / Context:Phase-relationship identities permit rapid checks on consistency of lab data. Degree of saturation links the volumetric water content to mass-based water content via specific gravity and void ratio—crucial for compaction, seepage, and strength interpretations.

Given Data / Assumptions:

• Water content w = 0.40 (40%).
• Specific gravity G = 2.70.
• Void ratio e = 1.35.
• Standard identity for partially saturated soils applies.

Concept / Approach:Use the fundamental relationship w = (Sr * e) / G. Rearranging gives Sr = (w * G) / e. Insert given values and convert the decimal result to a percentage for reporting.

Step-by-Step Solution:

Verification / Alternative check:Check bounds: Sr must be between 0 and 1; 80% is reasonable for these values. Also, if e halves or G increases, Sr changes accordingly consistent with physics.

Why Other Options Are Wrong:

• 70%, 75%, 85%, 90% do not satisfy the identity with the provided numbers.

Common Pitfalls:Using w in percent rather than decimal inside the formula; mixing e with porosity n (n = e / (1 + e)); rounding too early.

Final Answer:80%