Compute void ratio from mass–volume data: A moist soil sample has total mass 108 g and volume 60 cm³. Its water content is 25% and specific gravity of solids G = 2.52. Determine the void ratio e.

Introduction / Context:This numerical problem uses basic phase relationships to compute void ratio e from measured mass, volume, water content, and specific gravity. It illustrates how laboratory data translate to structure-defining parameters like e that control compressibility and permeability.

Given Data / Assumptions:

• Total mass M = 108 g, total volume V = 60 cm³.
• Water content w = 25% = 0.25 (decimal).
• Specific gravity of solids G = 2.52; take density of water = 1 g/cm³.

Concept / Approach:Water content w = Mw / Ms ⇒ M = Ms + Mw = Ms (1 + w). Solve for solids mass Ms, then compute volume of solids Vs = Ms / (G * ρw). With total volume V known, void volume is Vv = V − Vs. Finally, e = Vv / Vs.

Step-by-Step Solution:

Verification / Alternative check:Check porosity n = e / (1 + e) ≈ 0.75 / 1.75 ≈ 0.429 (about 43%), a reasonable value for a moist, medium-density fine-grained soil.

Why Other Options Are Wrong:

• 0.55, 0.65, 0.80, 0.95: Do not match the computed ratio based on mass–volume consistency.

Common Pitfalls:Using w in percent without converting to decimal; forgetting that total volume V = Vs + Vv even in partially saturated states; using G incorrectly (it multiplies ρw).

Final Answer:0.75