Void ratio from mass specific gravity and water content: A soil has mass specific gravity G_m = 1.92 and water content w = 30%. If the specific gravity of solids G_s = 2.75, determine the void ratio e.

Introduction / Context:
Relating mass specific gravity G_m, water content w, and specific gravity of solids G_s to the void ratio e is a common task in soil phase-relationship problems. Using two standard equations allows elimination of degree of saturation S and solution for e directly.

Given Data / Assumptions:

• G_m = γ/γ_w = 1.92.
• w = 0.30 (30%).
• G_s = 2.75.
• Water unit weight/ density normalization is implied.

Concept / Approach:

Key relations:
1) G_m = (G_s + S e) / (1 + e).
2) w = (S e) / G_s.
Use (2) to substitute S e = w G_s into (1), then solve for e.

Step-by-Step Solution:

Verification / Alternative check:

Back-calculate S from w = S e / G_s → S = (w G_s) / e ≈ 0.825 / 0.862 ≈ 0.957 (reasonable near full saturation), confirming consistency.

Why Other Options Are Wrong:

0.858, 0.860, 0.864 are close but reflect rounding beyond justified precision; 0.880 deviates from the derived e.

Common Pitfalls:

Using bulk unit weight formula for saturated soil; forgetting to eliminate S correctly; rounding too early.

Final Answer:

0.862