Partially saturated soil mechanics — a soil sample has unit weight 2.0 g/cm³, specific gravity of solids Gs = 2.6, and moisture content w = 20%. Determine the degree of saturation (as a percentage).

Introduction / Context:
In civil engineering soil mechanics, determining the degree of saturation (S) connects field-measured bulk unit weight, water content, and grain specific gravity. This parameter indicates how much of the void space is filled with water and is essential for evaluating compressibility, shear strength, and seepage susceptibility.

Given Data / Assumptions:

• Bulk (moist) unit weight γ = 2.0 g/cm³.
• Specific gravity of solids Gs = 2.6.
• Moisture content w = 20% = 0.20 (mass of water / mass of dry solids).
• Unit weight of water γw ≈ 1.0 g/cm³ (consistent units).
• Standard phase-relationship equations apply; soil is partially saturated (0 < S < 1).

Concept / Approach:

Use two key relationships eliminating the void ratio e. First, moisture content relates to S and e by w = (S * e) / Gs. Second, bulk unit weight relates to S and e by γ = γw * (Gs + S * e) / (1 + e). Eliminating e yields a direct equation for S in terms of γ, Gs, w, and γw.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

An alternative is to compute e from S using e = w * Gs / S, then back-calculate γ using γ = γw * (Gs + S * e) / (1 + e) to confirm γ ≈ 2.0 g/cm³. Substituting S = 0.9286 gives e ≈ 0.56; recomputing γ returns ≈ 2.0 g/cm³, verifying consistency.

Why Other Options Are Wrong:

20% or 77% contradict the derived equation; they would not satisfy the given γ simultaneously.

“None of these” is false since 92% matches the computation.

68% is a distractor from misapplying formulas or using γw ≠ 1 in mixed units.

Common Pitfalls (misconceptions, mistakes):

Mixing SI and gravimetric units; using γw = 9.81 kN/m³ with g/cm³ values; forgetting that w is mass-based while S is volume-based; attempting direct proportionality between w and S without accounting for e.

Final Answer:

92%