Saturated soil: compute dry density from water content and Gs A saturated soil sample has water content w = 30% and specific gravity of soil solids Gs = 2.60. Assuming full saturation (S = 100%), calculate the dry density of the soil mass (in g/cm³).

Introduction / Context:This problem tests basic phase-relationship calculations for saturated soils. Under full saturation, the void ratio e relates directly to water content w and the specific gravity of solids Gs. Once e is known, dry density can be obtained from a standard formula used in geotechnical engineering.

Given Data / Assumptions:

• Saturation S = 100% (fully saturated).
• Water content w = 30% = 0.30 (mass of water / mass of dry soil).
• Specific gravity of soil solids Gs = 2.60.
• Unit density of water ρw = 1.0 g/cm³.

Concept / Approach:

For saturated soil, the key relationships are: e = (w * Gs) / S (with S = 1 for full saturation) ρd = (Gs * ρw) / (1 + e) These arise from the definitions of water content, degree of saturation, and the volumes of solids and voids.

Step-by-Step Solution:

Verification / Alternative check:

If w increases for the same Gs at S = 100%, e increases, and ρd decreases. The computed value aligns with this physical trend.

Why Other Options Are Wrong:

1.82 and 1.91 g/cm³ are too high for the given w and Gs; 1.32 g/cm³ is too low; “none of these” is invalid because a correct numeric value exists.

Common Pitfalls:

Confusing bulk density with dry density; forgetting that S = 100% implies e = w * Gs.

Final Answer:

1.47 g/cm³