Degree of saturation from compaction data: A compacted soil has moisture content w = 10% and bulk density rho = 2.0 g/cm^3. Given Gs = 2.7 and rho_w = 1.0 g/cm^3, determine the degree of saturation S.

Introduction / Context:

The degree of saturation S indicates how much of a soil’s void space is filled with water. It is a critical parameter for compaction control, permeability assessment, and predicting volume change behavior. From routine compaction data (bulk density and water content), along with specific gravity, S can be calculated using standard index relationships.

Given Data / Assumptions:

• w = 10% = 0.10.
• rho = 2.0 g/cm^3 (bulk density).
• Gs = 2.7, rho_w = 1.0 g/cm^3.
• Representative sample with no unusual chemical effects.

Concept / Approach:

Use two key relations. First, rho_d = rho / (1 + w). Second, rho_d = (Gs / (1 + e)) * rho_w, which gives 1 + e = (Gs * rho_w) / rho_d. With e known, use w = (S * e) / Gs, so S = (w * Gs) / e.

Step-by-Step Solution:

Verification / Alternative check:

Back-calculate w using w = (S * e) / Gs = (0.556 * 0.485) / 2.7 = 0.10 = 10%, confirming consistency.

Why Other Options Are Wrong:

• 11.1% and 33.3% are too low given the computed e and w.
• 69.6% is higher than the value indicated by the mass-volume relationships.
• None of these is incorrect because 55.6% matches the calculation.

Common Pitfalls:

• Confusing porosity n with void ratio e; here formulas use e.
• Forgetting to convert percentage to decimal form before substitution.

Final Answer:

55.6%