Compaction test – dry unit weight from mould measurement: If W is the wet (as-compacted) weight of soil at water content w (decimal) placed in a Proctor mould of volume V, what is the dry unit weight gamma_d of the soil?

Introduction / Context:
Compaction control relies on converting measured wet unit weight in a mould to dry unit weight. This requires correcting for the water present at the time of compaction using the measured water content w (decimal), yielding gamma_d for comparison with Proctor curves.

Given Data / Assumptions:

• W is total wet weight of compacted specimen.
• V is volume of Proctor mould (e.g., 944 cc for standard mould).
• w is water content as a decimal (w = Mw / Ms).

Concept / Approach:
Wet unit weight gamma = W / V. Since W = Ws + Ww and Ws = W / (1 + w), the dry unit weight gamma_d equals the unit weight associated with solids only: gamma_d = (W / (1 + w)) / V = (W / V) * 1 / (1 + w).

Step-by-Step Solution:

Verification / Alternative check:
Example: W/V = 20 kN/m^3, w = 0.10 → gamma_d = 20 / 1.10 ≈ 18.18 kN/m^3, matching standard lab conversions.

Why Other Options Are Wrong:

• Multiplying by (1 + w) would increase gamma_d above wet unit weight, impossible.
• (1 − w) forms are dimensionally and conceptually incorrect.
• Dividing by w alone would blow up at small w.

Common Pitfalls:
Using w in percent instead of decimal; mixing mass-density with unit weight without g conversion; incorrect mould volume.

Final Answer:
gamma_d = (W / V) * (1 / (1 + w))