Dry Unit Weight from Moist Unit Weight

A nuclear density gauge or a sand-cone test gives you the wet weight of a cubic metre of fill; the specification is written in dry weight, because only the solids stay after the sun comes out. Dividing by (1 + w) removes the water: a fill placed at γ = 19.6 kN/m³ and w = 12% has γd = 19.6 ÷ 1.12 = 17.5 kN/m³. In imperial terms 125 pcf at 15% moisture is 125 ÷ 1.15 = 108.7 pcf dry.

The trap is the units of w. The denominator is a pure ratio, so 12% must enter as 0.12; typing 12 gives you a dry unit weight thirteen times too small and it is the single most common error on a compaction report. The second trap is conceptual: adding water to a soil raises γ and lowers γd, which is why the compaction curve has a peak — up to optimum moisture the water lubricates the grains and lets them pack, past it the water occupies space the grains wanted. Ralph Proctor worked that curve out for the Los Angeles Bureau of Waterworks in 1933, and every earthwork specification on earth still cites him.