Dry Density from Wet Density and Water Content
Dry Density from Wet Density and Water Content
Soil unit weight is reported two ways in geotechnical practice: the wet (total) unit weight actually measured in the field or lab, and the dry unit weight with all water removed, which is the more fundamental property used in compaction specifications and settlement calculations. Converting between the two requires knowing the water content, because a soil sample's weight includes whatever moisture it holds at the time of sampling — a wet unit weight alone, without a paired water content, cannot be used to judge whether a fill has been compacted to spec.
Dry unit weight is gamma_d = gamma_wet/(1+w), where w is the gravimetric water content expressed as a decimal. where gamma_wet is the measured wet (total) unit weight and w_content is the water content (mass of water divided by mass of solids), as a decimal fraction.
Inputs
gamma_wet := 19.5 kN/m^3=19500 kg/m^2/s^2
w_content := 0.12=0.12
Dividing by (1 + w) strips out the weight contributed by the pore water, leaving just the weight of the solid soil skeleton per unit total volume.
gamma_d := gamma_wet/(1 + w_content)=17410.71 kg/m^2/s^2
Results
A dry unit weight around 17 kN/m^3 from a 19.5 kN/m^3 wet reading at 12% water content is a normal result for a compacted fill soil, and this is the value compared against the Proctor maximum dry density to compute relative compaction. Because the denominator only grows slowly with water content, dry density is fairly forgiving of small water content measurement errors, but a badly wrong w still directly biases every compaction check that follows.
Assumptions & limitations
- Water content assumed uniform through the sample.
- Wet unit weight assumed measured accurately (e.g., via ring or nuclear density test).
- No allowance for air voids beyond what is implicit in the wet unit weight measurement.
- Formula assumes water content is expressed as a fraction of dry solids mass, the standard convention.