Dry Unit Weight from Gs and Void Ratio

$G_s \gamma_w$ is the unit weight the soil would have with no voids at all: solid quartz, about 26 kN/m³ or 165 pcf. Spreading that solid over (1 + e) volumes of soil gives the dry unit weight. With $G_s$ = 2.65, $\gamma_w$ = 9.81 kN/m³ and e = 0.65 the result is 25.997 ÷ 1.65 = 15.76 kN/m³. Rearranged for e it becomes the laboratory workhorse: measure $\gamma_d$ on a 105 pcf fill, take $G_s$ = 2.70, and e = (2.70 × 62.4) ÷ 105 − 1 = 0.605.

The trap is that this is the dry unit weight even when the soil is wet: the water is in the voids, and it is deliberately not counted. Pair it with γ = $\gamma_d$(1 + w) when you need the bulk value. The second trap is treating $G_s$ as a universal 2.65. It is close for quartz sands, but a soil with heavy minerals, mine tailings, or shell fragments will not behave, and a peat at $G_s$ = 1.6 will hand you a void ratio that is nonsense. Run the pycnometer if the answer matters.