Total Unit Weight of Soil Based on Parameters

Materials: Soil Properties

Given the following parameters for a soil sample, determine the total unit weight:

Void Ratio \(e=0.66\)
Water Content \(w=20 \%\)
Weight of Solids in Sample: \(W_s=10 \ lb\)
Volume of Solids in Sample: \(\sout{V_s=260 \ in^3} \ \ V_s=100\ in^3\)
Unit Weight of Water: \(γ_w=62.4 \ pcf\)

A) 105 pcf

B) 115 pcf

C) 125 pcf

D) 140 pcf


Answer: C) 125 pcf

We can calculate specific gravity based on the weight and volume of solids:
\[G_s= \frac{W_s}{V_s γ_w }= \frac{10 lb}{100 in^3×\frac{1}{(12 in)^3} ×62.4 pcf}=2.77\]

We can calculate total unit weight based on water content, specific gravity, and void ratio:
\[γ_t= \frac{(1+w) G_s γ_w}{1+e}\]

\[γ_t= \frac{(1+0.2)×2.77×62.4 pcf}{1+0.66}≈125 pcf\]